Identifier
-
Mp00108:
Permutations
—cycle type⟶
Integer partitions
St000182: Integer partitions ⟶ ℤ
Values
=>
Cc0002;cc-rep
[1]=>[1]=>1
[1,2]=>[1,1]=>1
[2,1]=>[2]=>1
[1,2,3]=>[1,1,1]=>1
[1,3,2]=>[2,1]=>3
[2,1,3]=>[2,1]=>3
[2,3,1]=>[3]=>2
[3,1,2]=>[3]=>2
[3,2,1]=>[2,1]=>3
[1,2,3,4]=>[1,1,1,1]=>1
[1,2,4,3]=>[2,1,1]=>6
[1,3,2,4]=>[2,1,1]=>6
[1,3,4,2]=>[3,1]=>8
[1,4,2,3]=>[3,1]=>8
[1,4,3,2]=>[2,1,1]=>6
[2,1,3,4]=>[2,1,1]=>6
[2,1,4,3]=>[2,2]=>3
[2,3,1,4]=>[3,1]=>8
[2,3,4,1]=>[4]=>6
[2,4,1,3]=>[4]=>6
[2,4,3,1]=>[3,1]=>8
[3,1,2,4]=>[3,1]=>8
[3,1,4,2]=>[4]=>6
[3,2,1,4]=>[2,1,1]=>6
[3,2,4,1]=>[3,1]=>8
[3,4,1,2]=>[2,2]=>3
[3,4,2,1]=>[4]=>6
[4,1,2,3]=>[4]=>6
[4,1,3,2]=>[3,1]=>8
[4,2,1,3]=>[3,1]=>8
[4,2,3,1]=>[2,1,1]=>6
[4,3,1,2]=>[4]=>6
[4,3,2,1]=>[2,2]=>3
[1,2,3,4,5]=>[1,1,1,1,1]=>1
[1,2,3,5,4]=>[2,1,1,1]=>10
[1,2,4,3,5]=>[2,1,1,1]=>10
[1,2,4,5,3]=>[3,1,1]=>20
[1,2,5,3,4]=>[3,1,1]=>20
[1,2,5,4,3]=>[2,1,1,1]=>10
[1,3,2,4,5]=>[2,1,1,1]=>10
[1,3,2,5,4]=>[2,2,1]=>15
[1,3,4,2,5]=>[3,1,1]=>20
[1,3,4,5,2]=>[4,1]=>30
[1,3,5,2,4]=>[4,1]=>30
[1,3,5,4,2]=>[3,1,1]=>20
[1,4,2,3,5]=>[3,1,1]=>20
[1,4,2,5,3]=>[4,1]=>30
[1,4,3,2,5]=>[2,1,1,1]=>10
[1,4,3,5,2]=>[3,1,1]=>20
[1,4,5,2,3]=>[2,2,1]=>15
[1,4,5,3,2]=>[4,1]=>30
[1,5,2,3,4]=>[4,1]=>30
[1,5,2,4,3]=>[3,1,1]=>20
[1,5,3,2,4]=>[3,1,1]=>20
[1,5,3,4,2]=>[2,1,1,1]=>10
[1,5,4,2,3]=>[4,1]=>30
[1,5,4,3,2]=>[2,2,1]=>15
[2,1,3,4,5]=>[2,1,1,1]=>10
[2,1,3,5,4]=>[2,2,1]=>15
[2,1,4,3,5]=>[2,2,1]=>15
[2,1,4,5,3]=>[3,2]=>20
[2,1,5,3,4]=>[3,2]=>20
[2,1,5,4,3]=>[2,2,1]=>15
[2,3,1,4,5]=>[3,1,1]=>20
[2,3,1,5,4]=>[3,2]=>20
[2,3,4,1,5]=>[4,1]=>30
[2,3,4,5,1]=>[5]=>24
[2,3,5,1,4]=>[5]=>24
[2,3,5,4,1]=>[4,1]=>30
[2,4,1,3,5]=>[4,1]=>30
[2,4,1,5,3]=>[5]=>24
[2,4,3,1,5]=>[3,1,1]=>20
[2,4,3,5,1]=>[4,1]=>30
[2,4,5,1,3]=>[3,2]=>20
[2,4,5,3,1]=>[5]=>24
[2,5,1,3,4]=>[5]=>24
[2,5,1,4,3]=>[4,1]=>30
[2,5,3,1,4]=>[4,1]=>30
[2,5,3,4,1]=>[3,1,1]=>20
[2,5,4,1,3]=>[5]=>24
[2,5,4,3,1]=>[3,2]=>20
[3,1,2,4,5]=>[3,1,1]=>20
[3,1,2,5,4]=>[3,2]=>20
[3,1,4,2,5]=>[4,1]=>30
[3,1,4,5,2]=>[5]=>24
[3,1,5,2,4]=>[5]=>24
[3,1,5,4,2]=>[4,1]=>30
[3,2,1,4,5]=>[2,1,1,1]=>10
[3,2,1,5,4]=>[2,2,1]=>15
[3,2,4,1,5]=>[3,1,1]=>20
[3,2,4,5,1]=>[4,1]=>30
[3,2,5,1,4]=>[4,1]=>30
[3,2,5,4,1]=>[3,1,1]=>20
[3,4,1,2,5]=>[2,2,1]=>15
[3,4,1,5,2]=>[3,2]=>20
[3,4,2,1,5]=>[4,1]=>30
[3,4,2,5,1]=>[5]=>24
[3,4,5,1,2]=>[5]=>24
[3,4,5,2,1]=>[3,2]=>20
[3,5,1,2,4]=>[3,2]=>20
[3,5,1,4,2]=>[2,2,1]=>15
[3,5,2,1,4]=>[5]=>24
[3,5,2,4,1]=>[4,1]=>30
[3,5,4,1,2]=>[3,2]=>20
[3,5,4,2,1]=>[5]=>24
[4,1,2,3,5]=>[4,1]=>30
[4,1,2,5,3]=>[5]=>24
[4,1,3,2,5]=>[3,1,1]=>20
[4,1,3,5,2]=>[4,1]=>30
[4,1,5,2,3]=>[3,2]=>20
[4,1,5,3,2]=>[5]=>24
[4,2,1,3,5]=>[3,1,1]=>20
[4,2,1,5,3]=>[4,1]=>30
[4,2,3,1,5]=>[2,1,1,1]=>10
[4,2,3,5,1]=>[3,1,1]=>20
[4,2,5,1,3]=>[2,2,1]=>15
[4,2,5,3,1]=>[4,1]=>30
[4,3,1,2,5]=>[4,1]=>30
[4,3,1,5,2]=>[5]=>24
[4,3,2,1,5]=>[2,2,1]=>15
[4,3,2,5,1]=>[3,2]=>20
[4,3,5,1,2]=>[3,2]=>20
[4,3,5,2,1]=>[5]=>24
[4,5,1,2,3]=>[5]=>24
[4,5,1,3,2]=>[3,2]=>20
[4,5,2,1,3]=>[3,2]=>20
[4,5,2,3,1]=>[5]=>24
[4,5,3,1,2]=>[2,2,1]=>15
[4,5,3,2,1]=>[4,1]=>30
[5,1,2,3,4]=>[5]=>24
[5,1,2,4,3]=>[4,1]=>30
[5,1,3,2,4]=>[4,1]=>30
[5,1,3,4,2]=>[3,1,1]=>20
[5,1,4,2,3]=>[5]=>24
[5,1,4,3,2]=>[3,2]=>20
[5,2,1,3,4]=>[4,1]=>30
[5,2,1,4,3]=>[3,1,1]=>20
[5,2,3,1,4]=>[3,1,1]=>20
[5,2,3,4,1]=>[2,1,1,1]=>10
[5,2,4,1,3]=>[4,1]=>30
[5,2,4,3,1]=>[2,2,1]=>15
[5,3,1,2,4]=>[5]=>24
[5,3,1,4,2]=>[4,1]=>30
[5,3,2,1,4]=>[3,2]=>20
[5,3,2,4,1]=>[2,2,1]=>15
[5,3,4,1,2]=>[5]=>24
[5,3,4,2,1]=>[3,2]=>20
[5,4,1,2,3]=>[3,2]=>20
[5,4,1,3,2]=>[5]=>24
[5,4,2,1,3]=>[5]=>24
[5,4,2,3,1]=>[3,2]=>20
[5,4,3,1,2]=>[4,1]=>30
[5,4,3,2,1]=>[2,2,1]=>15
[1,2,3,4,5,6]=>[1,1,1,1,1,1]=>1
[1,2,3,4,6,5]=>[2,1,1,1,1]=>15
[1,2,3,5,4,6]=>[2,1,1,1,1]=>15
[1,2,3,5,6,4]=>[3,1,1,1]=>40
[1,2,3,6,4,5]=>[3,1,1,1]=>40
[1,2,3,6,5,4]=>[2,1,1,1,1]=>15
[1,2,4,3,5,6]=>[2,1,1,1,1]=>15
[1,2,4,3,6,5]=>[2,2,1,1]=>45
[1,2,4,5,3,6]=>[3,1,1,1]=>40
[1,2,4,5,6,3]=>[4,1,1]=>90
[1,2,4,6,3,5]=>[4,1,1]=>90
[1,2,4,6,5,3]=>[3,1,1,1]=>40
[1,2,5,3,4,6]=>[3,1,1,1]=>40
[1,2,5,3,6,4]=>[4,1,1]=>90
[1,2,5,4,3,6]=>[2,1,1,1,1]=>15
[1,2,5,4,6,3]=>[3,1,1,1]=>40
[1,2,5,6,3,4]=>[2,2,1,1]=>45
[1,2,5,6,4,3]=>[4,1,1]=>90
[1,2,6,3,4,5]=>[4,1,1]=>90
[1,2,6,3,5,4]=>[3,1,1,1]=>40
[1,2,6,4,3,5]=>[3,1,1,1]=>40
[1,2,6,4,5,3]=>[2,1,1,1,1]=>15
[1,2,6,5,3,4]=>[4,1,1]=>90
[1,2,6,5,4,3]=>[2,2,1,1]=>45
[1,3,2,4,5,6]=>[2,1,1,1,1]=>15
[1,3,2,4,6,5]=>[2,2,1,1]=>45
[1,3,2,5,4,6]=>[2,2,1,1]=>45
[1,3,2,5,6,4]=>[3,2,1]=>120
[1,3,2,6,4,5]=>[3,2,1]=>120
[1,3,2,6,5,4]=>[2,2,1,1]=>45
[1,3,4,2,5,6]=>[3,1,1,1]=>40
[1,3,4,2,6,5]=>[3,2,1]=>120
[1,3,4,5,2,6]=>[4,1,1]=>90
[1,3,4,5,6,2]=>[5,1]=>144
[1,3,4,6,2,5]=>[5,1]=>144
[1,3,4,6,5,2]=>[4,1,1]=>90
[1,3,5,2,4,6]=>[4,1,1]=>90
[1,3,5,2,6,4]=>[5,1]=>144
[1,3,5,4,2,6]=>[3,1,1,1]=>40
[1,3,5,4,6,2]=>[4,1,1]=>90
[1,3,5,6,2,4]=>[3,2,1]=>120
[1,3,5,6,4,2]=>[5,1]=>144
[1,3,6,2,4,5]=>[5,1]=>144
[1,3,6,2,5,4]=>[4,1,1]=>90
[1,3,6,4,2,5]=>[4,1,1]=>90
[1,3,6,4,5,2]=>[3,1,1,1]=>40
[1,3,6,5,2,4]=>[5,1]=>144
[1,3,6,5,4,2]=>[3,2,1]=>120
[1,4,2,3,5,6]=>[3,1,1,1]=>40
[1,4,2,3,6,5]=>[3,2,1]=>120
[1,4,2,5,3,6]=>[4,1,1]=>90
[1,4,2,5,6,3]=>[5,1]=>144
[1,4,2,6,3,5]=>[5,1]=>144
[1,4,2,6,5,3]=>[4,1,1]=>90
[1,4,3,2,5,6]=>[2,1,1,1,1]=>15
[1,4,3,2,6,5]=>[2,2,1,1]=>45
[1,4,3,5,2,6]=>[3,1,1,1]=>40
[1,4,3,5,6,2]=>[4,1,1]=>90
[1,4,3,6,2,5]=>[4,1,1]=>90
[1,4,3,6,5,2]=>[3,1,1,1]=>40
[1,4,5,2,3,6]=>[2,2,1,1]=>45
[1,4,5,2,6,3]=>[3,2,1]=>120
[1,4,5,3,2,6]=>[4,1,1]=>90
[1,4,5,3,6,2]=>[5,1]=>144
[1,4,5,6,2,3]=>[5,1]=>144
[1,4,5,6,3,2]=>[3,2,1]=>120
[1,4,6,2,3,5]=>[3,2,1]=>120
[1,4,6,2,5,3]=>[2,2,1,1]=>45
[1,4,6,3,2,5]=>[5,1]=>144
[1,4,6,3,5,2]=>[4,1,1]=>90
[1,4,6,5,2,3]=>[3,2,1]=>120
[1,4,6,5,3,2]=>[5,1]=>144
[1,5,2,3,4,6]=>[4,1,1]=>90
[1,5,2,3,6,4]=>[5,1]=>144
[1,5,2,4,3,6]=>[3,1,1,1]=>40
[1,5,2,4,6,3]=>[4,1,1]=>90
[1,5,2,6,3,4]=>[3,2,1]=>120
[1,5,2,6,4,3]=>[5,1]=>144
[1,5,3,2,4,6]=>[3,1,1,1]=>40
[1,5,3,2,6,4]=>[4,1,1]=>90
[1,5,3,4,2,6]=>[2,1,1,1,1]=>15
[1,5,3,4,6,2]=>[3,1,1,1]=>40
[1,5,3,6,2,4]=>[2,2,1,1]=>45
[1,5,3,6,4,2]=>[4,1,1]=>90
[1,5,4,2,3,6]=>[4,1,1]=>90
[1,5,4,2,6,3]=>[5,1]=>144
[1,5,4,3,2,6]=>[2,2,1,1]=>45
[1,5,4,3,6,2]=>[3,2,1]=>120
[1,5,4,6,2,3]=>[3,2,1]=>120
[1,5,4,6,3,2]=>[5,1]=>144
[1,5,6,2,3,4]=>[5,1]=>144
[1,5,6,2,4,3]=>[3,2,1]=>120
[1,5,6,3,2,4]=>[3,2,1]=>120
[1,5,6,3,4,2]=>[5,1]=>144
[1,5,6,4,2,3]=>[2,2,1,1]=>45
[1,5,6,4,3,2]=>[4,1,1]=>90
[1,6,2,3,4,5]=>[5,1]=>144
[1,6,2,3,5,4]=>[4,1,1]=>90
[1,6,2,4,3,5]=>[4,1,1]=>90
[1,6,2,4,5,3]=>[3,1,1,1]=>40
[1,6,2,5,3,4]=>[5,1]=>144
[1,6,2,5,4,3]=>[3,2,1]=>120
[1,6,3,2,4,5]=>[4,1,1]=>90
[1,6,3,2,5,4]=>[3,1,1,1]=>40
[1,6,3,4,2,5]=>[3,1,1,1]=>40
[1,6,3,4,5,2]=>[2,1,1,1,1]=>15
[1,6,3,5,2,4]=>[4,1,1]=>90
[1,6,3,5,4,2]=>[2,2,1,1]=>45
[1,6,4,2,3,5]=>[5,1]=>144
[1,6,4,2,5,3]=>[4,1,1]=>90
[1,6,4,3,2,5]=>[3,2,1]=>120
[1,6,4,3,5,2]=>[2,2,1,1]=>45
[1,6,4,5,2,3]=>[5,1]=>144
[1,6,4,5,3,2]=>[3,2,1]=>120
[1,6,5,2,3,4]=>[3,2,1]=>120
[1,6,5,2,4,3]=>[5,1]=>144
[1,6,5,3,2,4]=>[5,1]=>144
[1,6,5,3,4,2]=>[3,2,1]=>120
[1,6,5,4,2,3]=>[4,1,1]=>90
[1,6,5,4,3,2]=>[2,2,1,1]=>45
[2,1,3,4,5,6]=>[2,1,1,1,1]=>15
[2,1,3,4,6,5]=>[2,2,1,1]=>45
[2,1,3,5,4,6]=>[2,2,1,1]=>45
[2,1,3,5,6,4]=>[3,2,1]=>120
[2,1,3,6,4,5]=>[3,2,1]=>120
[2,1,3,6,5,4]=>[2,2,1,1]=>45
[2,1,4,3,5,6]=>[2,2,1,1]=>45
[2,1,4,3,6,5]=>[2,2,2]=>15
[2,1,4,5,3,6]=>[3,2,1]=>120
[2,1,4,5,6,3]=>[4,2]=>90
[2,1,4,6,3,5]=>[4,2]=>90
[2,1,4,6,5,3]=>[3,2,1]=>120
[2,1,5,3,4,6]=>[3,2,1]=>120
[2,1,5,3,6,4]=>[4,2]=>90
[2,1,5,4,3,6]=>[2,2,1,1]=>45
[2,1,5,4,6,3]=>[3,2,1]=>120
[2,1,5,6,3,4]=>[2,2,2]=>15
[2,1,5,6,4,3]=>[4,2]=>90
[2,1,6,3,4,5]=>[4,2]=>90
[2,1,6,3,5,4]=>[3,2,1]=>120
[2,1,6,4,3,5]=>[3,2,1]=>120
[2,1,6,4,5,3]=>[2,2,1,1]=>45
[2,1,6,5,3,4]=>[4,2]=>90
[2,1,6,5,4,3]=>[2,2,2]=>15
[2,3,1,4,5,6]=>[3,1,1,1]=>40
[2,3,1,4,6,5]=>[3,2,1]=>120
[2,3,1,5,4,6]=>[3,2,1]=>120
[2,3,1,5,6,4]=>[3,3]=>40
[2,3,1,6,4,5]=>[3,3]=>40
[2,3,1,6,5,4]=>[3,2,1]=>120
[2,3,4,1,5,6]=>[4,1,1]=>90
[2,3,4,1,6,5]=>[4,2]=>90
[2,3,4,5,1,6]=>[5,1]=>144
[2,3,4,5,6,1]=>[6]=>120
[2,3,4,6,1,5]=>[6]=>120
[2,3,4,6,5,1]=>[5,1]=>144
[2,3,5,1,4,6]=>[5,1]=>144
[2,3,5,1,6,4]=>[6]=>120
[2,3,5,4,1,6]=>[4,1,1]=>90
[2,3,5,4,6,1]=>[5,1]=>144
[2,3,5,6,1,4]=>[4,2]=>90
[2,3,5,6,4,1]=>[6]=>120
[2,3,6,1,4,5]=>[6]=>120
[2,3,6,1,5,4]=>[5,1]=>144
[2,3,6,4,1,5]=>[5,1]=>144
[2,3,6,4,5,1]=>[4,1,1]=>90
[2,3,6,5,1,4]=>[6]=>120
[2,3,6,5,4,1]=>[4,2]=>90
[2,4,1,3,5,6]=>[4,1,1]=>90
[2,4,1,3,6,5]=>[4,2]=>90
[2,4,1,5,3,6]=>[5,1]=>144
[2,4,1,5,6,3]=>[6]=>120
[2,4,1,6,3,5]=>[6]=>120
[2,4,1,6,5,3]=>[5,1]=>144
[2,4,3,1,5,6]=>[3,1,1,1]=>40
[2,4,3,1,6,5]=>[3,2,1]=>120
[2,4,3,5,1,6]=>[4,1,1]=>90
[2,4,3,5,6,1]=>[5,1]=>144
[2,4,3,6,1,5]=>[5,1]=>144
[2,4,3,6,5,1]=>[4,1,1]=>90
[2,4,5,1,3,6]=>[3,2,1]=>120
[2,4,5,1,6,3]=>[3,3]=>40
[2,4,5,3,1,6]=>[5,1]=>144
[2,4,5,3,6,1]=>[6]=>120
[2,4,5,6,1,3]=>[6]=>120
[2,4,5,6,3,1]=>[4,2]=>90
[2,4,6,1,3,5]=>[3,3]=>40
[2,4,6,1,5,3]=>[3,2,1]=>120
[2,4,6,3,1,5]=>[6]=>120
[2,4,6,3,5,1]=>[5,1]=>144
[2,4,6,5,1,3]=>[4,2]=>90
[2,4,6,5,3,1]=>[6]=>120
[2,5,1,3,4,6]=>[5,1]=>144
[2,5,1,3,6,4]=>[6]=>120
[2,5,1,4,3,6]=>[4,1,1]=>90
[2,5,1,4,6,3]=>[5,1]=>144
[2,5,1,6,3,4]=>[4,2]=>90
[2,5,1,6,4,3]=>[6]=>120
[2,5,3,1,4,6]=>[4,1,1]=>90
[2,5,3,1,6,4]=>[5,1]=>144
[2,5,3,4,1,6]=>[3,1,1,1]=>40
[2,5,3,4,6,1]=>[4,1,1]=>90
[2,5,3,6,1,4]=>[3,2,1]=>120
[2,5,3,6,4,1]=>[5,1]=>144
[2,5,4,1,3,6]=>[5,1]=>144
[2,5,4,1,6,3]=>[6]=>120
[2,5,4,3,1,6]=>[3,2,1]=>120
[2,5,4,3,6,1]=>[4,2]=>90
[2,5,4,6,1,3]=>[3,3]=>40
[2,5,4,6,3,1]=>[6]=>120
[2,5,6,1,3,4]=>[6]=>120
[2,5,6,1,4,3]=>[4,2]=>90
[2,5,6,3,1,4]=>[3,3]=>40
[2,5,6,3,4,1]=>[6]=>120
[2,5,6,4,1,3]=>[3,2,1]=>120
[2,5,6,4,3,1]=>[5,1]=>144
[2,6,1,3,4,5]=>[6]=>120
[2,6,1,3,5,4]=>[5,1]=>144
[2,6,1,4,3,5]=>[5,1]=>144
[2,6,1,4,5,3]=>[4,1,1]=>90
[2,6,1,5,3,4]=>[6]=>120
[2,6,1,5,4,3]=>[4,2]=>90
[2,6,3,1,4,5]=>[5,1]=>144
[2,6,3,1,5,4]=>[4,1,1]=>90
[2,6,3,4,1,5]=>[4,1,1]=>90
[2,6,3,4,5,1]=>[3,1,1,1]=>40
[2,6,3,5,1,4]=>[5,1]=>144
[2,6,3,5,4,1]=>[3,2,1]=>120
[2,6,4,1,3,5]=>[6]=>120
[2,6,4,1,5,3]=>[5,1]=>144
[2,6,4,3,1,5]=>[4,2]=>90
[2,6,4,3,5,1]=>[3,2,1]=>120
[2,6,4,5,1,3]=>[6]=>120
[2,6,4,5,3,1]=>[3,3]=>40
[2,6,5,1,3,4]=>[4,2]=>90
[2,6,5,1,4,3]=>[6]=>120
[2,6,5,3,1,4]=>[6]=>120
[2,6,5,3,4,1]=>[3,3]=>40
[2,6,5,4,1,3]=>[5,1]=>144
[2,6,5,4,3,1]=>[3,2,1]=>120
[3,1,2,4,5,6]=>[3,1,1,1]=>40
[3,1,2,4,6,5]=>[3,2,1]=>120
[3,1,2,5,4,6]=>[3,2,1]=>120
[3,1,2,5,6,4]=>[3,3]=>40
[3,1,2,6,4,5]=>[3,3]=>40
[3,1,2,6,5,4]=>[3,2,1]=>120
[3,1,4,2,5,6]=>[4,1,1]=>90
[3,1,4,2,6,5]=>[4,2]=>90
[3,1,4,5,2,6]=>[5,1]=>144
[3,1,4,5,6,2]=>[6]=>120
[3,1,4,6,2,5]=>[6]=>120
[3,1,4,6,5,2]=>[5,1]=>144
[3,1,5,2,4,6]=>[5,1]=>144
[3,1,5,2,6,4]=>[6]=>120
[3,1,5,4,2,6]=>[4,1,1]=>90
[3,1,5,4,6,2]=>[5,1]=>144
[3,1,5,6,2,4]=>[4,2]=>90
[3,1,5,6,4,2]=>[6]=>120
[3,1,6,2,4,5]=>[6]=>120
[3,1,6,2,5,4]=>[5,1]=>144
[3,1,6,4,2,5]=>[5,1]=>144
[3,1,6,4,5,2]=>[4,1,1]=>90
[3,1,6,5,2,4]=>[6]=>120
[3,1,6,5,4,2]=>[4,2]=>90
[3,2,1,4,5,6]=>[2,1,1,1,1]=>15
[3,2,1,4,6,5]=>[2,2,1,1]=>45
[3,2,1,5,4,6]=>[2,2,1,1]=>45
[3,2,1,5,6,4]=>[3,2,1]=>120
[3,2,1,6,4,5]=>[3,2,1]=>120
[3,2,1,6,5,4]=>[2,2,1,1]=>45
[3,2,4,1,5,6]=>[3,1,1,1]=>40
[3,2,4,1,6,5]=>[3,2,1]=>120
[3,2,4,5,1,6]=>[4,1,1]=>90
[3,2,4,5,6,1]=>[5,1]=>144
[3,2,4,6,1,5]=>[5,1]=>144
[3,2,4,6,5,1]=>[4,1,1]=>90
[3,2,5,1,4,6]=>[4,1,1]=>90
[3,2,5,1,6,4]=>[5,1]=>144
[3,2,5,4,1,6]=>[3,1,1,1]=>40
[3,2,5,4,6,1]=>[4,1,1]=>90
[3,2,5,6,1,4]=>[3,2,1]=>120
[3,2,5,6,4,1]=>[5,1]=>144
[3,2,6,1,4,5]=>[5,1]=>144
[3,2,6,1,5,4]=>[4,1,1]=>90
[3,2,6,4,1,5]=>[4,1,1]=>90
[3,2,6,4,5,1]=>[3,1,1,1]=>40
[3,2,6,5,1,4]=>[5,1]=>144
[3,2,6,5,4,1]=>[3,2,1]=>120
[3,4,1,2,5,6]=>[2,2,1,1]=>45
[3,4,1,2,6,5]=>[2,2,2]=>15
[3,4,1,5,2,6]=>[3,2,1]=>120
[3,4,1,5,6,2]=>[4,2]=>90
[3,4,1,6,2,5]=>[4,2]=>90
[3,4,1,6,5,2]=>[3,2,1]=>120
[3,4,2,1,5,6]=>[4,1,1]=>90
[3,4,2,1,6,5]=>[4,2]=>90
[3,4,2,5,1,6]=>[5,1]=>144
[3,4,2,5,6,1]=>[6]=>120
[3,4,2,6,1,5]=>[6]=>120
[3,4,2,6,5,1]=>[5,1]=>144
[3,4,5,1,2,6]=>[5,1]=>144
[3,4,5,1,6,2]=>[6]=>120
[3,4,5,2,1,6]=>[3,2,1]=>120
[3,4,5,2,6,1]=>[4,2]=>90
[3,4,5,6,1,2]=>[3,3]=>40
[3,4,5,6,2,1]=>[6]=>120
[3,4,6,1,2,5]=>[6]=>120
[3,4,6,1,5,2]=>[5,1]=>144
[3,4,6,2,1,5]=>[4,2]=>90
[3,4,6,2,5,1]=>[3,2,1]=>120
[3,4,6,5,1,2]=>[6]=>120
[3,4,6,5,2,1]=>[3,3]=>40
[3,5,1,2,4,6]=>[3,2,1]=>120
[3,5,1,2,6,4]=>[4,2]=>90
[3,5,1,4,2,6]=>[2,2,1,1]=>45
[3,5,1,4,6,2]=>[3,2,1]=>120
[3,5,1,6,2,4]=>[2,2,2]=>15
[3,5,1,6,4,2]=>[4,2]=>90
[3,5,2,1,4,6]=>[5,1]=>144
[3,5,2,1,6,4]=>[6]=>120
[3,5,2,4,1,6]=>[4,1,1]=>90
[3,5,2,4,6,1]=>[5,1]=>144
[3,5,2,6,1,4]=>[4,2]=>90
[3,5,2,6,4,1]=>[6]=>120
[3,5,4,1,2,6]=>[3,2,1]=>120
[3,5,4,1,6,2]=>[3,3]=>40
[3,5,4,2,1,6]=>[5,1]=>144
[3,5,4,2,6,1]=>[6]=>120
[3,5,4,6,1,2]=>[6]=>120
[3,5,4,6,2,1]=>[4,2]=>90
[3,5,6,1,2,4]=>[4,2]=>90
[3,5,6,1,4,2]=>[6]=>120
[3,5,6,2,1,4]=>[6]=>120
[3,5,6,2,4,1]=>[3,3]=>40
[3,5,6,4,1,2]=>[5,1]=>144
[3,5,6,4,2,1]=>[3,2,1]=>120
[3,6,1,2,4,5]=>[4,2]=>90
[3,6,1,2,5,4]=>[3,2,1]=>120
[3,6,1,4,2,5]=>[3,2,1]=>120
[3,6,1,4,5,2]=>[2,2,1,1]=>45
[3,6,1,5,2,4]=>[4,2]=>90
[3,6,1,5,4,2]=>[2,2,2]=>15
[3,6,2,1,4,5]=>[6]=>120
[3,6,2,1,5,4]=>[5,1]=>144
[3,6,2,4,1,5]=>[5,1]=>144
[3,6,2,4,5,1]=>[4,1,1]=>90
[3,6,2,5,1,4]=>[6]=>120
[3,6,2,5,4,1]=>[4,2]=>90
[3,6,4,1,2,5]=>[3,3]=>40
[3,6,4,1,5,2]=>[3,2,1]=>120
[3,6,4,2,1,5]=>[6]=>120
[3,6,4,2,5,1]=>[5,1]=>144
[3,6,4,5,1,2]=>[4,2]=>90
[3,6,4,5,2,1]=>[6]=>120
[3,6,5,1,2,4]=>[6]=>120
[3,6,5,1,4,2]=>[4,2]=>90
[3,6,5,2,1,4]=>[3,3]=>40
[3,6,5,2,4,1]=>[6]=>120
[3,6,5,4,1,2]=>[3,2,1]=>120
[3,6,5,4,2,1]=>[5,1]=>144
[4,1,2,3,5,6]=>[4,1,1]=>90
[4,1,2,3,6,5]=>[4,2]=>90
[4,1,2,5,3,6]=>[5,1]=>144
[4,1,2,5,6,3]=>[6]=>120
[4,1,2,6,3,5]=>[6]=>120
[4,1,2,6,5,3]=>[5,1]=>144
[4,1,3,2,5,6]=>[3,1,1,1]=>40
[4,1,3,2,6,5]=>[3,2,1]=>120
[4,1,3,5,2,6]=>[4,1,1]=>90
[4,1,3,5,6,2]=>[5,1]=>144
[4,1,3,6,2,5]=>[5,1]=>144
[4,1,3,6,5,2]=>[4,1,1]=>90
[4,1,5,2,3,6]=>[3,2,1]=>120
[4,1,5,2,6,3]=>[3,3]=>40
[4,1,5,3,2,6]=>[5,1]=>144
[4,1,5,3,6,2]=>[6]=>120
[4,1,5,6,2,3]=>[6]=>120
[4,1,5,6,3,2]=>[4,2]=>90
[4,1,6,2,3,5]=>[3,3]=>40
[4,1,6,2,5,3]=>[3,2,1]=>120
[4,1,6,3,2,5]=>[6]=>120
[4,1,6,3,5,2]=>[5,1]=>144
[4,1,6,5,2,3]=>[4,2]=>90
[4,1,6,5,3,2]=>[6]=>120
[4,2,1,3,5,6]=>[3,1,1,1]=>40
[4,2,1,3,6,5]=>[3,2,1]=>120
[4,2,1,5,3,6]=>[4,1,1]=>90
[4,2,1,5,6,3]=>[5,1]=>144
[4,2,1,6,3,5]=>[5,1]=>144
[4,2,1,6,5,3]=>[4,1,1]=>90
[4,2,3,1,5,6]=>[2,1,1,1,1]=>15
[4,2,3,1,6,5]=>[2,2,1,1]=>45
[4,2,3,5,1,6]=>[3,1,1,1]=>40
[4,2,3,5,6,1]=>[4,1,1]=>90
[4,2,3,6,1,5]=>[4,1,1]=>90
[4,2,3,6,5,1]=>[3,1,1,1]=>40
[4,2,5,1,3,6]=>[2,2,1,1]=>45
[4,2,5,1,6,3]=>[3,2,1]=>120
[4,2,5,3,1,6]=>[4,1,1]=>90
[4,2,5,3,6,1]=>[5,1]=>144
[4,2,5,6,1,3]=>[5,1]=>144
[4,2,5,6,3,1]=>[3,2,1]=>120
[4,2,6,1,3,5]=>[3,2,1]=>120
[4,2,6,1,5,3]=>[2,2,1,1]=>45
[4,2,6,3,1,5]=>[5,1]=>144
[4,2,6,3,5,1]=>[4,1,1]=>90
[4,2,6,5,1,3]=>[3,2,1]=>120
[4,2,6,5,3,1]=>[5,1]=>144
[4,3,1,2,5,6]=>[4,1,1]=>90
[4,3,1,2,6,5]=>[4,2]=>90
[4,3,1,5,2,6]=>[5,1]=>144
[4,3,1,5,6,2]=>[6]=>120
[4,3,1,6,2,5]=>[6]=>120
[4,3,1,6,5,2]=>[5,1]=>144
[4,3,2,1,5,6]=>[2,2,1,1]=>45
[4,3,2,1,6,5]=>[2,2,2]=>15
[4,3,2,5,1,6]=>[3,2,1]=>120
[4,3,2,5,6,1]=>[4,2]=>90
[4,3,2,6,1,5]=>[4,2]=>90
[4,3,2,6,5,1]=>[3,2,1]=>120
[4,3,5,1,2,6]=>[3,2,1]=>120
[4,3,5,1,6,2]=>[4,2]=>90
[4,3,5,2,1,6]=>[5,1]=>144
[4,3,5,2,6,1]=>[6]=>120
[4,3,5,6,1,2]=>[6]=>120
[4,3,5,6,2,1]=>[3,3]=>40
[4,3,6,1,2,5]=>[4,2]=>90
[4,3,6,1,5,2]=>[3,2,1]=>120
[4,3,6,2,1,5]=>[6]=>120
[4,3,6,2,5,1]=>[5,1]=>144
[4,3,6,5,1,2]=>[3,3]=>40
[4,3,6,5,2,1]=>[6]=>120
[4,5,1,2,3,6]=>[5,1]=>144
[4,5,1,2,6,3]=>[6]=>120
[4,5,1,3,2,6]=>[3,2,1]=>120
[4,5,1,3,6,2]=>[3,3]=>40
[4,5,1,6,2,3]=>[4,2]=>90
[4,5,1,6,3,2]=>[6]=>120
[4,5,2,1,3,6]=>[3,2,1]=>120
[4,5,2,1,6,3]=>[4,2]=>90
[4,5,2,3,1,6]=>[5,1]=>144
[4,5,2,3,6,1]=>[6]=>120
[4,5,2,6,1,3]=>[6]=>120
[4,5,2,6,3,1]=>[3,3]=>40
[4,5,3,1,2,6]=>[2,2,1,1]=>45
[4,5,3,1,6,2]=>[3,2,1]=>120
[4,5,3,2,1,6]=>[4,1,1]=>90
[4,5,3,2,6,1]=>[5,1]=>144
[4,5,3,6,1,2]=>[5,1]=>144
[4,5,3,6,2,1]=>[3,2,1]=>120
[4,5,6,1,2,3]=>[2,2,2]=>15
[4,5,6,1,3,2]=>[4,2]=>90
[4,5,6,2,1,3]=>[4,2]=>90
[4,5,6,2,3,1]=>[6]=>120
[4,5,6,3,1,2]=>[6]=>120
[4,5,6,3,2,1]=>[4,2]=>90
[4,6,1,2,3,5]=>[6]=>120
[4,6,1,2,5,3]=>[5,1]=>144
[4,6,1,3,2,5]=>[3,3]=>40
[4,6,1,3,5,2]=>[3,2,1]=>120
[4,6,1,5,2,3]=>[6]=>120
[4,6,1,5,3,2]=>[4,2]=>90
[4,6,2,1,3,5]=>[4,2]=>90
[4,6,2,1,5,3]=>[3,2,1]=>120
[4,6,2,3,1,5]=>[6]=>120
[4,6,2,3,5,1]=>[5,1]=>144
[4,6,2,5,1,3]=>[3,3]=>40
[4,6,2,5,3,1]=>[6]=>120
[4,6,3,1,2,5]=>[3,2,1]=>120
[4,6,3,1,5,2]=>[2,2,1,1]=>45
[4,6,3,2,1,5]=>[5,1]=>144
[4,6,3,2,5,1]=>[4,1,1]=>90
[4,6,3,5,1,2]=>[3,2,1]=>120
[4,6,3,5,2,1]=>[5,1]=>144
[4,6,5,1,2,3]=>[4,2]=>90
[4,6,5,1,3,2]=>[2,2,2]=>15
[4,6,5,2,1,3]=>[6]=>120
[4,6,5,2,3,1]=>[4,2]=>90
[4,6,5,3,1,2]=>[4,2]=>90
[4,6,5,3,2,1]=>[6]=>120
[5,1,2,3,4,6]=>[5,1]=>144
[5,1,2,3,6,4]=>[6]=>120
[5,1,2,4,3,6]=>[4,1,1]=>90
[5,1,2,4,6,3]=>[5,1]=>144
[5,1,2,6,3,4]=>[4,2]=>90
[5,1,2,6,4,3]=>[6]=>120
[5,1,3,2,4,6]=>[4,1,1]=>90
[5,1,3,2,6,4]=>[5,1]=>144
[5,1,3,4,2,6]=>[3,1,1,1]=>40
[5,1,3,4,6,2]=>[4,1,1]=>90
[5,1,3,6,2,4]=>[3,2,1]=>120
[5,1,3,6,4,2]=>[5,1]=>144
[5,1,4,2,3,6]=>[5,1]=>144
[5,1,4,2,6,3]=>[6]=>120
[5,1,4,3,2,6]=>[3,2,1]=>120
[5,1,4,3,6,2]=>[4,2]=>90
[5,1,4,6,2,3]=>[3,3]=>40
[5,1,4,6,3,2]=>[6]=>120
[5,1,6,2,3,4]=>[6]=>120
[5,1,6,2,4,3]=>[4,2]=>90
[5,1,6,3,2,4]=>[3,3]=>40
[5,1,6,3,4,2]=>[6]=>120
[5,1,6,4,2,3]=>[3,2,1]=>120
[5,1,6,4,3,2]=>[5,1]=>144
[5,2,1,3,4,6]=>[4,1,1]=>90
[5,2,1,3,6,4]=>[5,1]=>144
[5,2,1,4,3,6]=>[3,1,1,1]=>40
[5,2,1,4,6,3]=>[4,1,1]=>90
[5,2,1,6,3,4]=>[3,2,1]=>120
[5,2,1,6,4,3]=>[5,1]=>144
[5,2,3,1,4,6]=>[3,1,1,1]=>40
[5,2,3,1,6,4]=>[4,1,1]=>90
[5,2,3,4,1,6]=>[2,1,1,1,1]=>15
[5,2,3,4,6,1]=>[3,1,1,1]=>40
[5,2,3,6,1,4]=>[2,2,1,1]=>45
[5,2,3,6,4,1]=>[4,1,1]=>90
[5,2,4,1,3,6]=>[4,1,1]=>90
[5,2,4,1,6,3]=>[5,1]=>144
[5,2,4,3,1,6]=>[2,2,1,1]=>45
[5,2,4,3,6,1]=>[3,2,1]=>120
[5,2,4,6,1,3]=>[3,2,1]=>120
[5,2,4,6,3,1]=>[5,1]=>144
[5,2,6,1,3,4]=>[5,1]=>144
[5,2,6,1,4,3]=>[3,2,1]=>120
[5,2,6,3,1,4]=>[3,2,1]=>120
[5,2,6,3,4,1]=>[5,1]=>144
[5,2,6,4,1,3]=>[2,2,1,1]=>45
[5,2,6,4,3,1]=>[4,1,1]=>90
[5,3,1,2,4,6]=>[5,1]=>144
[5,3,1,2,6,4]=>[6]=>120
[5,3,1,4,2,6]=>[4,1,1]=>90
[5,3,1,4,6,2]=>[5,1]=>144
[5,3,1,6,2,4]=>[4,2]=>90
[5,3,1,6,4,2]=>[6]=>120
[5,3,2,1,4,6]=>[3,2,1]=>120
[5,3,2,1,6,4]=>[4,2]=>90
[5,3,2,4,1,6]=>[2,2,1,1]=>45
[5,3,2,4,6,1]=>[3,2,1]=>120
[5,3,2,6,1,4]=>[2,2,2]=>15
[5,3,2,6,4,1]=>[4,2]=>90
[5,3,4,1,2,6]=>[5,1]=>144
[5,3,4,1,6,2]=>[6]=>120
[5,3,4,2,1,6]=>[3,2,1]=>120
[5,3,4,2,6,1]=>[3,3]=>40
[5,3,4,6,1,2]=>[4,2]=>90
[5,3,4,6,2,1]=>[6]=>120
[5,3,6,1,2,4]=>[6]=>120
[5,3,6,1,4,2]=>[3,3]=>40
[5,3,6,2,1,4]=>[4,2]=>90
[5,3,6,2,4,1]=>[6]=>120
[5,3,6,4,1,2]=>[3,2,1]=>120
[5,3,6,4,2,1]=>[5,1]=>144
[5,4,1,2,3,6]=>[3,2,1]=>120
[5,4,1,2,6,3]=>[4,2]=>90
[5,4,1,3,2,6]=>[5,1]=>144
[5,4,1,3,6,2]=>[6]=>120
[5,4,1,6,2,3]=>[6]=>120
[5,4,1,6,3,2]=>[3,3]=>40
[5,4,2,1,3,6]=>[5,1]=>144
[5,4,2,1,6,3]=>[6]=>120
[5,4,2,3,1,6]=>[3,2,1]=>120
[5,4,2,3,6,1]=>[3,3]=>40
[5,4,2,6,1,3]=>[4,2]=>90
[5,4,2,6,3,1]=>[6]=>120
[5,4,3,1,2,6]=>[4,1,1]=>90
[5,4,3,1,6,2]=>[5,1]=>144
[5,4,3,2,1,6]=>[2,2,1,1]=>45
[5,4,3,2,6,1]=>[3,2,1]=>120
[5,4,3,6,1,2]=>[3,2,1]=>120
[5,4,3,6,2,1]=>[5,1]=>144
[5,4,6,1,2,3]=>[4,2]=>90
[5,4,6,1,3,2]=>[6]=>120
[5,4,6,2,1,3]=>[2,2,2]=>15
[5,4,6,2,3,1]=>[4,2]=>90
[5,4,6,3,1,2]=>[4,2]=>90
[5,4,6,3,2,1]=>[6]=>120
[5,6,1,2,3,4]=>[3,3]=>40
[5,6,1,2,4,3]=>[6]=>120
[5,6,1,3,2,4]=>[6]=>120
[5,6,1,3,4,2]=>[4,2]=>90
[5,6,1,4,2,3]=>[5,1]=>144
[5,6,1,4,3,2]=>[3,2,1]=>120
[5,6,2,1,3,4]=>[6]=>120
[5,6,2,1,4,3]=>[3,3]=>40
[5,6,2,3,1,4]=>[4,2]=>90
[5,6,2,3,4,1]=>[6]=>120
[5,6,2,4,1,3]=>[3,2,1]=>120
[5,6,2,4,3,1]=>[5,1]=>144
[5,6,3,1,2,4]=>[5,1]=>144
[5,6,3,1,4,2]=>[3,2,1]=>120
[5,6,3,2,1,4]=>[3,2,1]=>120
[5,6,3,2,4,1]=>[5,1]=>144
[5,6,3,4,1,2]=>[2,2,1,1]=>45
[5,6,3,4,2,1]=>[4,1,1]=>90
[5,6,4,1,2,3]=>[6]=>120
[5,6,4,1,3,2]=>[4,2]=>90
[5,6,4,2,1,3]=>[4,2]=>90
[5,6,4,2,3,1]=>[6]=>120
[5,6,4,3,1,2]=>[2,2,2]=>15
[5,6,4,3,2,1]=>[4,2]=>90
[6,1,2,3,4,5]=>[6]=>120
[6,1,2,3,5,4]=>[5,1]=>144
[6,1,2,4,3,5]=>[5,1]=>144
[6,1,2,4,5,3]=>[4,1,1]=>90
[6,1,2,5,3,4]=>[6]=>120
[6,1,2,5,4,3]=>[4,2]=>90
[6,1,3,2,4,5]=>[5,1]=>144
[6,1,3,2,5,4]=>[4,1,1]=>90
[6,1,3,4,2,5]=>[4,1,1]=>90
[6,1,3,4,5,2]=>[3,1,1,1]=>40
[6,1,3,5,2,4]=>[5,1]=>144
[6,1,3,5,4,2]=>[3,2,1]=>120
[6,1,4,2,3,5]=>[6]=>120
[6,1,4,2,5,3]=>[5,1]=>144
[6,1,4,3,2,5]=>[4,2]=>90
[6,1,4,3,5,2]=>[3,2,1]=>120
[6,1,4,5,2,3]=>[6]=>120
[6,1,4,5,3,2]=>[3,3]=>40
[6,1,5,2,3,4]=>[4,2]=>90
[6,1,5,2,4,3]=>[6]=>120
[6,1,5,3,2,4]=>[6]=>120
[6,1,5,3,4,2]=>[3,3]=>40
[6,1,5,4,2,3]=>[5,1]=>144
[6,1,5,4,3,2]=>[3,2,1]=>120
[6,2,1,3,4,5]=>[5,1]=>144
[6,2,1,3,5,4]=>[4,1,1]=>90
[6,2,1,4,3,5]=>[4,1,1]=>90
[6,2,1,4,5,3]=>[3,1,1,1]=>40
[6,2,1,5,3,4]=>[5,1]=>144
[6,2,1,5,4,3]=>[3,2,1]=>120
[6,2,3,1,4,5]=>[4,1,1]=>90
[6,2,3,1,5,4]=>[3,1,1,1]=>40
[6,2,3,4,1,5]=>[3,1,1,1]=>40
[6,2,3,4,5,1]=>[2,1,1,1,1]=>15
[6,2,3,5,1,4]=>[4,1,1]=>90
[6,2,3,5,4,1]=>[2,2,1,1]=>45
[6,2,4,1,3,5]=>[5,1]=>144
[6,2,4,1,5,3]=>[4,1,1]=>90
[6,2,4,3,1,5]=>[3,2,1]=>120
[6,2,4,3,5,1]=>[2,2,1,1]=>45
[6,2,4,5,1,3]=>[5,1]=>144
[6,2,4,5,3,1]=>[3,2,1]=>120
[6,2,5,1,3,4]=>[3,2,1]=>120
[6,2,5,1,4,3]=>[5,1]=>144
[6,2,5,3,1,4]=>[5,1]=>144
[6,2,5,3,4,1]=>[3,2,1]=>120
[6,2,5,4,1,3]=>[4,1,1]=>90
[6,2,5,4,3,1]=>[2,2,1,1]=>45
[6,3,1,2,4,5]=>[6]=>120
[6,3,1,2,5,4]=>[5,1]=>144
[6,3,1,4,2,5]=>[5,1]=>144
[6,3,1,4,5,2]=>[4,1,1]=>90
[6,3,1,5,2,4]=>[6]=>120
[6,3,1,5,4,2]=>[4,2]=>90
[6,3,2,1,4,5]=>[4,2]=>90
[6,3,2,1,5,4]=>[3,2,1]=>120
[6,3,2,4,1,5]=>[3,2,1]=>120
[6,3,2,4,5,1]=>[2,2,1,1]=>45
[6,3,2,5,1,4]=>[4,2]=>90
[6,3,2,5,4,1]=>[2,2,2]=>15
[6,3,4,1,2,5]=>[6]=>120
[6,3,4,1,5,2]=>[5,1]=>144
[6,3,4,2,1,5]=>[3,3]=>40
[6,3,4,2,5,1]=>[3,2,1]=>120
[6,3,4,5,1,2]=>[6]=>120
[6,3,4,5,2,1]=>[4,2]=>90
[6,3,5,1,2,4]=>[3,3]=>40
[6,3,5,1,4,2]=>[6]=>120
[6,3,5,2,1,4]=>[6]=>120
[6,3,5,2,4,1]=>[4,2]=>90
[6,3,5,4,1,2]=>[5,1]=>144
[6,3,5,4,2,1]=>[3,2,1]=>120
[6,4,1,2,3,5]=>[4,2]=>90
[6,4,1,2,5,3]=>[3,2,1]=>120
[6,4,1,3,2,5]=>[6]=>120
[6,4,1,3,5,2]=>[5,1]=>144
[6,4,1,5,2,3]=>[3,3]=>40
[6,4,1,5,3,2]=>[6]=>120
[6,4,2,1,3,5]=>[6]=>120
[6,4,2,1,5,3]=>[5,1]=>144
[6,4,2,3,1,5]=>[3,3]=>40
[6,4,2,3,5,1]=>[3,2,1]=>120
[6,4,2,5,1,3]=>[6]=>120
[6,4,2,5,3,1]=>[4,2]=>90
[6,4,3,1,2,5]=>[5,1]=>144
[6,4,3,1,5,2]=>[4,1,1]=>90
[6,4,3,2,1,5]=>[3,2,1]=>120
[6,4,3,2,5,1]=>[2,2,1,1]=>45
[6,4,3,5,1,2]=>[5,1]=>144
[6,4,3,5,2,1]=>[3,2,1]=>120
[6,4,5,1,2,3]=>[6]=>120
[6,4,5,1,3,2]=>[4,2]=>90
[6,4,5,2,1,3]=>[4,2]=>90
[6,4,5,2,3,1]=>[2,2,2]=>15
[6,4,5,3,1,2]=>[6]=>120
[6,4,5,3,2,1]=>[4,2]=>90
[6,5,1,2,3,4]=>[6]=>120
[6,5,1,2,4,3]=>[3,3]=>40
[6,5,1,3,2,4]=>[4,2]=>90
[6,5,1,3,4,2]=>[6]=>120
[6,5,1,4,2,3]=>[3,2,1]=>120
[6,5,1,4,3,2]=>[5,1]=>144
[6,5,2,1,3,4]=>[3,3]=>40
[6,5,2,1,4,3]=>[6]=>120
[6,5,2,3,1,4]=>[6]=>120
[6,5,2,3,4,1]=>[4,2]=>90
[6,5,2,4,1,3]=>[5,1]=>144
[6,5,2,4,3,1]=>[3,2,1]=>120
[6,5,3,1,2,4]=>[3,2,1]=>120
[6,5,3,1,4,2]=>[5,1]=>144
[6,5,3,2,1,4]=>[5,1]=>144
[6,5,3,2,4,1]=>[3,2,1]=>120
[6,5,3,4,1,2]=>[4,1,1]=>90
[6,5,3,4,2,1]=>[2,2,1,1]=>45
[6,5,4,1,2,3]=>[4,2]=>90
[6,5,4,1,3,2]=>[6]=>120
[6,5,4,2,1,3]=>[6]=>120
[6,5,4,2,3,1]=>[4,2]=>90
[6,5,4,3,1,2]=>[4,2]=>90
[6,5,4,3,2,1]=>[2,2,2]=>15
[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1]=>1
[1,2,3,4,5,7,6]=>[2,1,1,1,1,1]=>21
[1,2,3,4,6,5,7]=>[2,1,1,1,1,1]=>21
[1,2,3,4,6,7,5]=>[3,1,1,1,1]=>70
[1,2,3,4,7,5,6]=>[3,1,1,1,1]=>70
[1,2,3,4,7,6,5]=>[2,1,1,1,1,1]=>21
[1,2,3,5,4,6,7]=>[2,1,1,1,1,1]=>21
[1,2,3,5,4,7,6]=>[2,2,1,1,1]=>105
[1,2,3,5,6,4,7]=>[3,1,1,1,1]=>70
[1,2,3,5,6,7,4]=>[4,1,1,1]=>210
[1,2,3,5,7,4,6]=>[4,1,1,1]=>210
[1,2,3,5,7,6,4]=>[3,1,1,1,1]=>70
[1,2,3,6,4,5,7]=>[3,1,1,1,1]=>70
[1,2,3,6,4,7,5]=>[4,1,1,1]=>210
[1,2,3,6,5,4,7]=>[2,1,1,1,1,1]=>21
[1,2,3,6,5,7,4]=>[3,1,1,1,1]=>70
[1,2,3,6,7,4,5]=>[2,2,1,1,1]=>105
[1,2,3,6,7,5,4]=>[4,1,1,1]=>210
[1,2,3,7,4,5,6]=>[4,1,1,1]=>210
[1,2,3,7,4,6,5]=>[3,1,1,1,1]=>70
[1,2,3,7,5,4,6]=>[3,1,1,1,1]=>70
[1,2,3,7,5,6,4]=>[2,1,1,1,1,1]=>21
[1,2,3,7,6,4,5]=>[4,1,1,1]=>210
[1,2,3,7,6,5,4]=>[2,2,1,1,1]=>105
[1,2,4,3,5,6,7]=>[2,1,1,1,1,1]=>21
[1,2,4,3,5,7,6]=>[2,2,1,1,1]=>105
[1,2,4,3,6,5,7]=>[2,2,1,1,1]=>105
[1,2,4,3,6,7,5]=>[3,2,1,1]=>420
[1,2,4,3,7,5,6]=>[3,2,1,1]=>420
[1,2,4,3,7,6,5]=>[2,2,1,1,1]=>105
[1,2,4,5,3,6,7]=>[3,1,1,1,1]=>70
[1,2,4,5,3,7,6]=>[3,2,1,1]=>420
[1,2,4,5,6,3,7]=>[4,1,1,1]=>210
[1,2,4,5,6,7,3]=>[5,1,1]=>504
[1,2,4,5,7,3,6]=>[5,1,1]=>504
[1,2,4,5,7,6,3]=>[4,1,1,1]=>210
[1,2,4,6,3,5,7]=>[4,1,1,1]=>210
[1,2,4,6,3,7,5]=>[5,1,1]=>504
[1,2,4,6,5,3,7]=>[3,1,1,1,1]=>70
[1,2,4,6,5,7,3]=>[4,1,1,1]=>210
[1,2,4,6,7,3,5]=>[3,2,1,1]=>420
[1,2,4,6,7,5,3]=>[5,1,1]=>504
[1,2,4,7,3,5,6]=>[5,1,1]=>504
[1,2,4,7,3,6,5]=>[4,1,1,1]=>210
[1,2,4,7,5,3,6]=>[4,1,1,1]=>210
[1,2,4,7,5,6,3]=>[3,1,1,1,1]=>70
[1,2,4,7,6,3,5]=>[5,1,1]=>504
[1,2,4,7,6,5,3]=>[3,2,1,1]=>420
[1,2,5,3,4,6,7]=>[3,1,1,1,1]=>70
[1,2,5,3,4,7,6]=>[3,2,1,1]=>420
[1,2,5,3,6,4,7]=>[4,1,1,1]=>210
[1,2,5,3,6,7,4]=>[5,1,1]=>504
[1,2,5,3,7,4,6]=>[5,1,1]=>504
[1,2,5,3,7,6,4]=>[4,1,1,1]=>210
[1,2,5,4,3,6,7]=>[2,1,1,1,1,1]=>21
[1,2,5,4,3,7,6]=>[2,2,1,1,1]=>105
[1,2,5,4,6,3,7]=>[3,1,1,1,1]=>70
[1,2,5,4,6,7,3]=>[4,1,1,1]=>210
[1,2,5,4,7,3,6]=>[4,1,1,1]=>210
[1,2,5,4,7,6,3]=>[3,1,1,1,1]=>70
[1,2,5,6,3,4,7]=>[2,2,1,1,1]=>105
[1,2,5,6,3,7,4]=>[3,2,1,1]=>420
[1,2,5,6,4,3,7]=>[4,1,1,1]=>210
[1,2,5,6,4,7,3]=>[5,1,1]=>504
[1,2,5,6,7,3,4]=>[5,1,1]=>504
[1,2,5,6,7,4,3]=>[3,2,1,1]=>420
[1,2,5,7,3,4,6]=>[3,2,1,1]=>420
[1,2,5,7,3,6,4]=>[2,2,1,1,1]=>105
[1,2,5,7,4,3,6]=>[5,1,1]=>504
[1,2,5,7,4,6,3]=>[4,1,1,1]=>210
[1,2,5,7,6,3,4]=>[3,2,1,1]=>420
[1,2,5,7,6,4,3]=>[5,1,1]=>504
[1,2,6,3,4,5,7]=>[4,1,1,1]=>210
[1,2,6,3,4,7,5]=>[5,1,1]=>504
[1,2,6,3,5,4,7]=>[3,1,1,1,1]=>70
[1,2,6,3,5,7,4]=>[4,1,1,1]=>210
[1,2,6,3,7,4,5]=>[3,2,1,1]=>420
[1,2,6,3,7,5,4]=>[5,1,1]=>504
[1,2,6,4,3,5,7]=>[3,1,1,1,1]=>70
[1,2,6,4,3,7,5]=>[4,1,1,1]=>210
[1,2,6,4,5,3,7]=>[2,1,1,1,1,1]=>21
[1,2,6,4,5,7,3]=>[3,1,1,1,1]=>70
[1,2,6,4,7,3,5]=>[2,2,1,1,1]=>105
[1,2,6,4,7,5,3]=>[4,1,1,1]=>210
[1,2,6,5,3,4,7]=>[4,1,1,1]=>210
[1,2,6,5,3,7,4]=>[5,1,1]=>504
[1,2,6,5,4,3,7]=>[2,2,1,1,1]=>105
[1,2,6,5,4,7,3]=>[3,2,1,1]=>420
[1,2,6,5,7,3,4]=>[3,2,1,1]=>420
[1,2,6,5,7,4,3]=>[5,1,1]=>504
[1,2,6,7,3,4,5]=>[5,1,1]=>504
[1,2,6,7,3,5,4]=>[3,2,1,1]=>420
[1,2,6,7,4,3,5]=>[3,2,1,1]=>420
[1,2,6,7,4,5,3]=>[5,1,1]=>504
[1,2,6,7,5,3,4]=>[2,2,1,1,1]=>105
[1,2,6,7,5,4,3]=>[4,1,1,1]=>210
[1,2,7,3,4,5,6]=>[5,1,1]=>504
[1,2,7,3,4,6,5]=>[4,1,1,1]=>210
[1,2,7,3,5,4,6]=>[4,1,1,1]=>210
[1,2,7,3,5,6,4]=>[3,1,1,1,1]=>70
[1,2,7,3,6,4,5]=>[5,1,1]=>504
[1,2,7,3,6,5,4]=>[3,2,1,1]=>420
[1,2,7,4,3,5,6]=>[4,1,1,1]=>210
[1,2,7,4,3,6,5]=>[3,1,1,1,1]=>70
[1,2,7,4,5,3,6]=>[3,1,1,1,1]=>70
[1,2,7,4,5,6,3]=>[2,1,1,1,1,1]=>21
[1,2,7,4,6,3,5]=>[4,1,1,1]=>210
[1,2,7,4,6,5,3]=>[2,2,1,1,1]=>105
[1,2,7,5,3,4,6]=>[5,1,1]=>504
[1,2,7,5,3,6,4]=>[4,1,1,1]=>210
[1,2,7,5,4,3,6]=>[3,2,1,1]=>420
[1,2,7,5,4,6,3]=>[2,2,1,1,1]=>105
[1,2,7,5,6,3,4]=>[5,1,1]=>504
[1,2,7,5,6,4,3]=>[3,2,1,1]=>420
[1,2,7,6,3,4,5]=>[3,2,1,1]=>420
[1,2,7,6,3,5,4]=>[5,1,1]=>504
[1,2,7,6,4,3,5]=>[5,1,1]=>504
[1,2,7,6,4,5,3]=>[3,2,1,1]=>420
[1,2,7,6,5,3,4]=>[4,1,1,1]=>210
[1,2,7,6,5,4,3]=>[2,2,1,1,1]=>105
[1,3,2,4,5,6,7]=>[2,1,1,1,1,1]=>21
[1,3,2,4,5,7,6]=>[2,2,1,1,1]=>105
[1,3,2,4,6,5,7]=>[2,2,1,1,1]=>105
[1,3,2,4,6,7,5]=>[3,2,1,1]=>420
[1,3,2,4,7,5,6]=>[3,2,1,1]=>420
[1,3,2,4,7,6,5]=>[2,2,1,1,1]=>105
[1,3,2,5,4,6,7]=>[2,2,1,1,1]=>105
[1,3,2,5,4,7,6]=>[2,2,2,1]=>105
[1,3,2,5,6,4,7]=>[3,2,1,1]=>420
[1,3,2,5,6,7,4]=>[4,2,1]=>630
[1,3,2,5,7,4,6]=>[4,2,1]=>630
[1,3,2,5,7,6,4]=>[3,2,1,1]=>420
[1,3,2,6,4,5,7]=>[3,2,1,1]=>420
[1,3,2,6,4,7,5]=>[4,2,1]=>630
[1,3,2,6,5,4,7]=>[2,2,1,1,1]=>105
[1,3,2,6,5,7,4]=>[3,2,1,1]=>420
[1,3,2,6,7,4,5]=>[2,2,2,1]=>105
[1,3,2,6,7,5,4]=>[4,2,1]=>630
[1,3,2,7,4,5,6]=>[4,2,1]=>630
[1,3,2,7,4,6,5]=>[3,2,1,1]=>420
[1,3,2,7,5,4,6]=>[3,2,1,1]=>420
[1,3,2,7,5,6,4]=>[2,2,1,1,1]=>105
[1,3,2,7,6,4,5]=>[4,2,1]=>630
[1,3,2,7,6,5,4]=>[2,2,2,1]=>105
[1,3,4,2,5,6,7]=>[3,1,1,1,1]=>70
[1,3,4,2,5,7,6]=>[3,2,1,1]=>420
[1,3,4,2,6,5,7]=>[3,2,1,1]=>420
[1,3,4,2,6,7,5]=>[3,3,1]=>280
[1,3,4,2,7,5,6]=>[3,3,1]=>280
[1,3,4,2,7,6,5]=>[3,2,1,1]=>420
[1,3,4,5,2,6,7]=>[4,1,1,1]=>210
[1,3,4,5,2,7,6]=>[4,2,1]=>630
[1,3,4,5,6,2,7]=>[5,1,1]=>504
[1,3,4,5,6,7,2]=>[6,1]=>840
[1,3,4,5,7,2,6]=>[6,1]=>840
[1,3,4,5,7,6,2]=>[5,1,1]=>504
[1,3,4,6,2,5,7]=>[5,1,1]=>504
[1,3,4,6,2,7,5]=>[6,1]=>840
[1,3,4,6,5,2,7]=>[4,1,1,1]=>210
[1,3,4,6,5,7,2]=>[5,1,1]=>504
[1,3,4,6,7,2,5]=>[4,2,1]=>630
[1,3,4,6,7,5,2]=>[6,1]=>840
[1,3,4,7,2,5,6]=>[6,1]=>840
[1,3,4,7,2,6,5]=>[5,1,1]=>504
[1,3,4,7,5,2,6]=>[5,1,1]=>504
[1,3,4,7,5,6,2]=>[4,1,1,1]=>210
[1,3,4,7,6,2,5]=>[6,1]=>840
[1,3,4,7,6,5,2]=>[4,2,1]=>630
[1,3,5,2,4,6,7]=>[4,1,1,1]=>210
[1,3,5,2,4,7,6]=>[4,2,1]=>630
[1,3,5,2,6,4,7]=>[5,1,1]=>504
[1,3,5,2,6,7,4]=>[6,1]=>840
[1,3,5,2,7,4,6]=>[6,1]=>840
[1,3,5,2,7,6,4]=>[5,1,1]=>504
[1,3,5,4,2,6,7]=>[3,1,1,1,1]=>70
[1,3,5,4,2,7,6]=>[3,2,1,1]=>420
[1,3,5,4,6,2,7]=>[4,1,1,1]=>210
[1,3,5,4,6,7,2]=>[5,1,1]=>504
[1,3,5,4,7,2,6]=>[5,1,1]=>504
[1,3,5,4,7,6,2]=>[4,1,1,1]=>210
[1,3,5,6,2,4,7]=>[3,2,1,1]=>420
[1,3,5,6,2,7,4]=>[3,3,1]=>280
[1,3,5,6,4,2,7]=>[5,1,1]=>504
[1,3,5,6,4,7,2]=>[6,1]=>840
[1,3,5,6,7,2,4]=>[6,1]=>840
[1,3,5,6,7,4,2]=>[4,2,1]=>630
[1,3,5,7,2,4,6]=>[3,3,1]=>280
[1,3,5,7,2,6,4]=>[3,2,1,1]=>420
[1,3,5,7,4,2,6]=>[6,1]=>840
[1,3,5,7,4,6,2]=>[5,1,1]=>504
[1,3,5,7,6,2,4]=>[4,2,1]=>630
[1,3,5,7,6,4,2]=>[6,1]=>840
[1,3,6,2,4,5,7]=>[5,1,1]=>504
[1,3,6,2,4,7,5]=>[6,1]=>840
[1,3,6,2,5,4,7]=>[4,1,1,1]=>210
[1,3,6,2,5,7,4]=>[5,1,1]=>504
[1,3,6,2,7,4,5]=>[4,2,1]=>630
[1,3,6,2,7,5,4]=>[6,1]=>840
[1,3,6,4,2,5,7]=>[4,1,1,1]=>210
[1,3,6,4,2,7,5]=>[5,1,1]=>504
[1,3,6,4,5,2,7]=>[3,1,1,1,1]=>70
[1,3,6,4,5,7,2]=>[4,1,1,1]=>210
[1,3,6,4,7,2,5]=>[3,2,1,1]=>420
[1,3,6,4,7,5,2]=>[5,1,1]=>504
[1,3,6,5,2,4,7]=>[5,1,1]=>504
[1,3,6,5,2,7,4]=>[6,1]=>840
[1,3,6,5,4,2,7]=>[3,2,1,1]=>420
[1,3,6,5,4,7,2]=>[4,2,1]=>630
[1,3,6,5,7,2,4]=>[3,3,1]=>280
[1,3,6,5,7,4,2]=>[6,1]=>840
[1,3,6,7,2,4,5]=>[6,1]=>840
[1,3,6,7,2,5,4]=>[4,2,1]=>630
[1,3,6,7,4,2,5]=>[3,3,1]=>280
[1,3,6,7,4,5,2]=>[6,1]=>840
[1,3,6,7,5,2,4]=>[3,2,1,1]=>420
[1,3,6,7,5,4,2]=>[5,1,1]=>504
[1,3,7,2,4,5,6]=>[6,1]=>840
[1,3,7,2,4,6,5]=>[5,1,1]=>504
[1,3,7,2,5,4,6]=>[5,1,1]=>504
[1,3,7,2,5,6,4]=>[4,1,1,1]=>210
[1,3,7,2,6,4,5]=>[6,1]=>840
[1,3,7,2,6,5,4]=>[4,2,1]=>630
[1,3,7,4,2,5,6]=>[5,1,1]=>504
[1,3,7,4,2,6,5]=>[4,1,1,1]=>210
[1,3,7,4,5,2,6]=>[4,1,1,1]=>210
[1,3,7,4,5,6,2]=>[3,1,1,1,1]=>70
[1,3,7,4,6,2,5]=>[5,1,1]=>504
[1,3,7,4,6,5,2]=>[3,2,1,1]=>420
[1,3,7,5,2,4,6]=>[6,1]=>840
[1,3,7,5,2,6,4]=>[5,1,1]=>504
[1,3,7,5,4,2,6]=>[4,2,1]=>630
[1,3,7,5,4,6,2]=>[3,2,1,1]=>420
[1,3,7,5,6,2,4]=>[6,1]=>840
[1,3,7,5,6,4,2]=>[3,3,1]=>280
[1,3,7,6,2,4,5]=>[4,2,1]=>630
[1,3,7,6,2,5,4]=>[6,1]=>840
[1,3,7,6,4,2,5]=>[6,1]=>840
[1,3,7,6,4,5,2]=>[3,3,1]=>280
[1,3,7,6,5,2,4]=>[5,1,1]=>504
[1,3,7,6,5,4,2]=>[3,2,1,1]=>420
[1,4,2,3,5,6,7]=>[3,1,1,1,1]=>70
[1,4,2,3,5,7,6]=>[3,2,1,1]=>420
[1,4,2,3,6,5,7]=>[3,2,1,1]=>420
[1,4,2,3,6,7,5]=>[3,3,1]=>280
[1,4,2,3,7,5,6]=>[3,3,1]=>280
[1,4,2,3,7,6,5]=>[3,2,1,1]=>420
[1,4,2,5,3,6,7]=>[4,1,1,1]=>210
[1,4,2,5,3,7,6]=>[4,2,1]=>630
[1,4,2,5,6,3,7]=>[5,1,1]=>504
[1,4,2,5,6,7,3]=>[6,1]=>840
[1,4,2,5,7,3,6]=>[6,1]=>840
[1,4,2,5,7,6,3]=>[5,1,1]=>504
[1,4,2,6,3,5,7]=>[5,1,1]=>504
[1,4,2,6,3,7,5]=>[6,1]=>840
[1,4,2,6,5,3,7]=>[4,1,1,1]=>210
[1,4,2,6,5,7,3]=>[5,1,1]=>504
[1,4,2,6,7,3,5]=>[4,2,1]=>630
[1,4,2,6,7,5,3]=>[6,1]=>840
[1,4,2,7,3,5,6]=>[6,1]=>840
[1,4,2,7,3,6,5]=>[5,1,1]=>504
[1,4,2,7,5,3,6]=>[5,1,1]=>504
[1,4,2,7,5,6,3]=>[4,1,1,1]=>210
[1,4,2,7,6,3,5]=>[6,1]=>840
[1,4,2,7,6,5,3]=>[4,2,1]=>630
[1,4,3,2,5,6,7]=>[2,1,1,1,1,1]=>21
[1,4,3,2,5,7,6]=>[2,2,1,1,1]=>105
[1,4,3,2,6,5,7]=>[2,2,1,1,1]=>105
[1,4,3,2,6,7,5]=>[3,2,1,1]=>420
[1,4,3,2,7,5,6]=>[3,2,1,1]=>420
[1,4,3,2,7,6,5]=>[2,2,1,1,1]=>105
[1,4,3,5,2,6,7]=>[3,1,1,1,1]=>70
[1,4,3,5,2,7,6]=>[3,2,1,1]=>420
[1,4,3,5,6,2,7]=>[4,1,1,1]=>210
[1,4,3,5,6,7,2]=>[5,1,1]=>504
[1,4,3,5,7,2,6]=>[5,1,1]=>504
[1,4,3,5,7,6,2]=>[4,1,1,1]=>210
[1,4,3,6,2,5,7]=>[4,1,1,1]=>210
[1,4,3,6,2,7,5]=>[5,1,1]=>504
[1,4,3,6,5,2,7]=>[3,1,1,1,1]=>70
[1,4,3,6,5,7,2]=>[4,1,1,1]=>210
[1,4,3,6,7,2,5]=>[3,2,1,1]=>420
[1,4,3,6,7,5,2]=>[5,1,1]=>504
[1,4,3,7,2,5,6]=>[5,1,1]=>504
[1,4,3,7,2,6,5]=>[4,1,1,1]=>210
[1,4,3,7,5,2,6]=>[4,1,1,1]=>210
[1,4,3,7,5,6,2]=>[3,1,1,1,1]=>70
[1,4,3,7,6,2,5]=>[5,1,1]=>504
[1,4,3,7,6,5,2]=>[3,2,1,1]=>420
[1,4,5,2,3,6,7]=>[2,2,1,1,1]=>105
[1,4,5,2,3,7,6]=>[2,2,2,1]=>105
[1,4,5,2,6,3,7]=>[3,2,1,1]=>420
[1,4,5,2,6,7,3]=>[4,2,1]=>630
[1,4,5,2,7,3,6]=>[4,2,1]=>630
[1,4,5,2,7,6,3]=>[3,2,1,1]=>420
[1,4,5,3,2,6,7]=>[4,1,1,1]=>210
[1,4,5,3,2,7,6]=>[4,2,1]=>630
[1,4,5,3,6,2,7]=>[5,1,1]=>504
[1,4,5,3,6,7,2]=>[6,1]=>840
[1,4,5,3,7,2,6]=>[6,1]=>840
[1,4,5,3,7,6,2]=>[5,1,1]=>504
[1,4,5,6,2,3,7]=>[5,1,1]=>504
[1,4,5,6,2,7,3]=>[6,1]=>840
[1,4,5,6,3,2,7]=>[3,2,1,1]=>420
[1,4,5,6,3,7,2]=>[4,2,1]=>630
[1,4,5,6,7,2,3]=>[3,3,1]=>280
[1,4,5,6,7,3,2]=>[6,1]=>840
[1,4,5,7,2,3,6]=>[6,1]=>840
[1,4,5,7,2,6,3]=>[5,1,1]=>504
[1,4,5,7,3,2,6]=>[4,2,1]=>630
[1,4,5,7,3,6,2]=>[3,2,1,1]=>420
[1,4,5,7,6,2,3]=>[6,1]=>840
[1,4,5,7,6,3,2]=>[3,3,1]=>280
[1,4,6,2,3,5,7]=>[3,2,1,1]=>420
[1,4,6,2,3,7,5]=>[4,2,1]=>630
[1,4,6,2,5,3,7]=>[2,2,1,1,1]=>105
[1,4,6,2,5,7,3]=>[3,2,1,1]=>420
[1,4,6,2,7,3,5]=>[2,2,2,1]=>105
[1,4,6,2,7,5,3]=>[4,2,1]=>630
[1,4,6,3,2,5,7]=>[5,1,1]=>504
[1,4,6,3,2,7,5]=>[6,1]=>840
[1,4,6,3,5,2,7]=>[4,1,1,1]=>210
[1,4,6,3,5,7,2]=>[5,1,1]=>504
[1,4,6,3,7,2,5]=>[4,2,1]=>630
[1,4,6,3,7,5,2]=>[6,1]=>840
[1,4,6,5,2,3,7]=>[3,2,1,1]=>420
[1,4,6,5,2,7,3]=>[3,3,1]=>280
[1,4,6,5,3,2,7]=>[5,1,1]=>504
[1,4,6,5,3,7,2]=>[6,1]=>840
[1,4,6,5,7,2,3]=>[6,1]=>840
[1,4,6,5,7,3,2]=>[4,2,1]=>630
[1,4,6,7,2,3,5]=>[4,2,1]=>630
[1,4,6,7,2,5,3]=>[6,1]=>840
[1,4,6,7,3,2,5]=>[6,1]=>840
[1,4,6,7,3,5,2]=>[3,3,1]=>280
[1,4,6,7,5,2,3]=>[5,1,1]=>504
[1,4,6,7,5,3,2]=>[3,2,1,1]=>420
[1,4,7,2,3,5,6]=>[4,2,1]=>630
[1,4,7,2,3,6,5]=>[3,2,1,1]=>420
[1,4,7,2,5,3,6]=>[3,2,1,1]=>420
[1,4,7,2,5,6,3]=>[2,2,1,1,1]=>105
[1,4,7,2,6,3,5]=>[4,2,1]=>630
[1,4,7,2,6,5,3]=>[2,2,2,1]=>105
[1,4,7,3,2,5,6]=>[6,1]=>840
[1,4,7,3,2,6,5]=>[5,1,1]=>504
[1,4,7,3,5,2,6]=>[5,1,1]=>504
[1,4,7,3,5,6,2]=>[4,1,1,1]=>210
[1,4,7,3,6,2,5]=>[6,1]=>840
[1,4,7,3,6,5,2]=>[4,2,1]=>630
[1,4,7,5,2,3,6]=>[3,3,1]=>280
[1,4,7,5,2,6,3]=>[3,2,1,1]=>420
[1,4,7,5,3,2,6]=>[6,1]=>840
[1,4,7,5,3,6,2]=>[5,1,1]=>504
[1,4,7,5,6,2,3]=>[4,2,1]=>630
[1,4,7,5,6,3,2]=>[6,1]=>840
[1,4,7,6,2,3,5]=>[6,1]=>840
[1,4,7,6,2,5,3]=>[4,2,1]=>630
[1,4,7,6,3,2,5]=>[3,3,1]=>280
[1,4,7,6,3,5,2]=>[6,1]=>840
[1,4,7,6,5,2,3]=>[3,2,1,1]=>420
[1,4,7,6,5,3,2]=>[5,1,1]=>504
[1,5,2,3,4,6,7]=>[4,1,1,1]=>210
[1,5,2,3,4,7,6]=>[4,2,1]=>630
[1,5,2,3,6,4,7]=>[5,1,1]=>504
[1,5,2,3,6,7,4]=>[6,1]=>840
[1,5,2,3,7,4,6]=>[6,1]=>840
[1,5,2,3,7,6,4]=>[5,1,1]=>504
[1,5,2,4,3,6,7]=>[3,1,1,1,1]=>70
[1,5,2,4,3,7,6]=>[3,2,1,1]=>420
[1,5,2,4,6,3,7]=>[4,1,1,1]=>210
[1,5,2,4,6,7,3]=>[5,1,1]=>504
[1,5,2,4,7,3,6]=>[5,1,1]=>504
[1,5,2,4,7,6,3]=>[4,1,1,1]=>210
[1,5,2,6,3,4,7]=>[3,2,1,1]=>420
[1,5,2,6,3,7,4]=>[3,3,1]=>280
[1,5,2,6,4,3,7]=>[5,1,1]=>504
[1,5,2,6,4,7,3]=>[6,1]=>840
[1,5,2,6,7,3,4]=>[6,1]=>840
[1,5,2,6,7,4,3]=>[4,2,1]=>630
[1,5,2,7,3,4,6]=>[3,3,1]=>280
[1,5,2,7,3,6,4]=>[3,2,1,1]=>420
[1,5,2,7,4,3,6]=>[6,1]=>840
[1,5,2,7,4,6,3]=>[5,1,1]=>504
[1,5,2,7,6,3,4]=>[4,2,1]=>630
[1,5,2,7,6,4,3]=>[6,1]=>840
[1,5,3,2,4,6,7]=>[3,1,1,1,1]=>70
[1,5,3,2,4,7,6]=>[3,2,1,1]=>420
[1,5,3,2,6,4,7]=>[4,1,1,1]=>210
[1,5,3,2,6,7,4]=>[5,1,1]=>504
[1,5,3,2,7,4,6]=>[5,1,1]=>504
[1,5,3,2,7,6,4]=>[4,1,1,1]=>210
[1,5,3,4,2,6,7]=>[2,1,1,1,1,1]=>21
[1,5,3,4,2,7,6]=>[2,2,1,1,1]=>105
[1,5,3,4,6,2,7]=>[3,1,1,1,1]=>70
[1,5,3,4,6,7,2]=>[4,1,1,1]=>210
[1,5,3,4,7,2,6]=>[4,1,1,1]=>210
[1,5,3,4,7,6,2]=>[3,1,1,1,1]=>70
[1,5,3,6,2,4,7]=>[2,2,1,1,1]=>105
[1,5,3,6,2,7,4]=>[3,2,1,1]=>420
[1,5,3,6,4,2,7]=>[4,1,1,1]=>210
[1,5,3,6,4,7,2]=>[5,1,1]=>504
[1,5,3,6,7,2,4]=>[5,1,1]=>504
[1,5,3,6,7,4,2]=>[3,2,1,1]=>420
[1,5,3,7,2,4,6]=>[3,2,1,1]=>420
[1,5,3,7,2,6,4]=>[2,2,1,1,1]=>105
[1,5,3,7,4,2,6]=>[5,1,1]=>504
[1,5,3,7,4,6,2]=>[4,1,1,1]=>210
[1,5,3,7,6,2,4]=>[3,2,1,1]=>420
[1,5,3,7,6,4,2]=>[5,1,1]=>504
[1,5,4,2,3,6,7]=>[4,1,1,1]=>210
[1,5,4,2,3,7,6]=>[4,2,1]=>630
[1,5,4,2,6,3,7]=>[5,1,1]=>504
[1,5,4,2,6,7,3]=>[6,1]=>840
[1,5,4,2,7,3,6]=>[6,1]=>840
[1,5,4,2,7,6,3]=>[5,1,1]=>504
[1,5,4,3,2,6,7]=>[2,2,1,1,1]=>105
[1,5,4,3,2,7,6]=>[2,2,2,1]=>105
[1,5,4,3,6,2,7]=>[3,2,1,1]=>420
[1,5,4,3,6,7,2]=>[4,2,1]=>630
[1,5,4,3,7,2,6]=>[4,2,1]=>630
[1,5,4,3,7,6,2]=>[3,2,1,1]=>420
[1,5,4,6,2,3,7]=>[3,2,1,1]=>420
[1,5,4,6,2,7,3]=>[4,2,1]=>630
[1,5,4,6,3,2,7]=>[5,1,1]=>504
[1,5,4,6,3,7,2]=>[6,1]=>840
[1,5,4,6,7,2,3]=>[6,1]=>840
[1,5,4,6,7,3,2]=>[3,3,1]=>280
[1,5,4,7,2,3,6]=>[4,2,1]=>630
[1,5,4,7,2,6,3]=>[3,2,1,1]=>420
[1,5,4,7,3,2,6]=>[6,1]=>840
[1,5,4,7,3,6,2]=>[5,1,1]=>504
[1,5,4,7,6,2,3]=>[3,3,1]=>280
[1,5,4,7,6,3,2]=>[6,1]=>840
[1,5,6,2,3,4,7]=>[5,1,1]=>504
[1,5,6,2,3,7,4]=>[6,1]=>840
[1,5,6,2,4,3,7]=>[3,2,1,1]=>420
[1,5,6,2,4,7,3]=>[3,3,1]=>280
[1,5,6,2,7,3,4]=>[4,2,1]=>630
[1,5,6,2,7,4,3]=>[6,1]=>840
[1,5,6,3,2,4,7]=>[3,2,1,1]=>420
[1,5,6,3,2,7,4]=>[4,2,1]=>630
[1,5,6,3,4,2,7]=>[5,1,1]=>504
[1,5,6,3,4,7,2]=>[6,1]=>840
[1,5,6,3,7,2,4]=>[6,1]=>840
[1,5,6,3,7,4,2]=>[3,3,1]=>280
[1,5,6,4,2,3,7]=>[2,2,1,1,1]=>105
[1,5,6,4,2,7,3]=>[3,2,1,1]=>420
[1,5,6,4,3,2,7]=>[4,1,1,1]=>210
[1,5,6,4,3,7,2]=>[5,1,1]=>504
[1,5,6,4,7,2,3]=>[5,1,1]=>504
[1,5,6,4,7,3,2]=>[3,2,1,1]=>420
[1,5,6,7,2,3,4]=>[2,2,2,1]=>105
[1,5,6,7,2,4,3]=>[4,2,1]=>630
[1,5,6,7,3,2,4]=>[4,2,1]=>630
[1,5,6,7,3,4,2]=>[6,1]=>840
[1,5,6,7,4,2,3]=>[6,1]=>840
[1,5,6,7,4,3,2]=>[4,2,1]=>630
[1,5,7,2,3,4,6]=>[6,1]=>840
[1,5,7,2,3,6,4]=>[5,1,1]=>504
[1,5,7,2,4,3,6]=>[3,3,1]=>280
[1,5,7,2,4,6,3]=>[3,2,1,1]=>420
[1,5,7,2,6,3,4]=>[6,1]=>840
[1,5,7,2,6,4,3]=>[4,2,1]=>630
[1,5,7,3,2,4,6]=>[4,2,1]=>630
[1,5,7,3,2,6,4]=>[3,2,1,1]=>420
[1,5,7,3,4,2,6]=>[6,1]=>840
[1,5,7,3,4,6,2]=>[5,1,1]=>504
[1,5,7,3,6,2,4]=>[3,3,1]=>280
[1,5,7,3,6,4,2]=>[6,1]=>840
[1,5,7,4,2,3,6]=>[3,2,1,1]=>420
[1,5,7,4,2,6,3]=>[2,2,1,1,1]=>105
[1,5,7,4,3,2,6]=>[5,1,1]=>504
[1,5,7,4,3,6,2]=>[4,1,1,1]=>210
[1,5,7,4,6,2,3]=>[3,2,1,1]=>420
[1,5,7,4,6,3,2]=>[5,1,1]=>504
[1,5,7,6,2,3,4]=>[4,2,1]=>630
[1,5,7,6,2,4,3]=>[2,2,2,1]=>105
[1,5,7,6,3,2,4]=>[6,1]=>840
[1,5,7,6,3,4,2]=>[4,2,1]=>630
[1,5,7,6,4,2,3]=>[4,2,1]=>630
[1,5,7,6,4,3,2]=>[6,1]=>840
[1,6,2,3,4,5,7]=>[5,1,1]=>504
[1,6,2,3,4,7,5]=>[6,1]=>840
[1,6,2,3,5,4,7]=>[4,1,1,1]=>210
[1,6,2,3,5,7,4]=>[5,1,1]=>504
[1,6,2,3,7,4,5]=>[4,2,1]=>630
[1,6,2,3,7,5,4]=>[6,1]=>840
[1,6,2,4,3,5,7]=>[4,1,1,1]=>210
[1,6,2,4,3,7,5]=>[5,1,1]=>504
[1,6,2,4,5,3,7]=>[3,1,1,1,1]=>70
[1,6,2,4,5,7,3]=>[4,1,1,1]=>210
[1,6,2,4,7,3,5]=>[3,2,1,1]=>420
[1,6,2,4,7,5,3]=>[5,1,1]=>504
[1,6,2,5,3,4,7]=>[5,1,1]=>504
[1,6,2,5,3,7,4]=>[6,1]=>840
[1,6,2,5,4,3,7]=>[3,2,1,1]=>420
[1,6,2,5,4,7,3]=>[4,2,1]=>630
[1,6,2,5,7,3,4]=>[3,3,1]=>280
[1,6,2,5,7,4,3]=>[6,1]=>840
[1,6,2,7,3,4,5]=>[6,1]=>840
[1,6,2,7,3,5,4]=>[4,2,1]=>630
[1,6,2,7,4,3,5]=>[3,3,1]=>280
[1,6,2,7,4,5,3]=>[6,1]=>840
[1,6,2,7,5,3,4]=>[3,2,1,1]=>420
[1,6,2,7,5,4,3]=>[5,1,1]=>504
[1,6,3,2,4,5,7]=>[4,1,1,1]=>210
[1,6,3,2,4,7,5]=>[5,1,1]=>504
[1,6,3,2,5,4,7]=>[3,1,1,1,1]=>70
[1,6,3,2,5,7,4]=>[4,1,1,1]=>210
[1,6,3,2,7,4,5]=>[3,2,1,1]=>420
[1,6,3,2,7,5,4]=>[5,1,1]=>504
[1,6,3,4,2,5,7]=>[3,1,1,1,1]=>70
[1,6,3,4,2,7,5]=>[4,1,1,1]=>210
[1,6,3,4,5,2,7]=>[2,1,1,1,1,1]=>21
[1,6,3,4,5,7,2]=>[3,1,1,1,1]=>70
[1,6,3,4,7,2,5]=>[2,2,1,1,1]=>105
[1,6,3,4,7,5,2]=>[4,1,1,1]=>210
[1,6,3,5,2,4,7]=>[4,1,1,1]=>210
[1,6,3,5,2,7,4]=>[5,1,1]=>504
[1,6,3,5,4,2,7]=>[2,2,1,1,1]=>105
[1,6,3,5,4,7,2]=>[3,2,1,1]=>420
[1,6,3,5,7,2,4]=>[3,2,1,1]=>420
[1,6,3,5,7,4,2]=>[5,1,1]=>504
[1,6,3,7,2,4,5]=>[5,1,1]=>504
[1,6,3,7,2,5,4]=>[3,2,1,1]=>420
[1,6,3,7,4,2,5]=>[3,2,1,1]=>420
[1,6,3,7,4,5,2]=>[5,1,1]=>504
[1,6,3,7,5,2,4]=>[2,2,1,1,1]=>105
[1,6,3,7,5,4,2]=>[4,1,1,1]=>210
[1,6,4,2,3,5,7]=>[5,1,1]=>504
[1,6,4,2,3,7,5]=>[6,1]=>840
[1,6,4,2,5,3,7]=>[4,1,1,1]=>210
[1,6,4,2,5,7,3]=>[5,1,1]=>504
[1,6,4,2,7,3,5]=>[4,2,1]=>630
[1,6,4,2,7,5,3]=>[6,1]=>840
[1,6,4,3,2,5,7]=>[3,2,1,1]=>420
[1,6,4,3,2,7,5]=>[4,2,1]=>630
[1,6,4,3,5,2,7]=>[2,2,1,1,1]=>105
[1,6,4,3,5,7,2]=>[3,2,1,1]=>420
[1,6,4,3,7,2,5]=>[2,2,2,1]=>105
[1,6,4,3,7,5,2]=>[4,2,1]=>630
[1,6,4,5,2,3,7]=>[5,1,1]=>504
[1,6,4,5,2,7,3]=>[6,1]=>840
[1,6,4,5,3,2,7]=>[3,2,1,1]=>420
[1,6,4,5,3,7,2]=>[3,3,1]=>280
[1,6,4,5,7,2,3]=>[4,2,1]=>630
[1,6,4,5,7,3,2]=>[6,1]=>840
[1,6,4,7,2,3,5]=>[6,1]=>840
[1,6,4,7,2,5,3]=>[3,3,1]=>280
[1,6,4,7,3,2,5]=>[4,2,1]=>630
[1,6,4,7,3,5,2]=>[6,1]=>840
[1,6,4,7,5,2,3]=>[3,2,1,1]=>420
[1,6,4,7,5,3,2]=>[5,1,1]=>504
[1,6,5,2,3,4,7]=>[3,2,1,1]=>420
[1,6,5,2,3,7,4]=>[4,2,1]=>630
[1,6,5,2,4,3,7]=>[5,1,1]=>504
[1,6,5,2,4,7,3]=>[6,1]=>840
[1,6,5,2,7,3,4]=>[6,1]=>840
[1,6,5,2,7,4,3]=>[3,3,1]=>280
[1,6,5,3,2,4,7]=>[5,1,1]=>504
[1,6,5,3,2,7,4]=>[6,1]=>840
[1,6,5,3,4,2,7]=>[3,2,1,1]=>420
[1,6,5,3,4,7,2]=>[3,3,1]=>280
[1,6,5,3,7,2,4]=>[4,2,1]=>630
[1,6,5,3,7,4,2]=>[6,1]=>840
[1,6,5,4,2,3,7]=>[4,1,1,1]=>210
[1,6,5,4,2,7,3]=>[5,1,1]=>504
[1,6,5,4,3,2,7]=>[2,2,1,1,1]=>105
[1,6,5,4,3,7,2]=>[3,2,1,1]=>420
[1,6,5,4,7,2,3]=>[3,2,1,1]=>420
[1,6,5,4,7,3,2]=>[5,1,1]=>504
[1,6,5,7,2,3,4]=>[4,2,1]=>630
[1,6,5,7,2,4,3]=>[6,1]=>840
[1,6,5,7,3,2,4]=>[2,2,2,1]=>105
[1,6,5,7,3,4,2]=>[4,2,1]=>630
[1,6,5,7,4,2,3]=>[4,2,1]=>630
[1,6,5,7,4,3,2]=>[6,1]=>840
[1,6,7,2,3,4,5]=>[3,3,1]=>280
[1,6,7,2,3,5,4]=>[6,1]=>840
[1,6,7,2,4,3,5]=>[6,1]=>840
[1,6,7,2,4,5,3]=>[4,2,1]=>630
[1,6,7,2,5,3,4]=>[5,1,1]=>504
[1,6,7,2,5,4,3]=>[3,2,1,1]=>420
[1,6,7,3,2,4,5]=>[6,1]=>840
[1,6,7,3,2,5,4]=>[3,3,1]=>280
[1,6,7,3,4,2,5]=>[4,2,1]=>630
[1,6,7,3,4,5,2]=>[6,1]=>840
[1,6,7,3,5,2,4]=>[3,2,1,1]=>420
[1,6,7,3,5,4,2]=>[5,1,1]=>504
[1,6,7,4,2,3,5]=>[5,1,1]=>504
[1,6,7,4,2,5,3]=>[3,2,1,1]=>420
[1,6,7,4,3,2,5]=>[3,2,1,1]=>420
[1,6,7,4,3,5,2]=>[5,1,1]=>504
[1,6,7,4,5,2,3]=>[2,2,1,1,1]=>105
[1,6,7,4,5,3,2]=>[4,1,1,1]=>210
[1,6,7,5,2,3,4]=>[6,1]=>840
[1,6,7,5,2,4,3]=>[4,2,1]=>630
[1,6,7,5,3,2,4]=>[4,2,1]=>630
[1,6,7,5,3,4,2]=>[6,1]=>840
[1,6,7,5,4,2,3]=>[2,2,2,1]=>105
[1,6,7,5,4,3,2]=>[4,2,1]=>630
[1,7,2,3,4,5,6]=>[6,1]=>840
[1,7,2,3,4,6,5]=>[5,1,1]=>504
[1,7,2,3,5,4,6]=>[5,1,1]=>504
[1,7,2,3,5,6,4]=>[4,1,1,1]=>210
[1,7,2,3,6,4,5]=>[6,1]=>840
[1,7,2,3,6,5,4]=>[4,2,1]=>630
[1,7,2,4,3,5,6]=>[5,1,1]=>504
[1,7,2,4,3,6,5]=>[4,1,1,1]=>210
[1,7,2,4,5,3,6]=>[4,1,1,1]=>210
[1,7,2,4,5,6,3]=>[3,1,1,1,1]=>70
[1,7,2,4,6,3,5]=>[5,1,1]=>504
[1,7,2,4,6,5,3]=>[3,2,1,1]=>420
[1,7,2,5,3,4,6]=>[6,1]=>840
[1,7,2,5,3,6,4]=>[5,1,1]=>504
[1,7,2,5,4,3,6]=>[4,2,1]=>630
[1,7,2,5,4,6,3]=>[3,2,1,1]=>420
[1,7,2,5,6,3,4]=>[6,1]=>840
[1,7,2,5,6,4,3]=>[3,3,1]=>280
[1,7,2,6,3,4,5]=>[4,2,1]=>630
[1,7,2,6,3,5,4]=>[6,1]=>840
[1,7,2,6,4,3,5]=>[6,1]=>840
[1,7,2,6,4,5,3]=>[3,3,1]=>280
[1,7,2,6,5,3,4]=>[5,1,1]=>504
[1,7,2,6,5,4,3]=>[3,2,1,1]=>420
[1,7,3,2,4,5,6]=>[5,1,1]=>504
[1,7,3,2,4,6,5]=>[4,1,1,1]=>210
[1,7,3,2,5,4,6]=>[4,1,1,1]=>210
[1,7,3,2,5,6,4]=>[3,1,1,1,1]=>70
[1,7,3,2,6,4,5]=>[5,1,1]=>504
[1,7,3,2,6,5,4]=>[3,2,1,1]=>420
[1,7,3,4,2,5,6]=>[4,1,1,1]=>210
[1,7,3,4,2,6,5]=>[3,1,1,1,1]=>70
[1,7,3,4,5,2,6]=>[3,1,1,1,1]=>70
[1,7,3,4,5,6,2]=>[2,1,1,1,1,1]=>21
[1,7,3,4,6,2,5]=>[4,1,1,1]=>210
[1,7,3,4,6,5,2]=>[2,2,1,1,1]=>105
[1,7,3,5,2,4,6]=>[5,1,1]=>504
[1,7,3,5,2,6,4]=>[4,1,1,1]=>210
[1,7,3,5,4,2,6]=>[3,2,1,1]=>420
[1,7,3,5,4,6,2]=>[2,2,1,1,1]=>105
[1,7,3,5,6,2,4]=>[5,1,1]=>504
[1,7,3,5,6,4,2]=>[3,2,1,1]=>420
[1,7,3,6,2,4,5]=>[3,2,1,1]=>420
[1,7,3,6,2,5,4]=>[5,1,1]=>504
[1,7,3,6,4,2,5]=>[5,1,1]=>504
[1,7,3,6,4,5,2]=>[3,2,1,1]=>420
[1,7,3,6,5,2,4]=>[4,1,1,1]=>210
[1,7,3,6,5,4,2]=>[2,2,1,1,1]=>105
[1,7,4,2,3,5,6]=>[6,1]=>840
[1,7,4,2,3,6,5]=>[5,1,1]=>504
[1,7,4,2,5,3,6]=>[5,1,1]=>504
[1,7,4,2,5,6,3]=>[4,1,1,1]=>210
[1,7,4,2,6,3,5]=>[6,1]=>840
[1,7,4,2,6,5,3]=>[4,2,1]=>630
[1,7,4,3,2,5,6]=>[4,2,1]=>630
[1,7,4,3,2,6,5]=>[3,2,1,1]=>420
[1,7,4,3,5,2,6]=>[3,2,1,1]=>420
[1,7,4,3,5,6,2]=>[2,2,1,1,1]=>105
[1,7,4,3,6,2,5]=>[4,2,1]=>630
[1,7,4,3,6,5,2]=>[2,2,2,1]=>105
[1,7,4,5,2,3,6]=>[6,1]=>840
[1,7,4,5,2,6,3]=>[5,1,1]=>504
[1,7,4,5,3,2,6]=>[3,3,1]=>280
[1,7,4,5,3,6,2]=>[3,2,1,1]=>420
[1,7,4,5,6,2,3]=>[6,1]=>840
[1,7,4,5,6,3,2]=>[4,2,1]=>630
[1,7,4,6,2,3,5]=>[3,3,1]=>280
[1,7,4,6,2,5,3]=>[6,1]=>840
[1,7,4,6,3,2,5]=>[6,1]=>840
[1,7,4,6,3,5,2]=>[4,2,1]=>630
[1,7,4,6,5,2,3]=>[5,1,1]=>504
[1,7,4,6,5,3,2]=>[3,2,1,1]=>420
[1,7,5,2,3,4,6]=>[4,2,1]=>630
[1,7,5,2,3,6,4]=>[3,2,1,1]=>420
[1,7,5,2,4,3,6]=>[6,1]=>840
[1,7,5,2,4,6,3]=>[5,1,1]=>504
[1,7,5,2,6,3,4]=>[3,3,1]=>280
[1,7,5,2,6,4,3]=>[6,1]=>840
[1,7,5,3,2,4,6]=>[6,1]=>840
[1,7,5,3,2,6,4]=>[5,1,1]=>504
[1,7,5,3,4,2,6]=>[3,3,1]=>280
[1,7,5,3,4,6,2]=>[3,2,1,1]=>420
[1,7,5,3,6,2,4]=>[6,1]=>840
[1,7,5,3,6,4,2]=>[4,2,1]=>630
[1,7,5,4,2,3,6]=>[5,1,1]=>504
[1,7,5,4,2,6,3]=>[4,1,1,1]=>210
[1,7,5,4,3,2,6]=>[3,2,1,1]=>420
[1,7,5,4,3,6,2]=>[2,2,1,1,1]=>105
[1,7,5,4,6,2,3]=>[5,1,1]=>504
[1,7,5,4,6,3,2]=>[3,2,1,1]=>420
[1,7,5,6,2,3,4]=>[6,1]=>840
[1,7,5,6,2,4,3]=>[4,2,1]=>630
[1,7,5,6,3,2,4]=>[4,2,1]=>630
[1,7,5,6,3,4,2]=>[2,2,2,1]=>105
[1,7,5,6,4,2,3]=>[6,1]=>840
[1,7,5,6,4,3,2]=>[4,2,1]=>630
[1,7,6,2,3,4,5]=>[6,1]=>840
[1,7,6,2,3,5,4]=>[3,3,1]=>280
[1,7,6,2,4,3,5]=>[4,2,1]=>630
[1,7,6,2,4,5,3]=>[6,1]=>840
[1,7,6,2,5,3,4]=>[3,2,1,1]=>420
[1,7,6,2,5,4,3]=>[5,1,1]=>504
[1,7,6,3,2,4,5]=>[3,3,1]=>280
[1,7,6,3,2,5,4]=>[6,1]=>840
[1,7,6,3,4,2,5]=>[6,1]=>840
[1,7,6,3,4,5,2]=>[4,2,1]=>630
[1,7,6,3,5,2,4]=>[5,1,1]=>504
[1,7,6,3,5,4,2]=>[3,2,1,1]=>420
[1,7,6,4,2,3,5]=>[3,2,1,1]=>420
[1,7,6,4,2,5,3]=>[5,1,1]=>504
[1,7,6,4,3,2,5]=>[5,1,1]=>504
[1,7,6,4,3,5,2]=>[3,2,1,1]=>420
[1,7,6,4,5,2,3]=>[4,1,1,1]=>210
[1,7,6,4,5,3,2]=>[2,2,1,1,1]=>105
[1,7,6,5,2,3,4]=>[4,2,1]=>630
[1,7,6,5,2,4,3]=>[6,1]=>840
[1,7,6,5,3,2,4]=>[6,1]=>840
[1,7,6,5,3,4,2]=>[4,2,1]=>630
[1,7,6,5,4,2,3]=>[4,2,1]=>630
[1,7,6,5,4,3,2]=>[2,2,2,1]=>105
[2,1,3,4,5,6,7]=>[2,1,1,1,1,1]=>21
[2,1,3,4,5,7,6]=>[2,2,1,1,1]=>105
[2,1,3,4,6,5,7]=>[2,2,1,1,1]=>105
[2,1,3,4,6,7,5]=>[3,2,1,1]=>420
[2,1,3,4,7,5,6]=>[3,2,1,1]=>420
[2,1,3,4,7,6,5]=>[2,2,1,1,1]=>105
[2,1,3,5,4,6,7]=>[2,2,1,1,1]=>105
[2,1,3,5,4,7,6]=>[2,2,2,1]=>105
[2,1,3,5,6,4,7]=>[3,2,1,1]=>420
[2,1,3,5,6,7,4]=>[4,2,1]=>630
[2,1,3,5,7,4,6]=>[4,2,1]=>630
[2,1,3,5,7,6,4]=>[3,2,1,1]=>420
[2,1,3,6,4,5,7]=>[3,2,1,1]=>420
[2,1,3,6,4,7,5]=>[4,2,1]=>630
[2,1,3,6,5,4,7]=>[2,2,1,1,1]=>105
[2,1,3,6,5,7,4]=>[3,2,1,1]=>420
[2,1,3,6,7,4,5]=>[2,2,2,1]=>105
[2,1,3,6,7,5,4]=>[4,2,1]=>630
[2,1,3,7,4,5,6]=>[4,2,1]=>630
[2,1,3,7,4,6,5]=>[3,2,1,1]=>420
[2,1,3,7,5,4,6]=>[3,2,1,1]=>420
[2,1,3,7,5,6,4]=>[2,2,1,1,1]=>105
[2,1,3,7,6,4,5]=>[4,2,1]=>630
[2,1,3,7,6,5,4]=>[2,2,2,1]=>105
[2,1,4,3,5,6,7]=>[2,2,1,1,1]=>105
[2,1,4,3,5,7,6]=>[2,2,2,1]=>105
[2,1,4,3,6,5,7]=>[2,2,2,1]=>105
[2,1,4,3,6,7,5]=>[3,2,2]=>210
[2,1,4,3,7,5,6]=>[3,2,2]=>210
[2,1,4,3,7,6,5]=>[2,2,2,1]=>105
[2,1,4,5,3,6,7]=>[3,2,1,1]=>420
[2,1,4,5,3,7,6]=>[3,2,2]=>210
[2,1,4,5,6,3,7]=>[4,2,1]=>630
[2,1,4,5,6,7,3]=>[5,2]=>504
[2,1,4,5,7,3,6]=>[5,2]=>504
[2,1,4,5,7,6,3]=>[4,2,1]=>630
[2,1,4,6,3,5,7]=>[4,2,1]=>630
[2,1,4,6,3,7,5]=>[5,2]=>504
[2,1,4,6,5,3,7]=>[3,2,1,1]=>420
[2,1,4,6,5,7,3]=>[4,2,1]=>630
[2,1,4,6,7,3,5]=>[3,2,2]=>210
[2,1,4,6,7,5,3]=>[5,2]=>504
[2,1,4,7,3,5,6]=>[5,2]=>504
[2,1,4,7,3,6,5]=>[4,2,1]=>630
[2,1,4,7,5,3,6]=>[4,2,1]=>630
[2,1,4,7,5,6,3]=>[3,2,1,1]=>420
[2,1,4,7,6,3,5]=>[5,2]=>504
[2,1,4,7,6,5,3]=>[3,2,2]=>210
[2,1,5,3,4,6,7]=>[3,2,1,1]=>420
[2,1,5,3,4,7,6]=>[3,2,2]=>210
[2,1,5,3,6,4,7]=>[4,2,1]=>630
[2,1,5,3,6,7,4]=>[5,2]=>504
[2,1,5,3,7,4,6]=>[5,2]=>504
[2,1,5,3,7,6,4]=>[4,2,1]=>630
[2,1,5,4,3,6,7]=>[2,2,1,1,1]=>105
[2,1,5,4,3,7,6]=>[2,2,2,1]=>105
[2,1,5,4,6,3,7]=>[3,2,1,1]=>420
[2,1,5,4,6,7,3]=>[4,2,1]=>630
[2,1,5,4,7,3,6]=>[4,2,1]=>630
[2,1,5,4,7,6,3]=>[3,2,1,1]=>420
[2,1,5,6,3,4,7]=>[2,2,2,1]=>105
[2,1,5,6,3,7,4]=>[3,2,2]=>210
[2,1,5,6,4,3,7]=>[4,2,1]=>630
[2,1,5,6,4,7,3]=>[5,2]=>504
[2,1,5,6,7,3,4]=>[5,2]=>504
[2,1,5,6,7,4,3]=>[3,2,2]=>210
[2,1,5,7,3,4,6]=>[3,2,2]=>210
[2,1,5,7,3,6,4]=>[2,2,2,1]=>105
[2,1,5,7,4,3,6]=>[5,2]=>504
[2,1,5,7,4,6,3]=>[4,2,1]=>630
[2,1,5,7,6,3,4]=>[3,2,2]=>210
[2,1,5,7,6,4,3]=>[5,2]=>504
[2,1,6,3,4,5,7]=>[4,2,1]=>630
[2,1,6,3,4,7,5]=>[5,2]=>504
[2,1,6,3,5,4,7]=>[3,2,1,1]=>420
[2,1,6,3,5,7,4]=>[4,2,1]=>630
[2,1,6,3,7,4,5]=>[3,2,2]=>210
[2,1,6,3,7,5,4]=>[5,2]=>504
[2,1,6,4,3,5,7]=>[3,2,1,1]=>420
[2,1,6,4,3,7,5]=>[4,2,1]=>630
[2,1,6,4,5,3,7]=>[2,2,1,1,1]=>105
[2,1,6,4,5,7,3]=>[3,2,1,1]=>420
[2,1,6,4,7,3,5]=>[2,2,2,1]=>105
[2,1,6,4,7,5,3]=>[4,2,1]=>630
[2,1,6,5,3,4,7]=>[4,2,1]=>630
[2,1,6,5,3,7,4]=>[5,2]=>504
[2,1,6,5,4,3,7]=>[2,2,2,1]=>105
[2,1,6,5,4,7,3]=>[3,2,2]=>210
[2,1,6,5,7,3,4]=>[3,2,2]=>210
[2,1,6,5,7,4,3]=>[5,2]=>504
[2,1,6,7,3,4,5]=>[5,2]=>504
[2,1,6,7,3,5,4]=>[3,2,2]=>210
[2,1,6,7,4,3,5]=>[3,2,2]=>210
[2,1,6,7,4,5,3]=>[5,2]=>504
[2,1,6,7,5,3,4]=>[2,2,2,1]=>105
[2,1,6,7,5,4,3]=>[4,2,1]=>630
[2,1,7,3,4,5,6]=>[5,2]=>504
[2,1,7,3,4,6,5]=>[4,2,1]=>630
[2,1,7,3,5,4,6]=>[4,2,1]=>630
[2,1,7,3,5,6,4]=>[3,2,1,1]=>420
[2,1,7,3,6,4,5]=>[5,2]=>504
[2,1,7,3,6,5,4]=>[3,2,2]=>210
[2,1,7,4,3,5,6]=>[4,2,1]=>630
[2,1,7,4,3,6,5]=>[3,2,1,1]=>420
[2,1,7,4,5,3,6]=>[3,2,1,1]=>420
[2,1,7,4,5,6,3]=>[2,2,1,1,1]=>105
[2,1,7,4,6,3,5]=>[4,2,1]=>630
[2,1,7,4,6,5,3]=>[2,2,2,1]=>105
[2,1,7,5,3,4,6]=>[5,2]=>504
[2,1,7,5,3,6,4]=>[4,2,1]=>630
[2,1,7,5,4,3,6]=>[3,2,2]=>210
[2,1,7,5,4,6,3]=>[2,2,2,1]=>105
[2,1,7,5,6,3,4]=>[5,2]=>504
[2,1,7,5,6,4,3]=>[3,2,2]=>210
[2,1,7,6,3,4,5]=>[3,2,2]=>210
[2,1,7,6,3,5,4]=>[5,2]=>504
[2,1,7,6,4,3,5]=>[5,2]=>504
[2,1,7,6,4,5,3]=>[3,2,2]=>210
[2,1,7,6,5,3,4]=>[4,2,1]=>630
[2,1,7,6,5,4,3]=>[2,2,2,1]=>105
[2,3,1,4,5,6,7]=>[3,1,1,1,1]=>70
[2,3,1,4,5,7,6]=>[3,2,1,1]=>420
[2,3,1,4,6,5,7]=>[3,2,1,1]=>420
[2,3,1,4,6,7,5]=>[3,3,1]=>280
[2,3,1,4,7,5,6]=>[3,3,1]=>280
[2,3,1,4,7,6,5]=>[3,2,1,1]=>420
[2,3,1,5,4,6,7]=>[3,2,1,1]=>420
[2,3,1,5,4,7,6]=>[3,2,2]=>210
[2,3,1,5,6,4,7]=>[3,3,1]=>280
[2,3,1,5,6,7,4]=>[4,3]=>420
[2,3,1,5,7,4,6]=>[4,3]=>420
[2,3,1,5,7,6,4]=>[3,3,1]=>280
[2,3,1,6,4,5,7]=>[3,3,1]=>280
[2,3,1,6,4,7,5]=>[4,3]=>420
[2,3,1,6,5,4,7]=>[3,2,1,1]=>420
[2,3,1,6,5,7,4]=>[3,3,1]=>280
[2,3,1,6,7,4,5]=>[3,2,2]=>210
[2,3,1,6,7,5,4]=>[4,3]=>420
[2,3,1,7,4,5,6]=>[4,3]=>420
[2,3,1,7,4,6,5]=>[3,3,1]=>280
[2,3,1,7,5,4,6]=>[3,3,1]=>280
[2,3,1,7,5,6,4]=>[3,2,1,1]=>420
[2,3,1,7,6,4,5]=>[4,3]=>420
[2,3,1,7,6,5,4]=>[3,2,2]=>210
[2,3,4,1,5,6,7]=>[4,1,1,1]=>210
[2,3,4,1,5,7,6]=>[4,2,1]=>630
[2,3,4,1,6,5,7]=>[4,2,1]=>630
[2,3,4,1,6,7,5]=>[4,3]=>420
[2,3,4,1,7,5,6]=>[4,3]=>420
[2,3,4,1,7,6,5]=>[4,2,1]=>630
[2,3,4,5,1,6,7]=>[5,1,1]=>504
[2,3,4,5,1,7,6]=>[5,2]=>504
[2,3,4,5,6,1,7]=>[6,1]=>840
[2,3,4,5,6,7,1]=>[7]=>720
[2,3,4,5,7,1,6]=>[7]=>720
[2,3,4,5,7,6,1]=>[6,1]=>840
[2,3,4,6,1,5,7]=>[6,1]=>840
[2,3,4,6,1,7,5]=>[7]=>720
[2,3,4,6,5,1,7]=>[5,1,1]=>504
[2,3,4,6,5,7,1]=>[6,1]=>840
[2,3,4,6,7,1,5]=>[5,2]=>504
[2,3,4,6,7,5,1]=>[7]=>720
[2,3,4,7,1,5,6]=>[7]=>720
[2,3,4,7,1,6,5]=>[6,1]=>840
[2,3,4,7,5,1,6]=>[6,1]=>840
[2,3,4,7,5,6,1]=>[5,1,1]=>504
[2,3,4,7,6,1,5]=>[7]=>720
[2,3,4,7,6,5,1]=>[5,2]=>504
[2,3,5,1,4,6,7]=>[5,1,1]=>504
[2,3,5,1,4,7,6]=>[5,2]=>504
[2,3,5,1,6,4,7]=>[6,1]=>840
[2,3,5,1,6,7,4]=>[7]=>720
[2,3,5,1,7,4,6]=>[7]=>720
[2,3,5,1,7,6,4]=>[6,1]=>840
[2,3,5,4,1,6,7]=>[4,1,1,1]=>210
[2,3,5,4,1,7,6]=>[4,2,1]=>630
[2,3,5,4,6,1,7]=>[5,1,1]=>504
[2,3,5,4,6,7,1]=>[6,1]=>840
[2,3,5,4,7,1,6]=>[6,1]=>840
[2,3,5,4,7,6,1]=>[5,1,1]=>504
[2,3,5,6,1,4,7]=>[4,2,1]=>630
[2,3,5,6,1,7,4]=>[4,3]=>420
[2,3,5,6,4,1,7]=>[6,1]=>840
[2,3,5,6,4,7,1]=>[7]=>720
[2,3,5,6,7,1,4]=>[7]=>720
[2,3,5,6,7,4,1]=>[5,2]=>504
[2,3,5,7,1,4,6]=>[4,3]=>420
[2,3,5,7,1,6,4]=>[4,2,1]=>630
[2,3,5,7,4,1,6]=>[7]=>720
[2,3,5,7,4,6,1]=>[6,1]=>840
[2,3,5,7,6,1,4]=>[5,2]=>504
[2,3,5,7,6,4,1]=>[7]=>720
[2,3,6,1,4,5,7]=>[6,1]=>840
[2,3,6,1,4,7,5]=>[7]=>720
[2,3,6,1,5,4,7]=>[5,1,1]=>504
[2,3,6,1,5,7,4]=>[6,1]=>840
[2,3,6,1,7,4,5]=>[5,2]=>504
[2,3,6,1,7,5,4]=>[7]=>720
[2,3,6,4,1,5,7]=>[5,1,1]=>504
[2,3,6,4,1,7,5]=>[6,1]=>840
[2,3,6,4,5,1,7]=>[4,1,1,1]=>210
[2,3,6,4,5,7,1]=>[5,1,1]=>504
[2,3,6,4,7,1,5]=>[4,2,1]=>630
[2,3,6,4,7,5,1]=>[6,1]=>840
[2,3,6,5,1,4,7]=>[6,1]=>840
[2,3,6,5,1,7,4]=>[7]=>720
[2,3,6,5,4,1,7]=>[4,2,1]=>630
[2,3,6,5,4,7,1]=>[5,2]=>504
[2,3,6,5,7,1,4]=>[4,3]=>420
[2,3,6,5,7,4,1]=>[7]=>720
[2,3,6,7,1,4,5]=>[7]=>720
[2,3,6,7,1,5,4]=>[5,2]=>504
[2,3,6,7,4,1,5]=>[4,3]=>420
[2,3,6,7,4,5,1]=>[7]=>720
[2,3,6,7,5,1,4]=>[4,2,1]=>630
[2,3,6,7,5,4,1]=>[6,1]=>840
[2,3,7,1,4,5,6]=>[7]=>720
[2,3,7,1,4,6,5]=>[6,1]=>840
[2,3,7,1,5,4,6]=>[6,1]=>840
[2,3,7,1,5,6,4]=>[5,1,1]=>504
[2,3,7,1,6,4,5]=>[7]=>720
[2,3,7,1,6,5,4]=>[5,2]=>504
[2,3,7,4,1,5,6]=>[6,1]=>840
[2,3,7,4,1,6,5]=>[5,1,1]=>504
[2,3,7,4,5,1,6]=>[5,1,1]=>504
[2,3,7,4,5,6,1]=>[4,1,1,1]=>210
[2,3,7,4,6,1,5]=>[6,1]=>840
[2,3,7,4,6,5,1]=>[4,2,1]=>630
[2,3,7,5,1,4,6]=>[7]=>720
[2,3,7,5,1,6,4]=>[6,1]=>840
[2,3,7,5,4,1,6]=>[5,2]=>504
[2,3,7,5,4,6,1]=>[4,2,1]=>630
[2,3,7,5,6,1,4]=>[7]=>720
[2,3,7,5,6,4,1]=>[4,3]=>420
[2,3,7,6,1,4,5]=>[5,2]=>504
[2,3,7,6,1,5,4]=>[7]=>720
[2,3,7,6,4,1,5]=>[7]=>720
[2,3,7,6,4,5,1]=>[4,3]=>420
[2,3,7,6,5,1,4]=>[6,1]=>840
[2,3,7,6,5,4,1]=>[4,2,1]=>630
[2,4,1,3,5,6,7]=>[4,1,1,1]=>210
[2,4,1,3,5,7,6]=>[4,2,1]=>630
[2,4,1,3,6,5,7]=>[4,2,1]=>630
[2,4,1,3,6,7,5]=>[4,3]=>420
[2,4,1,3,7,5,6]=>[4,3]=>420
[2,4,1,3,7,6,5]=>[4,2,1]=>630
[2,4,1,5,3,6,7]=>[5,1,1]=>504
[2,4,1,5,3,7,6]=>[5,2]=>504
[2,4,1,5,6,3,7]=>[6,1]=>840
[2,4,1,5,6,7,3]=>[7]=>720
[2,4,1,5,7,3,6]=>[7]=>720
[2,4,1,5,7,6,3]=>[6,1]=>840
[2,4,1,6,3,5,7]=>[6,1]=>840
[2,4,1,6,3,7,5]=>[7]=>720
[2,4,1,6,5,3,7]=>[5,1,1]=>504
[2,4,1,6,5,7,3]=>[6,1]=>840
[2,4,1,6,7,3,5]=>[5,2]=>504
[2,4,1,6,7,5,3]=>[7]=>720
[2,4,1,7,3,5,6]=>[7]=>720
[2,4,1,7,3,6,5]=>[6,1]=>840
[2,4,1,7,5,3,6]=>[6,1]=>840
[2,4,1,7,5,6,3]=>[5,1,1]=>504
[2,4,1,7,6,3,5]=>[7]=>720
[2,4,1,7,6,5,3]=>[5,2]=>504
[2,4,3,1,5,6,7]=>[3,1,1,1,1]=>70
[2,4,3,1,5,7,6]=>[3,2,1,1]=>420
[2,4,3,1,6,5,7]=>[3,2,1,1]=>420
[2,4,3,1,6,7,5]=>[3,3,1]=>280
[2,4,3,1,7,5,6]=>[3,3,1]=>280
[2,4,3,1,7,6,5]=>[3,2,1,1]=>420
[2,4,3,5,1,6,7]=>[4,1,1,1]=>210
[2,4,3,5,1,7,6]=>[4,2,1]=>630
[2,4,3,5,6,1,7]=>[5,1,1]=>504
[2,4,3,5,6,7,1]=>[6,1]=>840
[2,4,3,5,7,1,6]=>[6,1]=>840
[2,4,3,5,7,6,1]=>[5,1,1]=>504
[2,4,3,6,1,5,7]=>[5,1,1]=>504
[2,4,3,6,1,7,5]=>[6,1]=>840
[2,4,3,6,5,1,7]=>[4,1,1,1]=>210
[2,4,3,6,5,7,1]=>[5,1,1]=>504
[2,4,3,6,7,1,5]=>[4,2,1]=>630
[2,4,3,6,7,5,1]=>[6,1]=>840
[2,4,3,7,1,5,6]=>[6,1]=>840
[2,4,3,7,1,6,5]=>[5,1,1]=>504
[2,4,3,7,5,1,6]=>[5,1,1]=>504
[2,4,3,7,5,6,1]=>[4,1,1,1]=>210
[2,4,3,7,6,1,5]=>[6,1]=>840
[2,4,3,7,6,5,1]=>[4,2,1]=>630
[2,4,5,1,3,6,7]=>[3,2,1,1]=>420
[2,4,5,1,3,7,6]=>[3,2,2]=>210
[2,4,5,1,6,3,7]=>[3,3,1]=>280
[2,4,5,1,6,7,3]=>[4,3]=>420
[2,4,5,1,7,3,6]=>[4,3]=>420
[2,4,5,1,7,6,3]=>[3,3,1]=>280
[2,4,5,3,1,6,7]=>[5,1,1]=>504
[2,4,5,3,1,7,6]=>[5,2]=>504
[2,4,5,3,6,1,7]=>[6,1]=>840
[2,4,5,3,6,7,1]=>[7]=>720
[2,4,5,3,7,1,6]=>[7]=>720
[2,4,5,3,7,6,1]=>[6,1]=>840
[2,4,5,6,1,3,7]=>[6,1]=>840
[2,4,5,6,1,7,3]=>[7]=>720
[2,4,5,6,3,1,7]=>[4,2,1]=>630
[2,4,5,6,3,7,1]=>[5,2]=>504
[2,4,5,6,7,1,3]=>[4,3]=>420
[2,4,5,6,7,3,1]=>[7]=>720
[2,4,5,7,1,3,6]=>[7]=>720
[2,4,5,7,1,6,3]=>[6,1]=>840
[2,4,5,7,3,1,6]=>[5,2]=>504
[2,4,5,7,3,6,1]=>[4,2,1]=>630
[2,4,5,7,6,1,3]=>[7]=>720
[2,4,5,7,6,3,1]=>[4,3]=>420
[2,4,6,1,3,5,7]=>[3,3,1]=>280
[2,4,6,1,3,7,5]=>[4,3]=>420
[2,4,6,1,5,3,7]=>[3,2,1,1]=>420
[2,4,6,1,5,7,3]=>[3,3,1]=>280
[2,4,6,1,7,3,5]=>[3,2,2]=>210
[2,4,6,1,7,5,3]=>[4,3]=>420
[2,4,6,3,1,5,7]=>[6,1]=>840
[2,4,6,3,1,7,5]=>[7]=>720
[2,4,6,3,5,1,7]=>[5,1,1]=>504
[2,4,6,3,5,7,1]=>[6,1]=>840
[2,4,6,3,7,1,5]=>[5,2]=>504
[2,4,6,3,7,5,1]=>[7]=>720
[2,4,6,5,1,3,7]=>[4,2,1]=>630
[2,4,6,5,1,7,3]=>[4,3]=>420
[2,4,6,5,3,1,7]=>[6,1]=>840
[2,4,6,5,3,7,1]=>[7]=>720
[2,4,6,5,7,1,3]=>[7]=>720
[2,4,6,5,7,3,1]=>[5,2]=>504
[2,4,6,7,1,3,5]=>[5,2]=>504
[2,4,6,7,1,5,3]=>[7]=>720
[2,4,6,7,3,1,5]=>[7]=>720
[2,4,6,7,3,5,1]=>[4,3]=>420
[2,4,6,7,5,1,3]=>[6,1]=>840
[2,4,6,7,5,3,1]=>[4,2,1]=>630
[2,4,7,1,3,5,6]=>[4,3]=>420
[2,4,7,1,3,6,5]=>[3,3,1]=>280
[2,4,7,1,5,3,6]=>[3,3,1]=>280
[2,4,7,1,5,6,3]=>[3,2,1,1]=>420
[2,4,7,1,6,3,5]=>[4,3]=>420
[2,4,7,1,6,5,3]=>[3,2,2]=>210
[2,4,7,3,1,5,6]=>[7]=>720
[2,4,7,3,1,6,5]=>[6,1]=>840
[2,4,7,3,5,1,6]=>[6,1]=>840
[2,4,7,3,5,6,1]=>[5,1,1]=>504
[2,4,7,3,6,1,5]=>[7]=>720
[2,4,7,3,6,5,1]=>[5,2]=>504
[2,4,7,5,1,3,6]=>[4,3]=>420
[2,4,7,5,1,6,3]=>[4,2,1]=>630
[2,4,7,5,3,1,6]=>[7]=>720
[2,4,7,5,3,6,1]=>[6,1]=>840
[2,4,7,5,6,1,3]=>[5,2]=>504
[2,4,7,5,6,3,1]=>[7]=>720
[2,4,7,6,1,3,5]=>[7]=>720
[2,4,7,6,1,5,3]=>[5,2]=>504
[2,4,7,6,3,1,5]=>[4,3]=>420
[2,4,7,6,3,5,1]=>[7]=>720
[2,4,7,6,5,1,3]=>[4,2,1]=>630
[2,4,7,6,5,3,1]=>[6,1]=>840
[2,5,1,3,4,6,7]=>[5,1,1]=>504
[2,5,1,3,4,7,6]=>[5,2]=>504
[2,5,1,3,6,4,7]=>[6,1]=>840
[2,5,1,3,6,7,4]=>[7]=>720
[2,5,1,3,7,4,6]=>[7]=>720
[2,5,1,3,7,6,4]=>[6,1]=>840
[2,5,1,4,3,6,7]=>[4,1,1,1]=>210
[2,5,1,4,3,7,6]=>[4,2,1]=>630
[2,5,1,4,6,3,7]=>[5,1,1]=>504
[2,5,1,4,6,7,3]=>[6,1]=>840
[2,5,1,4,7,3,6]=>[6,1]=>840
[2,5,1,4,7,6,3]=>[5,1,1]=>504
[2,5,1,6,3,4,7]=>[4,2,1]=>630
[2,5,1,6,3,7,4]=>[4,3]=>420
[2,5,1,6,4,3,7]=>[6,1]=>840
[2,5,1,6,4,7,3]=>[7]=>720
[2,5,1,6,7,3,4]=>[7]=>720
[2,5,1,6,7,4,3]=>[5,2]=>504
[2,5,1,7,3,4,6]=>[4,3]=>420
[2,5,1,7,3,6,4]=>[4,2,1]=>630
[2,5,1,7,4,3,6]=>[7]=>720
[2,5,1,7,4,6,3]=>[6,1]=>840
[2,5,1,7,6,3,4]=>[5,2]=>504
[2,5,1,7,6,4,3]=>[7]=>720
[2,5,3,1,4,6,7]=>[4,1,1,1]=>210
[2,5,3,1,4,7,6]=>[4,2,1]=>630
[2,5,3,1,6,4,7]=>[5,1,1]=>504
[2,5,3,1,6,7,4]=>[6,1]=>840
[2,5,3,1,7,4,6]=>[6,1]=>840
[2,5,3,1,7,6,4]=>[5,1,1]=>504
[2,5,3,4,1,6,7]=>[3,1,1,1,1]=>70
[2,5,3,4,1,7,6]=>[3,2,1,1]=>420
[2,5,3,4,6,1,7]=>[4,1,1,1]=>210
[2,5,3,4,6,7,1]=>[5,1,1]=>504
[2,5,3,4,7,1,6]=>[5,1,1]=>504
[2,5,3,4,7,6,1]=>[4,1,1,1]=>210
[2,5,3,6,1,4,7]=>[3,2,1,1]=>420
[2,5,3,6,1,7,4]=>[3,3,1]=>280
[2,5,3,6,4,1,7]=>[5,1,1]=>504
[2,5,3,6,4,7,1]=>[6,1]=>840
[2,5,3,6,7,1,4]=>[6,1]=>840
[2,5,3,6,7,4,1]=>[4,2,1]=>630
[2,5,3,7,1,4,6]=>[3,3,1]=>280
[2,5,3,7,1,6,4]=>[3,2,1,1]=>420
[2,5,3,7,4,1,6]=>[6,1]=>840
[2,5,3,7,4,6,1]=>[5,1,1]=>504
[2,5,3,7,6,1,4]=>[4,2,1]=>630
[2,5,3,7,6,4,1]=>[6,1]=>840
[2,5,4,1,3,6,7]=>[5,1,1]=>504
[2,5,4,1,3,7,6]=>[5,2]=>504
[2,5,4,1,6,3,7]=>[6,1]=>840
[2,5,4,1,6,7,3]=>[7]=>720
[2,5,4,1,7,3,6]=>[7]=>720
[2,5,4,1,7,6,3]=>[6,1]=>840
[2,5,4,3,1,6,7]=>[3,2,1,1]=>420
[2,5,4,3,1,7,6]=>[3,2,2]=>210
[2,5,4,3,6,1,7]=>[4,2,1]=>630
[2,5,4,3,6,7,1]=>[5,2]=>504
[2,5,4,3,7,1,6]=>[5,2]=>504
[2,5,4,3,7,6,1]=>[4,2,1]=>630
[2,5,4,6,1,3,7]=>[3,3,1]=>280
[2,5,4,6,1,7,3]=>[4,3]=>420
[2,5,4,6,3,1,7]=>[6,1]=>840
[2,5,4,6,3,7,1]=>[7]=>720
[2,5,4,6,7,1,3]=>[7]=>720
[2,5,4,6,7,3,1]=>[4,3]=>420
[2,5,4,7,1,3,6]=>[4,3]=>420
[2,5,4,7,1,6,3]=>[3,3,1]=>280
[2,5,4,7,3,1,6]=>[7]=>720
[2,5,4,7,3,6,1]=>[6,1]=>840
[2,5,4,7,6,1,3]=>[4,3]=>420
[2,5,4,7,6,3,1]=>[7]=>720
[2,5,6,1,3,4,7]=>[6,1]=>840
[2,5,6,1,3,7,4]=>[7]=>720
[2,5,6,1,4,3,7]=>[4,2,1]=>630
[2,5,6,1,4,7,3]=>[4,3]=>420
[2,5,6,1,7,3,4]=>[5,2]=>504
[2,5,6,1,7,4,3]=>[7]=>720
[2,5,6,3,1,4,7]=>[3,3,1]=>280
[2,5,6,3,1,7,4]=>[4,3]=>420
[2,5,6,3,4,1,7]=>[6,1]=>840
[2,5,6,3,4,7,1]=>[7]=>720
[2,5,6,3,7,1,4]=>[7]=>720
[2,5,6,3,7,4,1]=>[4,3]=>420
[2,5,6,4,1,3,7]=>[3,2,1,1]=>420
[2,5,6,4,1,7,3]=>[3,3,1]=>280
[2,5,6,4,3,1,7]=>[5,1,1]=>504
[2,5,6,4,3,7,1]=>[6,1]=>840
[2,5,6,4,7,1,3]=>[6,1]=>840
[2,5,6,4,7,3,1]=>[4,2,1]=>630
[2,5,6,7,1,3,4]=>[3,2,2]=>210
[2,5,6,7,1,4,3]=>[4,3]=>420
[2,5,6,7,3,1,4]=>[5,2]=>504
[2,5,6,7,3,4,1]=>[7]=>720
[2,5,6,7,4,1,3]=>[7]=>720
[2,5,6,7,4,3,1]=>[5,2]=>504
[2,5,7,1,3,4,6]=>[7]=>720
[2,5,7,1,3,6,4]=>[6,1]=>840
[2,5,7,1,4,3,6]=>[4,3]=>420
[2,5,7,1,4,6,3]=>[4,2,1]=>630
[2,5,7,1,6,3,4]=>[7]=>720
[2,5,7,1,6,4,3]=>[5,2]=>504
[2,5,7,3,1,4,6]=>[4,3]=>420
[2,5,7,3,1,6,4]=>[3,3,1]=>280
[2,5,7,3,4,1,6]=>[7]=>720
[2,5,7,3,4,6,1]=>[6,1]=>840
[2,5,7,3,6,1,4]=>[4,3]=>420
[2,5,7,3,6,4,1]=>[7]=>720
[2,5,7,4,1,3,6]=>[3,3,1]=>280
[2,5,7,4,1,6,3]=>[3,2,1,1]=>420
[2,5,7,4,3,1,6]=>[6,1]=>840
[2,5,7,4,3,6,1]=>[5,1,1]=>504
[2,5,7,4,6,1,3]=>[4,2,1]=>630
[2,5,7,4,6,3,1]=>[6,1]=>840
[2,5,7,6,1,3,4]=>[4,3]=>420
[2,5,7,6,1,4,3]=>[3,2,2]=>210
[2,5,7,6,3,1,4]=>[7]=>720
[2,5,7,6,3,4,1]=>[5,2]=>504
[2,5,7,6,4,1,3]=>[5,2]=>504
[2,5,7,6,4,3,1]=>[7]=>720
[2,6,1,3,4,5,7]=>[6,1]=>840
[2,6,1,3,4,7,5]=>[7]=>720
[2,6,1,3,5,4,7]=>[5,1,1]=>504
[2,6,1,3,5,7,4]=>[6,1]=>840
[2,6,1,3,7,4,5]=>[5,2]=>504
[2,6,1,3,7,5,4]=>[7]=>720
[2,6,1,4,3,5,7]=>[5,1,1]=>504
[2,6,1,4,3,7,5]=>[6,1]=>840
[2,6,1,4,5,3,7]=>[4,1,1,1]=>210
[2,6,1,4,5,7,3]=>[5,1,1]=>504
[2,6,1,4,7,3,5]=>[4,2,1]=>630
[2,6,1,4,7,5,3]=>[6,1]=>840
[2,6,1,5,3,4,7]=>[6,1]=>840
[2,6,1,5,3,7,4]=>[7]=>720
[2,6,1,5,4,3,7]=>[4,2,1]=>630
[2,6,1,5,4,7,3]=>[5,2]=>504
[2,6,1,5,7,3,4]=>[4,3]=>420
[2,6,1,5,7,4,3]=>[7]=>720
[2,6,1,7,3,4,5]=>[7]=>720
[2,6,1,7,3,5,4]=>[5,2]=>504
[2,6,1,7,4,3,5]=>[4,3]=>420
[2,6,1,7,4,5,3]=>[7]=>720
[2,6,1,7,5,3,4]=>[4,2,1]=>630
[2,6,1,7,5,4,3]=>[6,1]=>840
[2,6,3,1,4,5,7]=>[5,1,1]=>504
[2,6,3,1,4,7,5]=>[6,1]=>840
[2,6,3,1,5,4,7]=>[4,1,1,1]=>210
[2,6,3,1,5,7,4]=>[5,1,1]=>504
[2,6,3,1,7,4,5]=>[4,2,1]=>630
[2,6,3,1,7,5,4]=>[6,1]=>840
[2,6,3,4,1,5,7]=>[4,1,1,1]=>210
[2,6,3,4,1,7,5]=>[5,1,1]=>504
[2,6,3,4,5,1,7]=>[3,1,1,1,1]=>70
[2,6,3,4,5,7,1]=>[4,1,1,1]=>210
[2,6,3,4,7,1,5]=>[3,2,1,1]=>420
[2,6,3,4,7,5,1]=>[5,1,1]=>504
[2,6,3,5,1,4,7]=>[5,1,1]=>504
[2,6,3,5,1,7,4]=>[6,1]=>840
[2,6,3,5,4,1,7]=>[3,2,1,1]=>420
[2,6,3,5,4,7,1]=>[4,2,1]=>630
[2,6,3,5,7,1,4]=>[3,3,1]=>280
[2,6,3,5,7,4,1]=>[6,1]=>840
[2,6,3,7,1,4,5]=>[6,1]=>840
[2,6,3,7,1,5,4]=>[4,2,1]=>630
[2,6,3,7,4,1,5]=>[3,3,1]=>280
[2,6,3,7,4,5,1]=>[6,1]=>840
[2,6,3,7,5,1,4]=>[3,2,1,1]=>420
[2,6,3,7,5,4,1]=>[5,1,1]=>504
[2,6,4,1,3,5,7]=>[6,1]=>840
[2,6,4,1,3,7,5]=>[7]=>720
[2,6,4,1,5,3,7]=>[5,1,1]=>504
[2,6,4,1,5,7,3]=>[6,1]=>840
[2,6,4,1,7,3,5]=>[5,2]=>504
[2,6,4,1,7,5,3]=>[7]=>720
[2,6,4,3,1,5,7]=>[4,2,1]=>630
[2,6,4,3,1,7,5]=>[5,2]=>504
[2,6,4,3,5,1,7]=>[3,2,1,1]=>420
[2,6,4,3,5,7,1]=>[4,2,1]=>630
[2,6,4,3,7,1,5]=>[3,2,2]=>210
[2,6,4,3,7,5,1]=>[5,2]=>504
[2,6,4,5,1,3,7]=>[6,1]=>840
[2,6,4,5,1,7,3]=>[7]=>720
[2,6,4,5,3,1,7]=>[3,3,1]=>280
[2,6,4,5,3,7,1]=>[4,3]=>420
[2,6,4,5,7,1,3]=>[4,3]=>420
[2,6,4,5,7,3,1]=>[7]=>720
[2,6,4,7,1,3,5]=>[7]=>720
[2,6,4,7,1,5,3]=>[4,3]=>420
[2,6,4,7,3,1,5]=>[4,3]=>420
[2,6,4,7,3,5,1]=>[7]=>720
[2,6,4,7,5,1,3]=>[3,3,1]=>280
[2,6,4,7,5,3,1]=>[6,1]=>840
[2,6,5,1,3,4,7]=>[4,2,1]=>630
[2,6,5,1,3,7,4]=>[5,2]=>504
[2,6,5,1,4,3,7]=>[6,1]=>840
[2,6,5,1,4,7,3]=>[7]=>720
[2,6,5,1,7,3,4]=>[7]=>720
[2,6,5,1,7,4,3]=>[4,3]=>420
[2,6,5,3,1,4,7]=>[6,1]=>840
[2,6,5,3,1,7,4]=>[7]=>720
[2,6,5,3,4,1,7]=>[3,3,1]=>280
[2,6,5,3,4,7,1]=>[4,3]=>420
[2,6,5,3,7,1,4]=>[4,3]=>420
[2,6,5,3,7,4,1]=>[7]=>720
[2,6,5,4,1,3,7]=>[5,1,1]=>504
[2,6,5,4,1,7,3]=>[6,1]=>840
[2,6,5,4,3,1,7]=>[3,2,1,1]=>420
[2,6,5,4,3,7,1]=>[4,2,1]=>630
[2,6,5,4,7,1,3]=>[3,3,1]=>280
[2,6,5,4,7,3,1]=>[6,1]=>840
[2,6,5,7,1,3,4]=>[5,2]=>504
[2,6,5,7,1,4,3]=>[7]=>720
[2,6,5,7,3,1,4]=>[3,2,2]=>210
[2,6,5,7,3,4,1]=>[5,2]=>504
[2,6,5,7,4,1,3]=>[4,3]=>420
[2,6,5,7,4,3,1]=>[7]=>720
[2,6,7,1,3,4,5]=>[4,3]=>420
[2,6,7,1,3,5,4]=>[7]=>720
[2,6,7,1,4,3,5]=>[7]=>720
[2,6,7,1,4,5,3]=>[5,2]=>504
[2,6,7,1,5,3,4]=>[6,1]=>840
[2,6,7,1,5,4,3]=>[4,2,1]=>630
[2,6,7,3,1,4,5]=>[7]=>720
[2,6,7,3,1,5,4]=>[4,3]=>420
[2,6,7,3,4,1,5]=>[4,3]=>420
[2,6,7,3,4,5,1]=>[7]=>720
[2,6,7,3,5,1,4]=>[3,3,1]=>280
[2,6,7,3,5,4,1]=>[6,1]=>840
[2,6,7,4,1,3,5]=>[6,1]=>840
[2,6,7,4,1,5,3]=>[4,2,1]=>630
[2,6,7,4,3,1,5]=>[3,3,1]=>280
[2,6,7,4,3,5,1]=>[6,1]=>840
[2,6,7,4,5,1,3]=>[3,2,1,1]=>420
[2,6,7,4,5,3,1]=>[5,1,1]=>504
[2,6,7,5,1,3,4]=>[7]=>720
[2,6,7,5,1,4,3]=>[5,2]=>504
[2,6,7,5,3,1,4]=>[4,3]=>420
[2,6,7,5,3,4,1]=>[7]=>720
[2,6,7,5,4,1,3]=>[3,2,2]=>210
[2,6,7,5,4,3,1]=>[5,2]=>504
[2,7,1,3,4,5,6]=>[7]=>720
[2,7,1,3,4,6,5]=>[6,1]=>840
[2,7,1,3,5,4,6]=>[6,1]=>840
[2,7,1,3,5,6,4]=>[5,1,1]=>504
[2,7,1,3,6,4,5]=>[7]=>720
[2,7,1,3,6,5,4]=>[5,2]=>504
[2,7,1,4,3,5,6]=>[6,1]=>840
[2,7,1,4,3,6,5]=>[5,1,1]=>504
[2,7,1,4,5,3,6]=>[5,1,1]=>504
[2,7,1,4,5,6,3]=>[4,1,1,1]=>210
[2,7,1,4,6,3,5]=>[6,1]=>840
[2,7,1,4,6,5,3]=>[4,2,1]=>630
[2,7,1,5,3,4,6]=>[7]=>720
[2,7,1,5,3,6,4]=>[6,1]=>840
[2,7,1,5,4,3,6]=>[5,2]=>504
[2,7,1,5,4,6,3]=>[4,2,1]=>630
[2,7,1,5,6,3,4]=>[7]=>720
[2,7,1,5,6,4,3]=>[4,3]=>420
[2,7,1,6,3,4,5]=>[5,2]=>504
[2,7,1,6,3,5,4]=>[7]=>720
[2,7,1,6,4,3,5]=>[7]=>720
[2,7,1,6,4,5,3]=>[4,3]=>420
[2,7,1,6,5,3,4]=>[6,1]=>840
[2,7,1,6,5,4,3]=>[4,2,1]=>630
[2,7,3,1,4,5,6]=>[6,1]=>840
[2,7,3,1,4,6,5]=>[5,1,1]=>504
[2,7,3,1,5,4,6]=>[5,1,1]=>504
[2,7,3,1,5,6,4]=>[4,1,1,1]=>210
[2,7,3,1,6,4,5]=>[6,1]=>840
[2,7,3,1,6,5,4]=>[4,2,1]=>630
[2,7,3,4,1,5,6]=>[5,1,1]=>504
[2,7,3,4,1,6,5]=>[4,1,1,1]=>210
[2,7,3,4,5,1,6]=>[4,1,1,1]=>210
[2,7,3,4,5,6,1]=>[3,1,1,1,1]=>70
[2,7,3,4,6,1,5]=>[5,1,1]=>504
[2,7,3,4,6,5,1]=>[3,2,1,1]=>420
[2,7,3,5,1,4,6]=>[6,1]=>840
[2,7,3,5,1,6,4]=>[5,1,1]=>504
[2,7,3,5,4,1,6]=>[4,2,1]=>630
[2,7,3,5,4,6,1]=>[3,2,1,1]=>420
[2,7,3,5,6,1,4]=>[6,1]=>840
[2,7,3,5,6,4,1]=>[3,3,1]=>280
[2,7,3,6,1,4,5]=>[4,2,1]=>630
[2,7,3,6,1,5,4]=>[6,1]=>840
[2,7,3,6,4,1,5]=>[6,1]=>840
[2,7,3,6,4,5,1]=>[3,3,1]=>280
[2,7,3,6,5,1,4]=>[5,1,1]=>504
[2,7,3,6,5,4,1]=>[3,2,1,1]=>420
[2,7,4,1,3,5,6]=>[7]=>720
[2,7,4,1,3,6,5]=>[6,1]=>840
[2,7,4,1,5,3,6]=>[6,1]=>840
[2,7,4,1,5,6,3]=>[5,1,1]=>504
[2,7,4,1,6,3,5]=>[7]=>720
[2,7,4,1,6,5,3]=>[5,2]=>504
[2,7,4,3,1,5,6]=>[5,2]=>504
[2,7,4,3,1,6,5]=>[4,2,1]=>630
[2,7,4,3,5,1,6]=>[4,2,1]=>630
[2,7,4,3,5,6,1]=>[3,2,1,1]=>420
[2,7,4,3,6,1,5]=>[5,2]=>504
[2,7,4,3,6,5,1]=>[3,2,2]=>210
[2,7,4,5,1,3,6]=>[7]=>720
[2,7,4,5,1,6,3]=>[6,1]=>840
[2,7,4,5,3,1,6]=>[4,3]=>420
[2,7,4,5,3,6,1]=>[3,3,1]=>280
[2,7,4,5,6,1,3]=>[7]=>720
[2,7,4,5,6,3,1]=>[4,3]=>420
[2,7,4,6,1,3,5]=>[4,3]=>420
[2,7,4,6,1,5,3]=>[7]=>720
[2,7,4,6,3,1,5]=>[7]=>720
[2,7,4,6,3,5,1]=>[4,3]=>420
[2,7,4,6,5,1,3]=>[6,1]=>840
[2,7,4,6,5,3,1]=>[3,3,1]=>280
[2,7,5,1,3,4,6]=>[5,2]=>504
[2,7,5,1,3,6,4]=>[4,2,1]=>630
[2,7,5,1,4,3,6]=>[7]=>720
[2,7,5,1,4,6,3]=>[6,1]=>840
[2,7,5,1,6,3,4]=>[4,3]=>420
[2,7,5,1,6,4,3]=>[7]=>720
[2,7,5,3,1,4,6]=>[7]=>720
[2,7,5,3,1,6,4]=>[6,1]=>840
[2,7,5,3,4,1,6]=>[4,3]=>420
[2,7,5,3,4,6,1]=>[3,3,1]=>280
[2,7,5,3,6,1,4]=>[7]=>720
[2,7,5,3,6,4,1]=>[4,3]=>420
[2,7,5,4,1,3,6]=>[6,1]=>840
[2,7,5,4,1,6,3]=>[5,1,1]=>504
[2,7,5,4,3,1,6]=>[4,2,1]=>630
[2,7,5,4,3,6,1]=>[3,2,1,1]=>420
[2,7,5,4,6,1,3]=>[6,1]=>840
[2,7,5,4,6,3,1]=>[3,3,1]=>280
[2,7,5,6,1,3,4]=>[7]=>720
[2,7,5,6,1,4,3]=>[5,2]=>504
[2,7,5,6,3,1,4]=>[5,2]=>504
[2,7,5,6,3,4,1]=>[3,2,2]=>210
[2,7,5,6,4,1,3]=>[7]=>720
[2,7,5,6,4,3,1]=>[4,3]=>420
[2,7,6,1,3,4,5]=>[7]=>720
[2,7,6,1,3,5,4]=>[4,3]=>420
[2,7,6,1,4,3,5]=>[5,2]=>504
[2,7,6,1,4,5,3]=>[7]=>720
[2,7,6,1,5,3,4]=>[4,2,1]=>630
[2,7,6,1,5,4,3]=>[6,1]=>840
[2,7,6,3,1,4,5]=>[4,3]=>420
[2,7,6,3,1,5,4]=>[7]=>720
[2,7,6,3,4,1,5]=>[7]=>720
[2,7,6,3,4,5,1]=>[4,3]=>420
[2,7,6,3,5,1,4]=>[6,1]=>840
[2,7,6,3,5,4,1]=>[3,3,1]=>280
[2,7,6,4,1,3,5]=>[4,2,1]=>630
[2,7,6,4,1,5,3]=>[6,1]=>840
[2,7,6,4,3,1,5]=>[6,1]=>840
[2,7,6,4,3,5,1]=>[3,3,1]=>280
[2,7,6,4,5,1,3]=>[5,1,1]=>504
[2,7,6,4,5,3,1]=>[3,2,1,1]=>420
[2,7,6,5,1,3,4]=>[5,2]=>504
[2,7,6,5,1,4,3]=>[7]=>720
[2,7,6,5,3,1,4]=>[7]=>720
[2,7,6,5,3,4,1]=>[4,3]=>420
[2,7,6,5,4,1,3]=>[5,2]=>504
[2,7,6,5,4,3,1]=>[3,2,2]=>210
[3,1,2,4,5,6,7]=>[3,1,1,1,1]=>70
[3,1,2,4,5,7,6]=>[3,2,1,1]=>420
[3,1,2,4,6,5,7]=>[3,2,1,1]=>420
[3,1,2,4,6,7,5]=>[3,3,1]=>280
[3,1,2,4,7,5,6]=>[3,3,1]=>280
[3,1,2,4,7,6,5]=>[3,2,1,1]=>420
[3,1,2,5,4,6,7]=>[3,2,1,1]=>420
[3,1,2,5,4,7,6]=>[3,2,2]=>210
[3,1,2,5,6,4,7]=>[3,3,1]=>280
[3,1,2,5,6,7,4]=>[4,3]=>420
[3,1,2,5,7,4,6]=>[4,3]=>420
[3,1,2,5,7,6,4]=>[3,3,1]=>280
[3,1,2,6,4,5,7]=>[3,3,1]=>280
[3,1,2,6,4,7,5]=>[4,3]=>420
[3,1,2,6,5,4,7]=>[3,2,1,1]=>420
[3,1,2,6,5,7,4]=>[3,3,1]=>280
[3,1,2,6,7,4,5]=>[3,2,2]=>210
[3,1,2,6,7,5,4]=>[4,3]=>420
[3,1,2,7,4,5,6]=>[4,3]=>420
[3,1,2,7,4,6,5]=>[3,3,1]=>280
[3,1,2,7,5,4,6]=>[3,3,1]=>280
[3,1,2,7,5,6,4]=>[3,2,1,1]=>420
[3,1,2,7,6,4,5]=>[4,3]=>420
[3,1,2,7,6,5,4]=>[3,2,2]=>210
[3,1,4,2,5,6,7]=>[4,1,1,1]=>210
[3,1,4,2,5,7,6]=>[4,2,1]=>630
[3,1,4,2,6,5,7]=>[4,2,1]=>630
[3,1,4,2,6,7,5]=>[4,3]=>420
[3,1,4,2,7,5,6]=>[4,3]=>420
[3,1,4,2,7,6,5]=>[4,2,1]=>630
[3,1,4,5,2,6,7]=>[5,1,1]=>504
[3,1,4,5,2,7,6]=>[5,2]=>504
[3,1,4,5,6,2,7]=>[6,1]=>840
[3,1,4,5,6,7,2]=>[7]=>720
[3,1,4,5,7,2,6]=>[7]=>720
[3,1,4,5,7,6,2]=>[6,1]=>840
[3,1,4,6,2,5,7]=>[6,1]=>840
[3,1,4,6,2,7,5]=>[7]=>720
[3,1,4,6,5,2,7]=>[5,1,1]=>504
[3,1,4,6,5,7,2]=>[6,1]=>840
[3,1,4,6,7,2,5]=>[5,2]=>504
[3,1,4,6,7,5,2]=>[7]=>720
[3,1,4,7,2,5,6]=>[7]=>720
[3,1,4,7,2,6,5]=>[6,1]=>840
[3,1,4,7,5,2,6]=>[6,1]=>840
[3,1,4,7,5,6,2]=>[5,1,1]=>504
[3,1,4,7,6,2,5]=>[7]=>720
[3,1,4,7,6,5,2]=>[5,2]=>504
[3,1,5,2,4,6,7]=>[5,1,1]=>504
[3,1,5,2,4,7,6]=>[5,2]=>504
[3,1,5,2,6,4,7]=>[6,1]=>840
[3,1,5,2,6,7,4]=>[7]=>720
[3,1,5,2,7,4,6]=>[7]=>720
[3,1,5,2,7,6,4]=>[6,1]=>840
[3,1,5,4,2,6,7]=>[4,1,1,1]=>210
[3,1,5,4,2,7,6]=>[4,2,1]=>630
[3,1,5,4,6,2,7]=>[5,1,1]=>504
[3,1,5,4,6,7,2]=>[6,1]=>840
[3,1,5,4,7,2,6]=>[6,1]=>840
[3,1,5,4,7,6,2]=>[5,1,1]=>504
[3,1,5,6,2,4,7]=>[4,2,1]=>630
[3,1,5,6,2,7,4]=>[4,3]=>420
[3,1,5,6,4,2,7]=>[6,1]=>840
[3,1,5,6,4,7,2]=>[7]=>720
[3,1,5,6,7,2,4]=>[7]=>720
[3,1,5,6,7,4,2]=>[5,2]=>504
[3,1,5,7,2,4,6]=>[4,3]=>420
[3,1,5,7,2,6,4]=>[4,2,1]=>630
[3,1,5,7,4,2,6]=>[7]=>720
[3,1,5,7,4,6,2]=>[6,1]=>840
[3,1,5,7,6,2,4]=>[5,2]=>504
[3,1,5,7,6,4,2]=>[7]=>720
[3,1,6,2,4,5,7]=>[6,1]=>840
[3,1,6,2,4,7,5]=>[7]=>720
[3,1,6,2,5,4,7]=>[5,1,1]=>504
[3,1,6,2,5,7,4]=>[6,1]=>840
[3,1,6,2,7,4,5]=>[5,2]=>504
[3,1,6,2,7,5,4]=>[7]=>720
[3,1,6,4,2,5,7]=>[5,1,1]=>504
[3,1,6,4,2,7,5]=>[6,1]=>840
[3,1,6,4,5,2,7]=>[4,1,1,1]=>210
[3,1,6,4,5,7,2]=>[5,1,1]=>504
[3,1,6,4,7,2,5]=>[4,2,1]=>630
[3,1,6,4,7,5,2]=>[6,1]=>840
[3,1,6,5,2,4,7]=>[6,1]=>840
[3,1,6,5,2,7,4]=>[7]=>720
[3,1,6,5,4,2,7]=>[4,2,1]=>630
[3,1,6,5,4,7,2]=>[5,2]=>504
[3,1,6,5,7,2,4]=>[4,3]=>420
[3,1,6,5,7,4,2]=>[7]=>720
[3,1,6,7,2,4,5]=>[7]=>720
[3,1,6,7,2,5,4]=>[5,2]=>504
[3,1,6,7,4,2,5]=>[4,3]=>420
[3,1,6,7,4,5,2]=>[7]=>720
[3,1,6,7,5,2,4]=>[4,2,1]=>630
[3,1,6,7,5,4,2]=>[6,1]=>840
[3,1,7,2,4,5,6]=>[7]=>720
[3,1,7,2,4,6,5]=>[6,1]=>840
[3,1,7,2,5,4,6]=>[6,1]=>840
[3,1,7,2,5,6,4]=>[5,1,1]=>504
[3,1,7,2,6,4,5]=>[7]=>720
[3,1,7,2,6,5,4]=>[5,2]=>504
[3,1,7,4,2,5,6]=>[6,1]=>840
[3,1,7,4,2,6,5]=>[5,1,1]=>504
[3,1,7,4,5,2,6]=>[5,1,1]=>504
[3,1,7,4,5,6,2]=>[4,1,1,1]=>210
[3,1,7,4,6,2,5]=>[6,1]=>840
[3,1,7,4,6,5,2]=>[4,2,1]=>630
[3,1,7,5,2,4,6]=>[7]=>720
[3,1,7,5,2,6,4]=>[6,1]=>840
[3,1,7,5,4,2,6]=>[5,2]=>504
[3,1,7,5,4,6,2]=>[4,2,1]=>630
[3,1,7,5,6,2,4]=>[7]=>720
[3,1,7,5,6,4,2]=>[4,3]=>420
[3,1,7,6,2,4,5]=>[5,2]=>504
[3,1,7,6,2,5,4]=>[7]=>720
[3,1,7,6,4,2,5]=>[7]=>720
[3,1,7,6,4,5,2]=>[4,3]=>420
[3,1,7,6,5,2,4]=>[6,1]=>840
[3,1,7,6,5,4,2]=>[4,2,1]=>630
[3,2,1,4,5,6,7]=>[2,1,1,1,1,1]=>21
[3,2,1,4,5,7,6]=>[2,2,1,1,1]=>105
[3,2,1,4,6,5,7]=>[2,2,1,1,1]=>105
[3,2,1,4,6,7,5]=>[3,2,1,1]=>420
[3,2,1,4,7,5,6]=>[3,2,1,1]=>420
[3,2,1,4,7,6,5]=>[2,2,1,1,1]=>105
[3,2,1,5,4,6,7]=>[2,2,1,1,1]=>105
[3,2,1,5,4,7,6]=>[2,2,2,1]=>105
[3,2,1,5,6,4,7]=>[3,2,1,1]=>420
[3,2,1,5,6,7,4]=>[4,2,1]=>630
[3,2,1,5,7,4,6]=>[4,2,1]=>630
[3,2,1,5,7,6,4]=>[3,2,1,1]=>420
[3,2,1,6,4,5,7]=>[3,2,1,1]=>420
[3,2,1,6,4,7,5]=>[4,2,1]=>630
[3,2,1,6,5,4,7]=>[2,2,1,1,1]=>105
[3,2,1,6,5,7,4]=>[3,2,1,1]=>420
[3,2,1,6,7,4,5]=>[2,2,2,1]=>105
[3,2,1,6,7,5,4]=>[4,2,1]=>630
[3,2,1,7,4,5,6]=>[4,2,1]=>630
[3,2,1,7,4,6,5]=>[3,2,1,1]=>420
[3,2,1,7,5,4,6]=>[3,2,1,1]=>420
[3,2,1,7,5,6,4]=>[2,2,1,1,1]=>105
[3,2,1,7,6,4,5]=>[4,2,1]=>630
[3,2,1,7,6,5,4]=>[2,2,2,1]=>105
[3,2,4,1,5,6,7]=>[3,1,1,1,1]=>70
[3,2,4,1,5,7,6]=>[3,2,1,1]=>420
[3,2,4,1,6,5,7]=>[3,2,1,1]=>420
[3,2,4,1,6,7,5]=>[3,3,1]=>280
[3,2,4,1,7,5,6]=>[3,3,1]=>280
[3,2,4,1,7,6,5]=>[3,2,1,1]=>420
[3,2,4,5,1,6,7]=>[4,1,1,1]=>210
[3,2,4,5,1,7,6]=>[4,2,1]=>630
[3,2,4,5,6,1,7]=>[5,1,1]=>504
[3,2,4,5,6,7,1]=>[6,1]=>840
[3,2,4,5,7,1,6]=>[6,1]=>840
[3,2,4,5,7,6,1]=>[5,1,1]=>504
[3,2,4,6,1,5,7]=>[5,1,1]=>504
[3,2,4,6,1,7,5]=>[6,1]=>840
[3,2,4,6,5,1,7]=>[4,1,1,1]=>210
[3,2,4,6,5,7,1]=>[5,1,1]=>504
[3,2,4,6,7,1,5]=>[4,2,1]=>630
[3,2,4,6,7,5,1]=>[6,1]=>840
[3,2,4,7,1,5,6]=>[6,1]=>840
[3,2,4,7,1,6,5]=>[5,1,1]=>504
[3,2,4,7,5,1,6]=>[5,1,1]=>504
[3,2,4,7,5,6,1]=>[4,1,1,1]=>210
[3,2,4,7,6,1,5]=>[6,1]=>840
[3,2,4,7,6,5,1]=>[4,2,1]=>630
[3,2,5,1,4,6,7]=>[4,1,1,1]=>210
[3,2,5,1,4,7,6]=>[4,2,1]=>630
[3,2,5,1,6,4,7]=>[5,1,1]=>504
[3,2,5,1,6,7,4]=>[6,1]=>840
[3,2,5,1,7,4,6]=>[6,1]=>840
[3,2,5,1,7,6,4]=>[5,1,1]=>504
[3,2,5,4,1,6,7]=>[3,1,1,1,1]=>70
[3,2,5,4,1,7,6]=>[3,2,1,1]=>420
[3,2,5,4,6,1,7]=>[4,1,1,1]=>210
[3,2,5,4,6,7,1]=>[5,1,1]=>504
[3,2,5,4,7,1,6]=>[5,1,1]=>504
[3,2,5,4,7,6,1]=>[4,1,1,1]=>210
[3,2,5,6,1,4,7]=>[3,2,1,1]=>420
[3,2,5,6,1,7,4]=>[3,3,1]=>280
[3,2,5,6,4,1,7]=>[5,1,1]=>504
[3,2,5,6,4,7,1]=>[6,1]=>840
[3,2,5,6,7,1,4]=>[6,1]=>840
[3,2,5,6,7,4,1]=>[4,2,1]=>630
[3,2,5,7,1,4,6]=>[3,3,1]=>280
[3,2,5,7,1,6,4]=>[3,2,1,1]=>420
[3,2,5,7,4,1,6]=>[6,1]=>840
[3,2,5,7,4,6,1]=>[5,1,1]=>504
[3,2,5,7,6,1,4]=>[4,2,1]=>630
[3,2,5,7,6,4,1]=>[6,1]=>840
[3,2,6,1,4,5,7]=>[5,1,1]=>504
[3,2,6,1,4,7,5]=>[6,1]=>840
[3,2,6,1,5,4,7]=>[4,1,1,1]=>210
[3,2,6,1,5,7,4]=>[5,1,1]=>504
[3,2,6,1,7,4,5]=>[4,2,1]=>630
[3,2,6,1,7,5,4]=>[6,1]=>840
[3,2,6,4,1,5,7]=>[4,1,1,1]=>210
[3,2,6,4,1,7,5]=>[5,1,1]=>504
[3,2,6,4,5,1,7]=>[3,1,1,1,1]=>70
[3,2,6,4,5,7,1]=>[4,1,1,1]=>210
[3,2,6,4,7,1,5]=>[3,2,1,1]=>420
[3,2,6,4,7,5,1]=>[5,1,1]=>504
[3,2,6,5,1,4,7]=>[5,1,1]=>504
[3,2,6,5,1,7,4]=>[6,1]=>840
[3,2,6,5,4,1,7]=>[3,2,1,1]=>420
[3,2,6,5,4,7,1]=>[4,2,1]=>630
[3,2,6,5,7,1,4]=>[3,3,1]=>280
[3,2,6,5,7,4,1]=>[6,1]=>840
[3,2,6,7,1,4,5]=>[6,1]=>840
[3,2,6,7,1,5,4]=>[4,2,1]=>630
[3,2,6,7,4,1,5]=>[3,3,1]=>280
[3,2,6,7,4,5,1]=>[6,1]=>840
[3,2,6,7,5,1,4]=>[3,2,1,1]=>420
[3,2,6,7,5,4,1]=>[5,1,1]=>504
[3,2,7,1,4,5,6]=>[6,1]=>840
[3,2,7,1,4,6,5]=>[5,1,1]=>504
[3,2,7,1,5,4,6]=>[5,1,1]=>504
[3,2,7,1,5,6,4]=>[4,1,1,1]=>210
[3,2,7,1,6,4,5]=>[6,1]=>840
[3,2,7,1,6,5,4]=>[4,2,1]=>630
[3,2,7,4,1,5,6]=>[5,1,1]=>504
[3,2,7,4,1,6,5]=>[4,1,1,1]=>210
[3,2,7,4,5,1,6]=>[4,1,1,1]=>210
[3,2,7,4,5,6,1]=>[3,1,1,1,1]=>70
[3,2,7,4,6,1,5]=>[5,1,1]=>504
[3,2,7,4,6,5,1]=>[3,2,1,1]=>420
[3,2,7,5,1,4,6]=>[6,1]=>840
[3,2,7,5,1,6,4]=>[5,1,1]=>504
[3,2,7,5,4,1,6]=>[4,2,1]=>630
[3,2,7,5,4,6,1]=>[3,2,1,1]=>420
[3,2,7,5,6,1,4]=>[6,1]=>840
[3,2,7,5,6,4,1]=>[3,3,1]=>280
[3,2,7,6,1,4,5]=>[4,2,1]=>630
[3,2,7,6,1,5,4]=>[6,1]=>840
[3,2,7,6,4,1,5]=>[6,1]=>840
[3,2,7,6,4,5,1]=>[3,3,1]=>280
[3,2,7,6,5,1,4]=>[5,1,1]=>504
[3,2,7,6,5,4,1]=>[3,2,1,1]=>420
[3,4,1,2,5,6,7]=>[2,2,1,1,1]=>105
[3,4,1,2,5,7,6]=>[2,2,2,1]=>105
[3,4,1,2,6,5,7]=>[2,2,2,1]=>105
[3,4,1,2,6,7,5]=>[3,2,2]=>210
[3,4,1,2,7,5,6]=>[3,2,2]=>210
[3,4,1,2,7,6,5]=>[2,2,2,1]=>105
[3,4,1,5,2,6,7]=>[3,2,1,1]=>420
[3,4,1,5,2,7,6]=>[3,2,2]=>210
[3,4,1,5,6,2,7]=>[4,2,1]=>630
[3,4,1,5,6,7,2]=>[5,2]=>504
[3,4,1,5,7,2,6]=>[5,2]=>504
[3,4,1,5,7,6,2]=>[4,2,1]=>630
[3,4,1,6,2,5,7]=>[4,2,1]=>630
[3,4,1,6,2,7,5]=>[5,2]=>504
[3,4,1,6,5,2,7]=>[3,2,1,1]=>420
[3,4,1,6,5,7,2]=>[4,2,1]=>630
[3,4,1,6,7,2,5]=>[3,2,2]=>210
[3,4,1,6,7,5,2]=>[5,2]=>504
[3,4,1,7,2,5,6]=>[5,2]=>504
[3,4,1,7,2,6,5]=>[4,2,1]=>630
[3,4,1,7,5,2,6]=>[4,2,1]=>630
[3,4,1,7,5,6,2]=>[3,2,1,1]=>420
[3,4,1,7,6,2,5]=>[5,2]=>504
[3,4,1,7,6,5,2]=>[3,2,2]=>210
[3,4,2,1,5,6,7]=>[4,1,1,1]=>210
[3,4,2,1,5,7,6]=>[4,2,1]=>630
[3,4,2,1,6,5,7]=>[4,2,1]=>630
[3,4,2,1,6,7,5]=>[4,3]=>420
[3,4,2,1,7,5,6]=>[4,3]=>420
[3,4,2,1,7,6,5]=>[4,2,1]=>630
[3,4,2,5,1,6,7]=>[5,1,1]=>504
[3,4,2,5,1,7,6]=>[5,2]=>504
[3,4,2,5,6,1,7]=>[6,1]=>840
[3,4,2,5,6,7,1]=>[7]=>720
[3,4,2,5,7,1,6]=>[7]=>720
[3,4,2,5,7,6,1]=>[6,1]=>840
[3,4,2,6,1,5,7]=>[6,1]=>840
[3,4,2,6,1,7,5]=>[7]=>720
[3,4,2,6,5,1,7]=>[5,1,1]=>504
[3,4,2,6,5,7,1]=>[6,1]=>840
[3,4,2,6,7,1,5]=>[5,2]=>504
[3,4,2,6,7,5,1]=>[7]=>720
[3,4,2,7,1,5,6]=>[7]=>720
[3,4,2,7,1,6,5]=>[6,1]=>840
[3,4,2,7,5,1,6]=>[6,1]=>840
[3,4,2,7,5,6,1]=>[5,1,1]=>504
[3,4,2,7,6,1,5]=>[7]=>720
[3,4,2,7,6,5,1]=>[5,2]=>504
[3,4,5,1,2,6,7]=>[5,1,1]=>504
[3,4,5,1,2,7,6]=>[5,2]=>504
[3,4,5,1,6,2,7]=>[6,1]=>840
[3,4,5,1,6,7,2]=>[7]=>720
[3,4,5,1,7,2,6]=>[7]=>720
[3,4,5,1,7,6,2]=>[6,1]=>840
[3,4,5,2,1,6,7]=>[3,2,1,1]=>420
[3,4,5,2,1,7,6]=>[3,2,2]=>210
[3,4,5,2,6,1,7]=>[4,2,1]=>630
[3,4,5,2,6,7,1]=>[5,2]=>504
[3,4,5,2,7,1,6]=>[5,2]=>504
[3,4,5,2,7,6,1]=>[4,2,1]=>630
[3,4,5,6,1,2,7]=>[3,3,1]=>280
[3,4,5,6,1,7,2]=>[4,3]=>420
[3,4,5,6,2,1,7]=>[6,1]=>840
[3,4,5,6,2,7,1]=>[7]=>720
[3,4,5,6,7,1,2]=>[7]=>720
[3,4,5,6,7,2,1]=>[4,3]=>420
[3,4,5,7,1,2,6]=>[4,3]=>420
[3,4,5,7,1,6,2]=>[3,3,1]=>280
[3,4,5,7,2,1,6]=>[7]=>720
[3,4,5,7,2,6,1]=>[6,1]=>840
[3,4,5,7,6,1,2]=>[4,3]=>420
[3,4,5,7,6,2,1]=>[7]=>720
[3,4,6,1,2,5,7]=>[6,1]=>840
[3,4,6,1,2,7,5]=>[7]=>720
[3,4,6,1,5,2,7]=>[5,1,1]=>504
[3,4,6,1,5,7,2]=>[6,1]=>840
[3,4,6,1,7,2,5]=>[5,2]=>504
[3,4,6,1,7,5,2]=>[7]=>720
[3,4,6,2,1,5,7]=>[4,2,1]=>630
[3,4,6,2,1,7,5]=>[5,2]=>504
[3,4,6,2,5,1,7]=>[3,2,1,1]=>420
[3,4,6,2,5,7,1]=>[4,2,1]=>630
[3,4,6,2,7,1,5]=>[3,2,2]=>210
[3,4,6,2,7,5,1]=>[5,2]=>504
[3,4,6,5,1,2,7]=>[6,1]=>840
[3,4,6,5,1,7,2]=>[7]=>720
[3,4,6,5,2,1,7]=>[3,3,1]=>280
[3,4,6,5,2,7,1]=>[4,3]=>420
[3,4,6,5,7,1,2]=>[4,3]=>420
[3,4,6,5,7,2,1]=>[7]=>720
[3,4,6,7,1,2,5]=>[7]=>720
[3,4,6,7,1,5,2]=>[4,3]=>420
[3,4,6,7,2,1,5]=>[4,3]=>420
[3,4,6,7,2,5,1]=>[7]=>720
[3,4,6,7,5,1,2]=>[3,3,1]=>280
[3,4,6,7,5,2,1]=>[6,1]=>840
[3,4,7,1,2,5,6]=>[7]=>720
[3,4,7,1,2,6,5]=>[6,1]=>840
[3,4,7,1,5,2,6]=>[6,1]=>840
[3,4,7,1,5,6,2]=>[5,1,1]=>504
[3,4,7,1,6,2,5]=>[7]=>720
[3,4,7,1,6,5,2]=>[5,2]=>504
[3,4,7,2,1,5,6]=>[5,2]=>504
[3,4,7,2,1,6,5]=>[4,2,1]=>630
[3,4,7,2,5,1,6]=>[4,2,1]=>630
[3,4,7,2,5,6,1]=>[3,2,1,1]=>420
[3,4,7,2,6,1,5]=>[5,2]=>504
[3,4,7,2,6,5,1]=>[3,2,2]=>210
[3,4,7,5,1,2,6]=>[7]=>720
[3,4,7,5,1,6,2]=>[6,1]=>840
[3,4,7,5,2,1,6]=>[4,3]=>420
[3,4,7,5,2,6,1]=>[3,3,1]=>280
[3,4,7,5,6,1,2]=>[7]=>720
[3,4,7,5,6,2,1]=>[4,3]=>420
[3,4,7,6,1,2,5]=>[4,3]=>420
[3,4,7,6,1,5,2]=>[7]=>720
[3,4,7,6,2,1,5]=>[7]=>720
[3,4,7,6,2,5,1]=>[4,3]=>420
[3,4,7,6,5,1,2]=>[6,1]=>840
[3,4,7,6,5,2,1]=>[3,3,1]=>280
[3,5,1,2,4,6,7]=>[3,2,1,1]=>420
[3,5,1,2,4,7,6]=>[3,2,2]=>210
[3,5,1,2,6,4,7]=>[4,2,1]=>630
[3,5,1,2,6,7,4]=>[5,2]=>504
[3,5,1,2,7,4,6]=>[5,2]=>504
[3,5,1,2,7,6,4]=>[4,2,1]=>630
[3,5,1,4,2,6,7]=>[2,2,1,1,1]=>105
[3,5,1,4,2,7,6]=>[2,2,2,1]=>105
[3,5,1,4,6,2,7]=>[3,2,1,1]=>420
[3,5,1,4,6,7,2]=>[4,2,1]=>630
[3,5,1,4,7,2,6]=>[4,2,1]=>630
[3,5,1,4,7,6,2]=>[3,2,1,1]=>420
[3,5,1,6,2,4,7]=>[2,2,2,1]=>105
[3,5,1,6,2,7,4]=>[3,2,2]=>210
[3,5,1,6,4,2,7]=>[4,2,1]=>630
[3,5,1,6,4,7,2]=>[5,2]=>504
[3,5,1,6,7,2,4]=>[5,2]=>504
[3,5,1,6,7,4,2]=>[3,2,2]=>210
[3,5,1,7,2,4,6]=>[3,2,2]=>210
[3,5,1,7,2,6,4]=>[2,2,2,1]=>105
[3,5,1,7,4,2,6]=>[5,2]=>504
[3,5,1,7,4,6,2]=>[4,2,1]=>630
[3,5,1,7,6,2,4]=>[3,2,2]=>210
[3,5,1,7,6,4,2]=>[5,2]=>504
[3,5,2,1,4,6,7]=>[5,1,1]=>504
[3,5,2,1,4,7,6]=>[5,2]=>504
[3,5,2,1,6,4,7]=>[6,1]=>840
[3,5,2,1,6,7,4]=>[7]=>720
[3,5,2,1,7,4,6]=>[7]=>720
[3,5,2,1,7,6,4]=>[6,1]=>840
[3,5,2,4,1,6,7]=>[4,1,1,1]=>210
[3,5,2,4,1,7,6]=>[4,2,1]=>630
[3,5,2,4,6,1,7]=>[5,1,1]=>504
[3,5,2,4,6,7,1]=>[6,1]=>840
[3,5,2,4,7,1,6]=>[6,1]=>840
[3,5,2,4,7,6,1]=>[5,1,1]=>504
[3,5,2,6,1,4,7]=>[4,2,1]=>630
[3,5,2,6,1,7,4]=>[4,3]=>420
[3,5,2,6,4,1,7]=>[6,1]=>840
[3,5,2,6,4,7,1]=>[7]=>720
[3,5,2,6,7,1,4]=>[7]=>720
[3,5,2,6,7,4,1]=>[5,2]=>504
[3,5,2,7,1,4,6]=>[4,3]=>420
[3,5,2,7,1,6,4]=>[4,2,1]=>630
[3,5,2,7,4,1,6]=>[7]=>720
[3,5,2,7,4,6,1]=>[6,1]=>840
[3,5,2,7,6,1,4]=>[5,2]=>504
[3,5,2,7,6,4,1]=>[7]=>720
[3,5,4,1,2,6,7]=>[3,2,1,1]=>420
[3,5,4,1,2,7,6]=>[3,2,2]=>210
[3,5,4,1,6,2,7]=>[3,3,1]=>280
[3,5,4,1,6,7,2]=>[4,3]=>420
[3,5,4,1,7,2,6]=>[4,3]=>420
[3,5,4,1,7,6,2]=>[3,3,1]=>280
[3,5,4,2,1,6,7]=>[5,1,1]=>504
[3,5,4,2,1,7,6]=>[5,2]=>504
[3,5,4,2,6,1,7]=>[6,1]=>840
[3,5,4,2,6,7,1]=>[7]=>720
[3,5,4,2,7,1,6]=>[7]=>720
[3,5,4,2,7,6,1]=>[6,1]=>840
[3,5,4,6,1,2,7]=>[6,1]=>840
[3,5,4,6,1,7,2]=>[7]=>720
[3,5,4,6,2,1,7]=>[4,2,1]=>630
[3,5,4,6,2,7,1]=>[5,2]=>504
[3,5,4,6,7,1,2]=>[4,3]=>420
[3,5,4,6,7,2,1]=>[7]=>720
[3,5,4,7,1,2,6]=>[7]=>720
[3,5,4,7,1,6,2]=>[6,1]=>840
[3,5,4,7,2,1,6]=>[5,2]=>504
[3,5,4,7,2,6,1]=>[4,2,1]=>630
[3,5,4,7,6,1,2]=>[7]=>720
[3,5,4,7,6,2,1]=>[4,3]=>420
[3,5,6,1,2,4,7]=>[4,2,1]=>630
[3,5,6,1,2,7,4]=>[5,2]=>504
[3,5,6,1,4,2,7]=>[6,1]=>840
[3,5,6,1,4,7,2]=>[7]=>720
[3,5,6,1,7,2,4]=>[7]=>720
[3,5,6,1,7,4,2]=>[4,3]=>420
[3,5,6,2,1,4,7]=>[6,1]=>840
[3,5,6,2,1,7,4]=>[7]=>720
[3,5,6,2,4,1,7]=>[3,3,1]=>280
[3,5,6,2,4,7,1]=>[4,3]=>420
[3,5,6,2,7,1,4]=>[4,3]=>420
[3,5,6,2,7,4,1]=>[7]=>720
[3,5,6,4,1,2,7]=>[5,1,1]=>504
[3,5,6,4,1,7,2]=>[6,1]=>840
[3,5,6,4,2,1,7]=>[3,2,1,1]=>420
[3,5,6,4,2,7,1]=>[4,2,1]=>630
[3,5,6,4,7,1,2]=>[3,3,1]=>280
[3,5,6,4,7,2,1]=>[6,1]=>840
[3,5,6,7,1,2,4]=>[5,2]=>504
[3,5,6,7,1,4,2]=>[7]=>720
[3,5,6,7,2,1,4]=>[3,2,2]=>210
[3,5,6,7,2,4,1]=>[5,2]=>504
[3,5,6,7,4,1,2]=>[4,3]=>420
[3,5,6,7,4,2,1]=>[7]=>720
[3,5,7,1,2,4,6]=>[5,2]=>504
[3,5,7,1,2,6,4]=>[4,2,1]=>630
[3,5,7,1,4,2,6]=>[7]=>720
[3,5,7,1,4,6,2]=>[6,1]=>840
[3,5,7,1,6,2,4]=>[4,3]=>420
[3,5,7,1,6,4,2]=>[7]=>720
[3,5,7,2,1,4,6]=>[7]=>720
[3,5,7,2,1,6,4]=>[6,1]=>840
[3,5,7,2,4,1,6]=>[4,3]=>420
[3,5,7,2,4,6,1]=>[3,3,1]=>280
[3,5,7,2,6,1,4]=>[7]=>720
[3,5,7,2,6,4,1]=>[4,3]=>420
[3,5,7,4,1,2,6]=>[6,1]=>840
[3,5,7,4,1,6,2]=>[5,1,1]=>504
[3,5,7,4,2,1,6]=>[4,2,1]=>630
[3,5,7,4,2,6,1]=>[3,2,1,1]=>420
[3,5,7,4,6,1,2]=>[6,1]=>840
[3,5,7,4,6,2,1]=>[3,3,1]=>280
[3,5,7,6,1,2,4]=>[7]=>720
[3,5,7,6,1,4,2]=>[5,2]=>504
[3,5,7,6,2,1,4]=>[5,2]=>504
[3,5,7,6,2,4,1]=>[3,2,2]=>210
[3,5,7,6,4,1,2]=>[7]=>720
[3,5,7,6,4,2,1]=>[4,3]=>420
[3,6,1,2,4,5,7]=>[4,2,1]=>630
[3,6,1,2,4,7,5]=>[5,2]=>504
[3,6,1,2,5,4,7]=>[3,2,1,1]=>420
[3,6,1,2,5,7,4]=>[4,2,1]=>630
[3,6,1,2,7,4,5]=>[3,2,2]=>210
[3,6,1,2,7,5,4]=>[5,2]=>504
[3,6,1,4,2,5,7]=>[3,2,1,1]=>420
[3,6,1,4,2,7,5]=>[4,2,1]=>630
[3,6,1,4,5,2,7]=>[2,2,1,1,1]=>105
[3,6,1,4,5,7,2]=>[3,2,1,1]=>420
[3,6,1,4,7,2,5]=>[2,2,2,1]=>105
[3,6,1,4,7,5,2]=>[4,2,1]=>630
[3,6,1,5,2,4,7]=>[4,2,1]=>630
[3,6,1,5,2,7,4]=>[5,2]=>504
[3,6,1,5,4,2,7]=>[2,2,2,1]=>105
[3,6,1,5,4,7,2]=>[3,2,2]=>210
[3,6,1,5,7,2,4]=>[3,2,2]=>210
[3,6,1,5,7,4,2]=>[5,2]=>504
[3,6,1,7,2,4,5]=>[5,2]=>504
[3,6,1,7,2,5,4]=>[3,2,2]=>210
[3,6,1,7,4,2,5]=>[3,2,2]=>210
[3,6,1,7,4,5,2]=>[5,2]=>504
[3,6,1,7,5,2,4]=>[2,2,2,1]=>105
[3,6,1,7,5,4,2]=>[4,2,1]=>630
[3,6,2,1,4,5,7]=>[6,1]=>840
[3,6,2,1,4,7,5]=>[7]=>720
[3,6,2,1,5,4,7]=>[5,1,1]=>504
[3,6,2,1,5,7,4]=>[6,1]=>840
[3,6,2,1,7,4,5]=>[5,2]=>504
[3,6,2,1,7,5,4]=>[7]=>720
[3,6,2,4,1,5,7]=>[5,1,1]=>504
[3,6,2,4,1,7,5]=>[6,1]=>840
[3,6,2,4,5,1,7]=>[4,1,1,1]=>210
[3,6,2,4,5,7,1]=>[5,1,1]=>504
[3,6,2,4,7,1,5]=>[4,2,1]=>630
[3,6,2,4,7,5,1]=>[6,1]=>840
[3,6,2,5,1,4,7]=>[6,1]=>840
[3,6,2,5,1,7,4]=>[7]=>720
[3,6,2,5,4,1,7]=>[4,2,1]=>630
[3,6,2,5,4,7,1]=>[5,2]=>504
[3,6,2,5,7,1,4]=>[4,3]=>420
[3,6,2,5,7,4,1]=>[7]=>720
[3,6,2,7,1,4,5]=>[7]=>720
[3,6,2,7,1,5,4]=>[5,2]=>504
[3,6,2,7,4,1,5]=>[4,3]=>420
[3,6,2,7,4,5,1]=>[7]=>720
[3,6,2,7,5,1,4]=>[4,2,1]=>630
[3,6,2,7,5,4,1]=>[6,1]=>840
[3,6,4,1,2,5,7]=>[3,3,1]=>280
[3,6,4,1,2,7,5]=>[4,3]=>420
[3,6,4,1,5,2,7]=>[3,2,1,1]=>420
[3,6,4,1,5,7,2]=>[3,3,1]=>280
[3,6,4,1,7,2,5]=>[3,2,2]=>210
[3,6,4,1,7,5,2]=>[4,3]=>420
[3,6,4,2,1,5,7]=>[6,1]=>840
[3,6,4,2,1,7,5]=>[7]=>720
[3,6,4,2,5,1,7]=>[5,1,1]=>504
[3,6,4,2,5,7,1]=>[6,1]=>840
[3,6,4,2,7,1,5]=>[5,2]=>504
[3,6,4,2,7,5,1]=>[7]=>720
[3,6,4,5,1,2,7]=>[4,2,1]=>630
[3,6,4,5,1,7,2]=>[4,3]=>420
[3,6,4,5,2,1,7]=>[6,1]=>840
[3,6,4,5,2,7,1]=>[7]=>720
[3,6,4,5,7,1,2]=>[7]=>720
[3,6,4,5,7,2,1]=>[5,2]=>504
[3,6,4,7,1,2,5]=>[5,2]=>504
[3,6,4,7,1,5,2]=>[7]=>720
[3,6,4,7,2,1,5]=>[7]=>720
[3,6,4,7,2,5,1]=>[4,3]=>420
[3,6,4,7,5,1,2]=>[6,1]=>840
[3,6,4,7,5,2,1]=>[4,2,1]=>630
[3,6,5,1,2,4,7]=>[6,1]=>840
[3,6,5,1,2,7,4]=>[7]=>720
[3,6,5,1,4,2,7]=>[4,2,1]=>630
[3,6,5,1,4,7,2]=>[4,3]=>420
[3,6,5,1,7,2,4]=>[5,2]=>504
[3,6,5,1,7,4,2]=>[7]=>720
[3,6,5,2,1,4,7]=>[3,3,1]=>280
[3,6,5,2,1,7,4]=>[4,3]=>420
[3,6,5,2,4,1,7]=>[6,1]=>840
[3,6,5,2,4,7,1]=>[7]=>720
[3,6,5,2,7,1,4]=>[7]=>720
[3,6,5,2,7,4,1]=>[4,3]=>420
[3,6,5,4,1,2,7]=>[3,2,1,1]=>420
[3,6,5,4,1,7,2]=>[3,3,1]=>280
[3,6,5,4,2,1,7]=>[5,1,1]=>504
[3,6,5,4,2,7,1]=>[6,1]=>840
[3,6,5,4,7,1,2]=>[6,1]=>840
[3,6,5,4,7,2,1]=>[4,2,1]=>630
[3,6,5,7,1,2,4]=>[3,2,2]=>210
[3,6,5,7,1,4,2]=>[4,3]=>420
[3,6,5,7,2,1,4]=>[5,2]=>504
[3,6,5,7,2,4,1]=>[7]=>720
[3,6,5,7,4,1,2]=>[7]=>720
[3,6,5,7,4,2,1]=>[5,2]=>504
[3,6,7,1,2,4,5]=>[7]=>720
[3,6,7,1,2,5,4]=>[4,3]=>420
[3,6,7,1,4,2,5]=>[5,2]=>504
[3,6,7,1,4,5,2]=>[7]=>720
[3,6,7,1,5,2,4]=>[4,2,1]=>630
[3,6,7,1,5,4,2]=>[6,1]=>840
[3,6,7,2,1,4,5]=>[4,3]=>420
[3,6,7,2,1,5,4]=>[7]=>720
[3,6,7,2,4,1,5]=>[7]=>720
[3,6,7,2,4,5,1]=>[4,3]=>420
[3,6,7,2,5,1,4]=>[6,1]=>840
[3,6,7,2,5,4,1]=>[3,3,1]=>280
[3,6,7,4,1,2,5]=>[4,2,1]=>630
[3,6,7,4,1,5,2]=>[6,1]=>840
[3,6,7,4,2,1,5]=>[6,1]=>840
[3,6,7,4,2,5,1]=>[3,3,1]=>280
[3,6,7,4,5,1,2]=>[5,1,1]=>504
[3,6,7,4,5,2,1]=>[3,2,1,1]=>420
[3,6,7,5,1,2,4]=>[5,2]=>504
[3,6,7,5,1,4,2]=>[7]=>720
[3,6,7,5,2,1,4]=>[7]=>720
[3,6,7,5,2,4,1]=>[4,3]=>420
[3,6,7,5,4,1,2]=>[5,2]=>504
[3,6,7,5,4,2,1]=>[3,2,2]=>210
[3,7,1,2,4,5,6]=>[5,2]=>504
[3,7,1,2,4,6,5]=>[4,2,1]=>630
[3,7,1,2,5,4,6]=>[4,2,1]=>630
[3,7,1,2,5,6,4]=>[3,2,1,1]=>420
[3,7,1,2,6,4,5]=>[5,2]=>504
[3,7,1,2,6,5,4]=>[3,2,2]=>210
[3,7,1,4,2,5,6]=>[4,2,1]=>630
[3,7,1,4,2,6,5]=>[3,2,1,1]=>420
[3,7,1,4,5,2,6]=>[3,2,1,1]=>420
[3,7,1,4,5,6,2]=>[2,2,1,1,1]=>105
[3,7,1,4,6,2,5]=>[4,2,1]=>630
[3,7,1,4,6,5,2]=>[2,2,2,1]=>105
[3,7,1,5,2,4,6]=>[5,2]=>504
[3,7,1,5,2,6,4]=>[4,2,1]=>630
[3,7,1,5,4,2,6]=>[3,2,2]=>210
[3,7,1,5,4,6,2]=>[2,2,2,1]=>105
[3,7,1,5,6,2,4]=>[5,2]=>504
[3,7,1,5,6,4,2]=>[3,2,2]=>210
[3,7,1,6,2,4,5]=>[3,2,2]=>210
[3,7,1,6,2,5,4]=>[5,2]=>504
[3,7,1,6,4,2,5]=>[5,2]=>504
[3,7,1,6,4,5,2]=>[3,2,2]=>210
[3,7,1,6,5,2,4]=>[4,2,1]=>630
[3,7,1,6,5,4,2]=>[2,2,2,1]=>105
[3,7,2,1,4,5,6]=>[7]=>720
[3,7,2,1,4,6,5]=>[6,1]=>840
[3,7,2,1,5,4,6]=>[6,1]=>840
[3,7,2,1,5,6,4]=>[5,1,1]=>504
[3,7,2,1,6,4,5]=>[7]=>720
[3,7,2,1,6,5,4]=>[5,2]=>504
[3,7,2,4,1,5,6]=>[6,1]=>840
[3,7,2,4,1,6,5]=>[5,1,1]=>504
[3,7,2,4,5,1,6]=>[5,1,1]=>504
[3,7,2,4,5,6,1]=>[4,1,1,1]=>210
[3,7,2,4,6,1,5]=>[6,1]=>840
[3,7,2,4,6,5,1]=>[4,2,1]=>630
[3,7,2,5,1,4,6]=>[7]=>720
[3,7,2,5,1,6,4]=>[6,1]=>840
[3,7,2,5,4,1,6]=>[5,2]=>504
[3,7,2,5,4,6,1]=>[4,2,1]=>630
[3,7,2,5,6,1,4]=>[7]=>720
[3,7,2,5,6,4,1]=>[4,3]=>420
[3,7,2,6,1,4,5]=>[5,2]=>504
[3,7,2,6,1,5,4]=>[7]=>720
[3,7,2,6,4,1,5]=>[7]=>720
[3,7,2,6,4,5,1]=>[4,3]=>420
[3,7,2,6,5,1,4]=>[6,1]=>840
[3,7,2,6,5,4,1]=>[4,2,1]=>630
[3,7,4,1,2,5,6]=>[4,3]=>420
[3,7,4,1,2,6,5]=>[3,3,1]=>280
[3,7,4,1,5,2,6]=>[3,3,1]=>280
[3,7,4,1,5,6,2]=>[3,2,1,1]=>420
[3,7,4,1,6,2,5]=>[4,3]=>420
[3,7,4,1,6,5,2]=>[3,2,2]=>210
[3,7,4,2,1,5,6]=>[7]=>720
[3,7,4,2,1,6,5]=>[6,1]=>840
[3,7,4,2,5,1,6]=>[6,1]=>840
[3,7,4,2,5,6,1]=>[5,1,1]=>504
[3,7,4,2,6,1,5]=>[7]=>720
[3,7,4,2,6,5,1]=>[5,2]=>504
[3,7,4,5,1,2,6]=>[4,3]=>420
[3,7,4,5,1,6,2]=>[4,2,1]=>630
[3,7,4,5,2,1,6]=>[7]=>720
[3,7,4,5,2,6,1]=>[6,1]=>840
[3,7,4,5,6,1,2]=>[5,2]=>504
[3,7,4,5,6,2,1]=>[7]=>720
[3,7,4,6,1,2,5]=>[7]=>720
[3,7,4,6,1,5,2]=>[5,2]=>504
[3,7,4,6,2,1,5]=>[4,3]=>420
[3,7,4,6,2,5,1]=>[7]=>720
[3,7,4,6,5,1,2]=>[4,2,1]=>630
[3,7,4,6,5,2,1]=>[6,1]=>840
[3,7,5,1,2,4,6]=>[7]=>720
[3,7,5,1,2,6,4]=>[6,1]=>840
[3,7,5,1,4,2,6]=>[4,3]=>420
[3,7,5,1,4,6,2]=>[4,2,1]=>630
[3,7,5,1,6,2,4]=>[7]=>720
[3,7,5,1,6,4,2]=>[5,2]=>504
[3,7,5,2,1,4,6]=>[4,3]=>420
[3,7,5,2,1,6,4]=>[3,3,1]=>280
[3,7,5,2,4,1,6]=>[7]=>720
[3,7,5,2,4,6,1]=>[6,1]=>840
[3,7,5,2,6,1,4]=>[4,3]=>420
[3,7,5,2,6,4,1]=>[7]=>720
[3,7,5,4,1,2,6]=>[3,3,1]=>280
[3,7,5,4,1,6,2]=>[3,2,1,1]=>420
[3,7,5,4,2,1,6]=>[6,1]=>840
[3,7,5,4,2,6,1]=>[5,1,1]=>504
[3,7,5,4,6,1,2]=>[4,2,1]=>630
[3,7,5,4,6,2,1]=>[6,1]=>840
[3,7,5,6,1,2,4]=>[4,3]=>420
[3,7,5,6,1,4,2]=>[3,2,2]=>210
[3,7,5,6,2,1,4]=>[7]=>720
[3,7,5,6,2,4,1]=>[5,2]=>504
[3,7,5,6,4,1,2]=>[5,2]=>504
[3,7,5,6,4,2,1]=>[7]=>720
[3,7,6,1,2,4,5]=>[4,3]=>420
[3,7,6,1,2,5,4]=>[7]=>720
[3,7,6,1,4,2,5]=>[7]=>720
[3,7,6,1,4,5,2]=>[5,2]=>504
[3,7,6,1,5,2,4]=>[6,1]=>840
[3,7,6,1,5,4,2]=>[4,2,1]=>630
[3,7,6,2,1,4,5]=>[7]=>720
[3,7,6,2,1,5,4]=>[4,3]=>420
[3,7,6,2,4,1,5]=>[4,3]=>420
[3,7,6,2,4,5,1]=>[7]=>720
[3,7,6,2,5,1,4]=>[3,3,1]=>280
[3,7,6,2,5,4,1]=>[6,1]=>840
[3,7,6,4,1,2,5]=>[6,1]=>840
[3,7,6,4,1,5,2]=>[4,2,1]=>630
[3,7,6,4,2,1,5]=>[3,3,1]=>280
[3,7,6,4,2,5,1]=>[6,1]=>840
[3,7,6,4,5,1,2]=>[3,2,1,1]=>420
[3,7,6,4,5,2,1]=>[5,1,1]=>504
[3,7,6,5,1,2,4]=>[7]=>720
[3,7,6,5,1,4,2]=>[5,2]=>504
[3,7,6,5,2,1,4]=>[4,3]=>420
[3,7,6,5,2,4,1]=>[7]=>720
[3,7,6,5,4,1,2]=>[3,2,2]=>210
[3,7,6,5,4,2,1]=>[5,2]=>504
[4,1,2,3,5,6,7]=>[4,1,1,1]=>210
[4,1,2,3,5,7,6]=>[4,2,1]=>630
[4,1,2,3,6,5,7]=>[4,2,1]=>630
[4,1,2,3,6,7,5]=>[4,3]=>420
[4,1,2,3,7,5,6]=>[4,3]=>420
[4,1,2,3,7,6,5]=>[4,2,1]=>630
[4,1,2,5,3,6,7]=>[5,1,1]=>504
[4,1,2,5,3,7,6]=>[5,2]=>504
[4,1,2,5,6,3,7]=>[6,1]=>840
[4,1,2,5,6,7,3]=>[7]=>720
[4,1,2,5,7,3,6]=>[7]=>720
[4,1,2,5,7,6,3]=>[6,1]=>840
[4,1,2,6,3,5,7]=>[6,1]=>840
[4,1,2,6,3,7,5]=>[7]=>720
[4,1,2,6,5,3,7]=>[5,1,1]=>504
[4,1,2,6,5,7,3]=>[6,1]=>840
[4,1,2,6,7,3,5]=>[5,2]=>504
[4,1,2,6,7,5,3]=>[7]=>720
[4,1,2,7,3,5,6]=>[7]=>720
[4,1,2,7,3,6,5]=>[6,1]=>840
[4,1,2,7,5,3,6]=>[6,1]=>840
[4,1,2,7,5,6,3]=>[5,1,1]=>504
[4,1,2,7,6,3,5]=>[7]=>720
[4,1,2,7,6,5,3]=>[5,2]=>504
[4,1,3,2,5,6,7]=>[3,1,1,1,1]=>70
[4,1,3,2,5,7,6]=>[3,2,1,1]=>420
[4,1,3,2,6,5,7]=>[3,2,1,1]=>420
[4,1,3,2,6,7,5]=>[3,3,1]=>280
[4,1,3,2,7,5,6]=>[3,3,1]=>280
[4,1,3,2,7,6,5]=>[3,2,1,1]=>420
[4,1,3,5,2,6,7]=>[4,1,1,1]=>210
[4,1,3,5,2,7,6]=>[4,2,1]=>630
[4,1,3,5,6,2,7]=>[5,1,1]=>504
[4,1,3,5,6,7,2]=>[6,1]=>840
[4,1,3,5,7,2,6]=>[6,1]=>840
[4,1,3,5,7,6,2]=>[5,1,1]=>504
[4,1,3,6,2,5,7]=>[5,1,1]=>504
[4,1,3,6,2,7,5]=>[6,1]=>840
[4,1,3,6,5,2,7]=>[4,1,1,1]=>210
[4,1,3,6,5,7,2]=>[5,1,1]=>504
[4,1,3,6,7,2,5]=>[4,2,1]=>630
[4,1,3,6,7,5,2]=>[6,1]=>840
[4,1,3,7,2,5,6]=>[6,1]=>840
[4,1,3,7,2,6,5]=>[5,1,1]=>504
[4,1,3,7,5,2,6]=>[5,1,1]=>504
[4,1,3,7,5,6,2]=>[4,1,1,1]=>210
[4,1,3,7,6,2,5]=>[6,1]=>840
[4,1,3,7,6,5,2]=>[4,2,1]=>630
[4,1,5,2,3,6,7]=>[3,2,1,1]=>420
[4,1,5,2,3,7,6]=>[3,2,2]=>210
[4,1,5,2,6,3,7]=>[3,3,1]=>280
[4,1,5,2,6,7,3]=>[4,3]=>420
[4,1,5,2,7,3,6]=>[4,3]=>420
[4,1,5,2,7,6,3]=>[3,3,1]=>280
[4,1,5,3,2,6,7]=>[5,1,1]=>504
[4,1,5,3,2,7,6]=>[5,2]=>504
[4,1,5,3,6,2,7]=>[6,1]=>840
[4,1,5,3,6,7,2]=>[7]=>720
[4,1,5,3,7,2,6]=>[7]=>720
[4,1,5,3,7,6,2]=>[6,1]=>840
[4,1,5,6,2,3,7]=>[6,1]=>840
[4,1,5,6,2,7,3]=>[7]=>720
[4,1,5,6,3,2,7]=>[4,2,1]=>630
[4,1,5,6,3,7,2]=>[5,2]=>504
[4,1,5,6,7,2,3]=>[4,3]=>420
[4,1,5,6,7,3,2]=>[7]=>720
[4,1,5,7,2,3,6]=>[7]=>720
[4,1,5,7,2,6,3]=>[6,1]=>840
[4,1,5,7,3,2,6]=>[5,2]=>504
[4,1,5,7,3,6,2]=>[4,2,1]=>630
[4,1,5,7,6,2,3]=>[7]=>720
[4,1,5,7,6,3,2]=>[4,3]=>420
[4,1,6,2,3,5,7]=>[3,3,1]=>280
[4,1,6,2,3,7,5]=>[4,3]=>420
[4,1,6,2,5,3,7]=>[3,2,1,1]=>420
[4,1,6,2,5,7,3]=>[3,3,1]=>280
[4,1,6,2,7,3,5]=>[3,2,2]=>210
[4,1,6,2,7,5,3]=>[4,3]=>420
[4,1,6,3,2,5,7]=>[6,1]=>840
[4,1,6,3,2,7,5]=>[7]=>720
[4,1,6,3,5,2,7]=>[5,1,1]=>504
[4,1,6,3,5,7,2]=>[6,1]=>840
[4,1,6,3,7,2,5]=>[5,2]=>504
[4,1,6,3,7,5,2]=>[7]=>720
[4,1,6,5,2,3,7]=>[4,2,1]=>630
[4,1,6,5,2,7,3]=>[4,3]=>420
[4,1,6,5,3,2,7]=>[6,1]=>840
[4,1,6,5,3,7,2]=>[7]=>720
[4,1,6,5,7,2,3]=>[7]=>720
[4,1,6,5,7,3,2]=>[5,2]=>504
[4,1,6,7,2,3,5]=>[5,2]=>504
[4,1,6,7,2,5,3]=>[7]=>720
[4,1,6,7,3,2,5]=>[7]=>720
[4,1,6,7,3,5,2]=>[4,3]=>420
[4,1,6,7,5,2,3]=>[6,1]=>840
[4,1,6,7,5,3,2]=>[4,2,1]=>630
[4,1,7,2,3,5,6]=>[4,3]=>420
[4,1,7,2,3,6,5]=>[3,3,1]=>280
[4,1,7,2,5,3,6]=>[3,3,1]=>280
[4,1,7,2,5,6,3]=>[3,2,1,1]=>420
[4,1,7,2,6,3,5]=>[4,3]=>420
[4,1,7,2,6,5,3]=>[3,2,2]=>210
[4,1,7,3,2,5,6]=>[7]=>720
[4,1,7,3,2,6,5]=>[6,1]=>840
[4,1,7,3,5,2,6]=>[6,1]=>840
[4,1,7,3,5,6,2]=>[5,1,1]=>504
[4,1,7,3,6,2,5]=>[7]=>720
[4,1,7,3,6,5,2]=>[5,2]=>504
[4,1,7,5,2,3,6]=>[4,3]=>420
[4,1,7,5,2,6,3]=>[4,2,1]=>630
[4,1,7,5,3,2,6]=>[7]=>720
[4,1,7,5,3,6,2]=>[6,1]=>840
[4,1,7,5,6,2,3]=>[5,2]=>504
[4,1,7,5,6,3,2]=>[7]=>720
[4,1,7,6,2,3,5]=>[7]=>720
[4,1,7,6,2,5,3]=>[5,2]=>504
[4,1,7,6,3,2,5]=>[4,3]=>420
[4,1,7,6,3,5,2]=>[7]=>720
[4,1,7,6,5,2,3]=>[4,2,1]=>630
[4,1,7,6,5,3,2]=>[6,1]=>840
[4,2,1,3,5,6,7]=>[3,1,1,1,1]=>70
[4,2,1,3,5,7,6]=>[3,2,1,1]=>420
[4,2,1,3,6,5,7]=>[3,2,1,1]=>420
[4,2,1,3,6,7,5]=>[3,3,1]=>280
[4,2,1,3,7,5,6]=>[3,3,1]=>280
[4,2,1,3,7,6,5]=>[3,2,1,1]=>420
[4,2,1,5,3,6,7]=>[4,1,1,1]=>210
[4,2,1,5,3,7,6]=>[4,2,1]=>630
[4,2,1,5,6,3,7]=>[5,1,1]=>504
[4,2,1,5,6,7,3]=>[6,1]=>840
[4,2,1,5,7,3,6]=>[6,1]=>840
[4,2,1,5,7,6,3]=>[5,1,1]=>504
[4,2,1,6,3,5,7]=>[5,1,1]=>504
[4,2,1,6,3,7,5]=>[6,1]=>840
[4,2,1,6,5,3,7]=>[4,1,1,1]=>210
[4,2,1,6,5,7,3]=>[5,1,1]=>504
[4,2,1,6,7,3,5]=>[4,2,1]=>630
[4,2,1,6,7,5,3]=>[6,1]=>840
[4,2,1,7,3,5,6]=>[6,1]=>840
[4,2,1,7,3,6,5]=>[5,1,1]=>504
[4,2,1,7,5,3,6]=>[5,1,1]=>504
[4,2,1,7,5,6,3]=>[4,1,1,1]=>210
[4,2,1,7,6,3,5]=>[6,1]=>840
[4,2,1,7,6,5,3]=>[4,2,1]=>630
[4,2,3,1,5,6,7]=>[2,1,1,1,1,1]=>21
[4,2,3,1,5,7,6]=>[2,2,1,1,1]=>105
[4,2,3,1,6,5,7]=>[2,2,1,1,1]=>105
[4,2,3,1,6,7,5]=>[3,2,1,1]=>420
[4,2,3,1,7,5,6]=>[3,2,1,1]=>420
[4,2,3,1,7,6,5]=>[2,2,1,1,1]=>105
[4,2,3,5,1,6,7]=>[3,1,1,1,1]=>70
[4,2,3,5,1,7,6]=>[3,2,1,1]=>420
[4,2,3,5,6,1,7]=>[4,1,1,1]=>210
[4,2,3,5,6,7,1]=>[5,1,1]=>504
[4,2,3,5,7,1,6]=>[5,1,1]=>504
[4,2,3,5,7,6,1]=>[4,1,1,1]=>210
[4,2,3,6,1,5,7]=>[4,1,1,1]=>210
[4,2,3,6,1,7,5]=>[5,1,1]=>504
[4,2,3,6,5,1,7]=>[3,1,1,1,1]=>70
[4,2,3,6,5,7,1]=>[4,1,1,1]=>210
[4,2,3,6,7,1,5]=>[3,2,1,1]=>420
[4,2,3,6,7,5,1]=>[5,1,1]=>504
[4,2,3,7,1,5,6]=>[5,1,1]=>504
[4,2,3,7,1,6,5]=>[4,1,1,1]=>210
[4,2,3,7,5,1,6]=>[4,1,1,1]=>210
[4,2,3,7,5,6,1]=>[3,1,1,1,1]=>70
[4,2,3,7,6,1,5]=>[5,1,1]=>504
[4,2,3,7,6,5,1]=>[3,2,1,1]=>420
[4,2,5,1,3,6,7]=>[2,2,1,1,1]=>105
[4,2,5,1,3,7,6]=>[2,2,2,1]=>105
[4,2,5,1,6,3,7]=>[3,2,1,1]=>420
[4,2,5,1,6,7,3]=>[4,2,1]=>630
[4,2,5,1,7,3,6]=>[4,2,1]=>630
[4,2,5,1,7,6,3]=>[3,2,1,1]=>420
[4,2,5,3,1,6,7]=>[4,1,1,1]=>210
[4,2,5,3,1,7,6]=>[4,2,1]=>630
[4,2,5,3,6,1,7]=>[5,1,1]=>504
[4,2,5,3,6,7,1]=>[6,1]=>840
[4,2,5,3,7,1,6]=>[6,1]=>840
[4,2,5,3,7,6,1]=>[5,1,1]=>504
[4,2,5,6,1,3,7]=>[5,1,1]=>504
[4,2,5,6,1,7,3]=>[6,1]=>840
[4,2,5,6,3,1,7]=>[3,2,1,1]=>420
[4,2,5,6,3,7,1]=>[4,2,1]=>630
[4,2,5,6,7,1,3]=>[3,3,1]=>280
[4,2,5,6,7,3,1]=>[6,1]=>840
[4,2,5,7,1,3,6]=>[6,1]=>840
[4,2,5,7,1,6,3]=>[5,1,1]=>504
[4,2,5,7,3,1,6]=>[4,2,1]=>630
[4,2,5,7,3,6,1]=>[3,2,1,1]=>420
[4,2,5,7,6,1,3]=>[6,1]=>840
[4,2,5,7,6,3,1]=>[3,3,1]=>280
[4,2,6,1,3,5,7]=>[3,2,1,1]=>420
[4,2,6,1,3,7,5]=>[4,2,1]=>630
[4,2,6,1,5,3,7]=>[2,2,1,1,1]=>105
[4,2,6,1,5,7,3]=>[3,2,1,1]=>420
[4,2,6,1,7,3,5]=>[2,2,2,1]=>105
[4,2,6,1,7,5,3]=>[4,2,1]=>630
[4,2,6,3,1,5,7]=>[5,1,1]=>504
[4,2,6,3,1,7,5]=>[6,1]=>840
[4,2,6,3,5,1,7]=>[4,1,1,1]=>210
[4,2,6,3,5,7,1]=>[5,1,1]=>504
[4,2,6,3,7,1,5]=>[4,2,1]=>630
[4,2,6,3,7,5,1]=>[6,1]=>840
[4,2,6,5,1,3,7]=>[3,2,1,1]=>420
[4,2,6,5,1,7,3]=>[3,3,1]=>280
[4,2,6,5,3,1,7]=>[5,1,1]=>504
[4,2,6,5,3,7,1]=>[6,1]=>840
[4,2,6,5,7,1,3]=>[6,1]=>840
[4,2,6,5,7,3,1]=>[4,2,1]=>630
[4,2,6,7,1,3,5]=>[4,2,1]=>630
[4,2,6,7,1,5,3]=>[6,1]=>840
[4,2,6,7,3,1,5]=>[6,1]=>840
[4,2,6,7,3,5,1]=>[3,3,1]=>280
[4,2,6,7,5,1,3]=>[5,1,1]=>504
[4,2,6,7,5,3,1]=>[3,2,1,1]=>420
[4,2,7,1,3,5,6]=>[4,2,1]=>630
[4,2,7,1,3,6,5]=>[3,2,1,1]=>420
[4,2,7,1,5,3,6]=>[3,2,1,1]=>420
[4,2,7,1,5,6,3]=>[2,2,1,1,1]=>105
[4,2,7,1,6,3,5]=>[4,2,1]=>630
[4,2,7,1,6,5,3]=>[2,2,2,1]=>105
[4,2,7,3,1,5,6]=>[6,1]=>840
[4,2,7,3,1,6,5]=>[5,1,1]=>504
[4,2,7,3,5,1,6]=>[5,1,1]=>504
[4,2,7,3,5,6,1]=>[4,1,1,1]=>210
[4,2,7,3,6,1,5]=>[6,1]=>840
[4,2,7,3,6,5,1]=>[4,2,1]=>630
[4,2,7,5,1,3,6]=>[3,3,1]=>280
[4,2,7,5,1,6,3]=>[3,2,1,1]=>420
[4,2,7,5,3,1,6]=>[6,1]=>840
[4,2,7,5,3,6,1]=>[5,1,1]=>504
[4,2,7,5,6,1,3]=>[4,2,1]=>630
[4,2,7,5,6,3,1]=>[6,1]=>840
[4,2,7,6,1,3,5]=>[6,1]=>840
[4,2,7,6,1,5,3]=>[4,2,1]=>630
[4,2,7,6,3,1,5]=>[3,3,1]=>280
[4,2,7,6,3,5,1]=>[6,1]=>840
[4,2,7,6,5,1,3]=>[3,2,1,1]=>420
[4,2,7,6,5,3,1]=>[5,1,1]=>504
[4,3,1,2,5,6,7]=>[4,1,1,1]=>210
[4,3,1,2,5,7,6]=>[4,2,1]=>630
[4,3,1,2,6,5,7]=>[4,2,1]=>630
[4,3,1,2,6,7,5]=>[4,3]=>420
[4,3,1,2,7,5,6]=>[4,3]=>420
[4,3,1,2,7,6,5]=>[4,2,1]=>630
[4,3,1,5,2,6,7]=>[5,1,1]=>504
[4,3,1,5,2,7,6]=>[5,2]=>504
[4,3,1,5,6,2,7]=>[6,1]=>840
[4,3,1,5,6,7,2]=>[7]=>720
[4,3,1,5,7,2,6]=>[7]=>720
[4,3,1,5,7,6,2]=>[6,1]=>840
[4,3,1,6,2,5,7]=>[6,1]=>840
[4,3,1,6,2,7,5]=>[7]=>720
[4,3,1,6,5,2,7]=>[5,1,1]=>504
[4,3,1,6,5,7,2]=>[6,1]=>840
[4,3,1,6,7,2,5]=>[5,2]=>504
[4,3,1,6,7,5,2]=>[7]=>720
[4,3,1,7,2,5,6]=>[7]=>720
[4,3,1,7,2,6,5]=>[6,1]=>840
[4,3,1,7,5,2,6]=>[6,1]=>840
[4,3,1,7,5,6,2]=>[5,1,1]=>504
[4,3,1,7,6,2,5]=>[7]=>720
[4,3,1,7,6,5,2]=>[5,2]=>504
[4,3,2,1,5,6,7]=>[2,2,1,1,1]=>105
[4,3,2,1,5,7,6]=>[2,2,2,1]=>105
[4,3,2,1,6,5,7]=>[2,2,2,1]=>105
[4,3,2,1,6,7,5]=>[3,2,2]=>210
[4,3,2,1,7,5,6]=>[3,2,2]=>210
[4,3,2,1,7,6,5]=>[2,2,2,1]=>105
[4,3,2,5,1,6,7]=>[3,2,1,1]=>420
[4,3,2,5,1,7,6]=>[3,2,2]=>210
[4,3,2,5,6,1,7]=>[4,2,1]=>630
[4,3,2,5,6,7,1]=>[5,2]=>504
[4,3,2,5,7,1,6]=>[5,2]=>504
[4,3,2,5,7,6,1]=>[4,2,1]=>630
[4,3,2,6,1,5,7]=>[4,2,1]=>630
[4,3,2,6,1,7,5]=>[5,2]=>504
[4,3,2,6,5,1,7]=>[3,2,1,1]=>420
[4,3,2,6,5,7,1]=>[4,2,1]=>630
[4,3,2,6,7,1,5]=>[3,2,2]=>210
[4,3,2,6,7,5,1]=>[5,2]=>504
[4,3,2,7,1,5,6]=>[5,2]=>504
[4,3,2,7,1,6,5]=>[4,2,1]=>630
[4,3,2,7,5,1,6]=>[4,2,1]=>630
[4,3,2,7,5,6,1]=>[3,2,1,1]=>420
[4,3,2,7,6,1,5]=>[5,2]=>504
[4,3,2,7,6,5,1]=>[3,2,2]=>210
[4,3,5,1,2,6,7]=>[3,2,1,1]=>420
[4,3,5,1,2,7,6]=>[3,2,2]=>210
[4,3,5,1,6,2,7]=>[4,2,1]=>630
[4,3,5,1,6,7,2]=>[5,2]=>504
[4,3,5,1,7,2,6]=>[5,2]=>504
[4,3,5,1,7,6,2]=>[4,2,1]=>630
[4,3,5,2,1,6,7]=>[5,1,1]=>504
[4,3,5,2,1,7,6]=>[5,2]=>504
[4,3,5,2,6,1,7]=>[6,1]=>840
[4,3,5,2,6,7,1]=>[7]=>720
[4,3,5,2,7,1,6]=>[7]=>720
[4,3,5,2,7,6,1]=>[6,1]=>840
[4,3,5,6,1,2,7]=>[6,1]=>840
[4,3,5,6,1,7,2]=>[7]=>720
[4,3,5,6,2,1,7]=>[3,3,1]=>280
[4,3,5,6,2,7,1]=>[4,3]=>420
[4,3,5,6,7,1,2]=>[4,3]=>420
[4,3,5,6,7,2,1]=>[7]=>720
[4,3,5,7,1,2,6]=>[7]=>720
[4,3,5,7,1,6,2]=>[6,1]=>840
[4,3,5,7,2,1,6]=>[4,3]=>420
[4,3,5,7,2,6,1]=>[3,3,1]=>280
[4,3,5,7,6,1,2]=>[7]=>720
[4,3,5,7,6,2,1]=>[4,3]=>420
[4,3,6,1,2,5,7]=>[4,2,1]=>630
[4,3,6,1,2,7,5]=>[5,2]=>504
[4,3,6,1,5,2,7]=>[3,2,1,1]=>420
[4,3,6,1,5,7,2]=>[4,2,1]=>630
[4,3,6,1,7,2,5]=>[3,2,2]=>210
[4,3,6,1,7,5,2]=>[5,2]=>504
[4,3,6,2,1,5,7]=>[6,1]=>840
[4,3,6,2,1,7,5]=>[7]=>720
[4,3,6,2,5,1,7]=>[5,1,1]=>504
[4,3,6,2,5,7,1]=>[6,1]=>840
[4,3,6,2,7,1,5]=>[5,2]=>504
[4,3,6,2,7,5,1]=>[7]=>720
[4,3,6,5,1,2,7]=>[3,3,1]=>280
[4,3,6,5,1,7,2]=>[4,3]=>420
[4,3,6,5,2,1,7]=>[6,1]=>840
[4,3,6,5,2,7,1]=>[7]=>720
[4,3,6,5,7,1,2]=>[7]=>720
[4,3,6,5,7,2,1]=>[4,3]=>420
[4,3,6,7,1,2,5]=>[4,3]=>420
[4,3,6,7,1,5,2]=>[7]=>720
[4,3,6,7,2,1,5]=>[7]=>720
[4,3,6,7,2,5,1]=>[4,3]=>420
[4,3,6,7,5,1,2]=>[6,1]=>840
[4,3,6,7,5,2,1]=>[3,3,1]=>280
[4,3,7,1,2,5,6]=>[5,2]=>504
[4,3,7,1,2,6,5]=>[4,2,1]=>630
[4,3,7,1,5,2,6]=>[4,2,1]=>630
[4,3,7,1,5,6,2]=>[3,2,1,1]=>420
[4,3,7,1,6,2,5]=>[5,2]=>504
[4,3,7,1,6,5,2]=>[3,2,2]=>210
[4,3,7,2,1,5,6]=>[7]=>720
[4,3,7,2,1,6,5]=>[6,1]=>840
[4,3,7,2,5,1,6]=>[6,1]=>840
[4,3,7,2,5,6,1]=>[5,1,1]=>504
[4,3,7,2,6,1,5]=>[7]=>720
[4,3,7,2,6,5,1]=>[5,2]=>504
[4,3,7,5,1,2,6]=>[4,3]=>420
[4,3,7,5,1,6,2]=>[3,3,1]=>280
[4,3,7,5,2,1,6]=>[7]=>720
[4,3,7,5,2,6,1]=>[6,1]=>840
[4,3,7,5,6,1,2]=>[4,3]=>420
[4,3,7,5,6,2,1]=>[7]=>720
[4,3,7,6,1,2,5]=>[7]=>720
[4,3,7,6,1,5,2]=>[4,3]=>420
[4,3,7,6,2,1,5]=>[4,3]=>420
[4,3,7,6,2,5,1]=>[7]=>720
[4,3,7,6,5,1,2]=>[3,3,1]=>280
[4,3,7,6,5,2,1]=>[6,1]=>840
[4,5,1,2,3,6,7]=>[5,1,1]=>504
[4,5,1,2,3,7,6]=>[5,2]=>504
[4,5,1,2,6,3,7]=>[6,1]=>840
[4,5,1,2,6,7,3]=>[7]=>720
[4,5,1,2,7,3,6]=>[7]=>720
[4,5,1,2,7,6,3]=>[6,1]=>840
[4,5,1,3,2,6,7]=>[3,2,1,1]=>420
[4,5,1,3,2,7,6]=>[3,2,2]=>210
[4,5,1,3,6,2,7]=>[3,3,1]=>280
[4,5,1,3,6,7,2]=>[4,3]=>420
[4,5,1,3,7,2,6]=>[4,3]=>420
[4,5,1,3,7,6,2]=>[3,3,1]=>280
[4,5,1,6,2,3,7]=>[4,2,1]=>630
[4,5,1,6,2,7,3]=>[5,2]=>504
[4,5,1,6,3,2,7]=>[6,1]=>840
[4,5,1,6,3,7,2]=>[7]=>720
[4,5,1,6,7,2,3]=>[7]=>720
[4,5,1,6,7,3,2]=>[4,3]=>420
[4,5,1,7,2,3,6]=>[5,2]=>504
[4,5,1,7,2,6,3]=>[4,2,1]=>630
[4,5,1,7,3,2,6]=>[7]=>720
[4,5,1,7,3,6,2]=>[6,1]=>840
[4,5,1,7,6,2,3]=>[4,3]=>420
[4,5,1,7,6,3,2]=>[7]=>720
[4,5,2,1,3,6,7]=>[3,2,1,1]=>420
[4,5,2,1,3,7,6]=>[3,2,2]=>210
[4,5,2,1,6,3,7]=>[4,2,1]=>630
[4,5,2,1,6,7,3]=>[5,2]=>504
[4,5,2,1,7,3,6]=>[5,2]=>504
[4,5,2,1,7,6,3]=>[4,2,1]=>630
[4,5,2,3,1,6,7]=>[5,1,1]=>504
[4,5,2,3,1,7,6]=>[5,2]=>504
[4,5,2,3,6,1,7]=>[6,1]=>840
[4,5,2,3,6,7,1]=>[7]=>720
[4,5,2,3,7,1,6]=>[7]=>720
[4,5,2,3,7,6,1]=>[6,1]=>840
[4,5,2,6,1,3,7]=>[6,1]=>840
[4,5,2,6,1,7,3]=>[7]=>720
[4,5,2,6,3,1,7]=>[3,3,1]=>280
[4,5,2,6,3,7,1]=>[4,3]=>420
[4,5,2,6,7,1,3]=>[4,3]=>420
[4,5,2,6,7,3,1]=>[7]=>720
[4,5,2,7,1,3,6]=>[7]=>720
[4,5,2,7,1,6,3]=>[6,1]=>840
[4,5,2,7,3,1,6]=>[4,3]=>420
[4,5,2,7,3,6,1]=>[3,3,1]=>280
[4,5,2,7,6,1,3]=>[7]=>720
[4,5,2,7,6,3,1]=>[4,3]=>420
[4,5,3,1,2,6,7]=>[2,2,1,1,1]=>105
[4,5,3,1,2,7,6]=>[2,2,2,1]=>105
[4,5,3,1,6,2,7]=>[3,2,1,1]=>420
[4,5,3,1,6,7,2]=>[4,2,1]=>630
[4,5,3,1,7,2,6]=>[4,2,1]=>630
[4,5,3,1,7,6,2]=>[3,2,1,1]=>420
[4,5,3,2,1,6,7]=>[4,1,1,1]=>210
[4,5,3,2,1,7,6]=>[4,2,1]=>630
[4,5,3,2,6,1,7]=>[5,1,1]=>504
[4,5,3,2,6,7,1]=>[6,1]=>840
[4,5,3,2,7,1,6]=>[6,1]=>840
[4,5,3,2,7,6,1]=>[5,1,1]=>504
[4,5,3,6,1,2,7]=>[5,1,1]=>504
[4,5,3,6,1,7,2]=>[6,1]=>840
[4,5,3,6,2,1,7]=>[3,2,1,1]=>420
[4,5,3,6,2,7,1]=>[4,2,1]=>630
[4,5,3,6,7,1,2]=>[3,3,1]=>280
[4,5,3,6,7,2,1]=>[6,1]=>840
[4,5,3,7,1,2,6]=>[6,1]=>840
[4,5,3,7,1,6,2]=>[5,1,1]=>504
[4,5,3,7,2,1,6]=>[4,2,1]=>630
[4,5,3,7,2,6,1]=>[3,2,1,1]=>420
[4,5,3,7,6,1,2]=>[6,1]=>840
[4,5,3,7,6,2,1]=>[3,3,1]=>280
[4,5,6,1,2,3,7]=>[2,2,2,1]=>105
[4,5,6,1,2,7,3]=>[3,2,2]=>210
[4,5,6,1,3,2,7]=>[4,2,1]=>630
[4,5,6,1,3,7,2]=>[5,2]=>504
[4,5,6,1,7,2,3]=>[5,2]=>504
[4,5,6,1,7,3,2]=>[3,2,2]=>210
[4,5,6,2,1,3,7]=>[4,2,1]=>630
[4,5,6,2,1,7,3]=>[4,3]=>420
[4,5,6,2,3,1,7]=>[6,1]=>840
[4,5,6,2,3,7,1]=>[7]=>720
[4,5,6,2,7,1,3]=>[7]=>720
[4,5,6,2,7,3,1]=>[5,2]=>504
[4,5,6,3,1,2,7]=>[6,1]=>840
[4,5,6,3,1,7,2]=>[7]=>720
[4,5,6,3,2,1,7]=>[4,2,1]=>630
[4,5,6,3,2,7,1]=>[5,2]=>504
[4,5,6,3,7,1,2]=>[4,3]=>420
[4,5,6,3,7,2,1]=>[7]=>720
[4,5,6,7,1,2,3]=>[7]=>720
[4,5,6,7,1,3,2]=>[5,2]=>504
[4,5,6,7,2,1,3]=>[5,2]=>504
[4,5,6,7,2,3,1]=>[3,2,2]=>210
[4,5,6,7,3,1,2]=>[7]=>720
[4,5,6,7,3,2,1]=>[4,3]=>420
[4,5,7,1,2,3,6]=>[3,2,2]=>210
[4,5,7,1,2,6,3]=>[2,2,2,1]=>105
[4,5,7,1,3,2,6]=>[5,2]=>504
[4,5,7,1,3,6,2]=>[4,2,1]=>630
[4,5,7,1,6,2,3]=>[3,2,2]=>210
[4,5,7,1,6,3,2]=>[5,2]=>504
[4,5,7,2,1,3,6]=>[4,3]=>420
[4,5,7,2,1,6,3]=>[4,2,1]=>630
[4,5,7,2,3,1,6]=>[7]=>720
[4,5,7,2,3,6,1]=>[6,1]=>840
[4,5,7,2,6,1,3]=>[5,2]=>504
[4,5,7,2,6,3,1]=>[7]=>720
[4,5,7,3,1,2,6]=>[7]=>720
[4,5,7,3,1,6,2]=>[6,1]=>840
[4,5,7,3,2,1,6]=>[5,2]=>504
[4,5,7,3,2,6,1]=>[4,2,1]=>630
[4,5,7,3,6,1,2]=>[7]=>720
[4,5,7,3,6,2,1]=>[4,3]=>420
[4,5,7,6,1,2,3]=>[5,2]=>504
[4,5,7,6,1,3,2]=>[7]=>720
[4,5,7,6,2,1,3]=>[3,2,2]=>210
[4,5,7,6,2,3,1]=>[5,2]=>504
[4,5,7,6,3,1,2]=>[4,3]=>420
[4,5,7,6,3,2,1]=>[7]=>720
[4,6,1,2,3,5,7]=>[6,1]=>840
[4,6,1,2,3,7,5]=>[7]=>720
[4,6,1,2,5,3,7]=>[5,1,1]=>504
[4,6,1,2,5,7,3]=>[6,1]=>840
[4,6,1,2,7,3,5]=>[5,2]=>504
[4,6,1,2,7,5,3]=>[7]=>720
[4,6,1,3,2,5,7]=>[3,3,1]=>280
[4,6,1,3,2,7,5]=>[4,3]=>420
[4,6,1,3,5,2,7]=>[3,2,1,1]=>420
[4,6,1,3,5,7,2]=>[3,3,1]=>280
[4,6,1,3,7,2,5]=>[3,2,2]=>210
[4,6,1,3,7,5,2]=>[4,3]=>420
[4,6,1,5,2,3,7]=>[6,1]=>840
[4,6,1,5,2,7,3]=>[7]=>720
[4,6,1,5,3,2,7]=>[4,2,1]=>630
[4,6,1,5,3,7,2]=>[4,3]=>420
[4,6,1,5,7,2,3]=>[5,2]=>504
[4,6,1,5,7,3,2]=>[7]=>720
[4,6,1,7,2,3,5]=>[7]=>720
[4,6,1,7,2,5,3]=>[4,3]=>420
[4,6,1,7,3,2,5]=>[5,2]=>504
[4,6,1,7,3,5,2]=>[7]=>720
[4,6,1,7,5,2,3]=>[4,2,1]=>630
[4,6,1,7,5,3,2]=>[6,1]=>840
[4,6,2,1,3,5,7]=>[4,2,1]=>630
[4,6,2,1,3,7,5]=>[5,2]=>504
[4,6,2,1,5,3,7]=>[3,2,1,1]=>420
[4,6,2,1,5,7,3]=>[4,2,1]=>630
[4,6,2,1,7,3,5]=>[3,2,2]=>210
[4,6,2,1,7,5,3]=>[5,2]=>504
[4,6,2,3,1,5,7]=>[6,1]=>840
[4,6,2,3,1,7,5]=>[7]=>720
[4,6,2,3,5,1,7]=>[5,1,1]=>504
[4,6,2,3,5,7,1]=>[6,1]=>840
[4,6,2,3,7,1,5]=>[5,2]=>504
[4,6,2,3,7,5,1]=>[7]=>720
[4,6,2,5,1,3,7]=>[3,3,1]=>280
[4,6,2,5,1,7,3]=>[4,3]=>420
[4,6,2,5,3,1,7]=>[6,1]=>840
[4,6,2,5,3,7,1]=>[7]=>720
[4,6,2,5,7,1,3]=>[7]=>720
[4,6,2,5,7,3,1]=>[4,3]=>420
[4,6,2,7,1,3,5]=>[4,3]=>420
[4,6,2,7,1,5,3]=>[7]=>720
[4,6,2,7,3,1,5]=>[7]=>720
[4,6,2,7,3,5,1]=>[4,3]=>420
[4,6,2,7,5,1,3]=>[6,1]=>840
[4,6,2,7,5,3,1]=>[3,3,1]=>280
[4,6,3,1,2,5,7]=>[3,2,1,1]=>420
[4,6,3,1,2,7,5]=>[4,2,1]=>630
[4,6,3,1,5,2,7]=>[2,2,1,1,1]=>105
[4,6,3,1,5,7,2]=>[3,2,1,1]=>420
[4,6,3,1,7,2,5]=>[2,2,2,1]=>105
[4,6,3,1,7,5,2]=>[4,2,1]=>630
[4,6,3,2,1,5,7]=>[5,1,1]=>504
[4,6,3,2,1,7,5]=>[6,1]=>840
[4,6,3,2,5,1,7]=>[4,1,1,1]=>210
[4,6,3,2,5,7,1]=>[5,1,1]=>504
[4,6,3,2,7,1,5]=>[4,2,1]=>630
[4,6,3,2,7,5,1]=>[6,1]=>840
[4,6,3,5,1,2,7]=>[3,2,1,1]=>420
[4,6,3,5,1,7,2]=>[3,3,1]=>280
[4,6,3,5,2,1,7]=>[5,1,1]=>504
[4,6,3,5,2,7,1]=>[6,1]=>840
[4,6,3,5,7,1,2]=>[6,1]=>840
[4,6,3,5,7,2,1]=>[4,2,1]=>630
[4,6,3,7,1,2,5]=>[4,2,1]=>630
[4,6,3,7,1,5,2]=>[6,1]=>840
[4,6,3,7,2,1,5]=>[6,1]=>840
[4,6,3,7,2,5,1]=>[3,3,1]=>280
[4,6,3,7,5,1,2]=>[5,1,1]=>504
[4,6,3,7,5,2,1]=>[3,2,1,1]=>420
[4,6,5,1,2,3,7]=>[4,2,1]=>630
[4,6,5,1,2,7,3]=>[5,2]=>504
[4,6,5,1,3,2,7]=>[2,2,2,1]=>105
[4,6,5,1,3,7,2]=>[3,2,2]=>210
[4,6,5,1,7,2,3]=>[3,2,2]=>210
[4,6,5,1,7,3,2]=>[5,2]=>504
[4,6,5,2,1,3,7]=>[6,1]=>840
[4,6,5,2,1,7,3]=>[7]=>720
[4,6,5,2,3,1,7]=>[4,2,1]=>630
[4,6,5,2,3,7,1]=>[5,2]=>504
[4,6,5,2,7,1,3]=>[4,3]=>420
[4,6,5,2,7,3,1]=>[7]=>720
[4,6,5,3,1,2,7]=>[4,2,1]=>630
[4,6,5,3,1,7,2]=>[4,3]=>420
[4,6,5,3,2,1,7]=>[6,1]=>840
[4,6,5,3,2,7,1]=>[7]=>720
[4,6,5,3,7,1,2]=>[7]=>720
[4,6,5,3,7,2,1]=>[5,2]=>504
[4,6,5,7,1,2,3]=>[5,2]=>504
[4,6,5,7,1,3,2]=>[7]=>720
[4,6,5,7,2,1,3]=>[7]=>720
[4,6,5,7,2,3,1]=>[4,3]=>420
[4,6,5,7,3,1,2]=>[5,2]=>504
[4,6,5,7,3,2,1]=>[3,2,2]=>210
[4,6,7,1,2,3,5]=>[5,2]=>504
[4,6,7,1,2,5,3]=>[3,2,2]=>210
[4,6,7,1,3,2,5]=>[3,2,2]=>210
[4,6,7,1,3,5,2]=>[5,2]=>504
[4,6,7,1,5,2,3]=>[2,2,2,1]=>105
[4,6,7,1,5,3,2]=>[4,2,1]=>630
[4,6,7,2,1,3,5]=>[7]=>720
[4,6,7,2,1,5,3]=>[5,2]=>504
[4,6,7,2,3,1,5]=>[4,3]=>420
[4,6,7,2,3,5,1]=>[7]=>720
[4,6,7,2,5,1,3]=>[4,2,1]=>630
[4,6,7,2,5,3,1]=>[6,1]=>840
[4,6,7,3,1,2,5]=>[5,2]=>504
[4,6,7,3,1,5,2]=>[7]=>720
[4,6,7,3,2,1,5]=>[7]=>720
[4,6,7,3,2,5,1]=>[4,3]=>420
[4,6,7,3,5,1,2]=>[6,1]=>840
[4,6,7,3,5,2,1]=>[4,2,1]=>630
[4,6,7,5,1,2,3]=>[3,2,2]=>210
[4,6,7,5,1,3,2]=>[4,3]=>420
[4,6,7,5,2,1,3]=>[5,2]=>504
[4,6,7,5,2,3,1]=>[7]=>720
[4,6,7,5,3,1,2]=>[7]=>720
[4,6,7,5,3,2,1]=>[5,2]=>504
[4,7,1,2,3,5,6]=>[7]=>720
[4,7,1,2,3,6,5]=>[6,1]=>840
[4,7,1,2,5,3,6]=>[6,1]=>840
[4,7,1,2,5,6,3]=>[5,1,1]=>504
[4,7,1,2,6,3,5]=>[7]=>720
[4,7,1,2,6,5,3]=>[5,2]=>504
[4,7,1,3,2,5,6]=>[4,3]=>420
[4,7,1,3,2,6,5]=>[3,3,1]=>280
[4,7,1,3,5,2,6]=>[3,3,1]=>280
[4,7,1,3,5,6,2]=>[3,2,1,1]=>420
[4,7,1,3,6,2,5]=>[4,3]=>420
[4,7,1,3,6,5,2]=>[3,2,2]=>210
[4,7,1,5,2,3,6]=>[7]=>720
[4,7,1,5,2,6,3]=>[6,1]=>840
[4,7,1,5,3,2,6]=>[4,3]=>420
[4,7,1,5,3,6,2]=>[4,2,1]=>630
[4,7,1,5,6,2,3]=>[7]=>720
[4,7,1,5,6,3,2]=>[5,2]=>504
[4,7,1,6,2,3,5]=>[4,3]=>420
[4,7,1,6,2,5,3]=>[7]=>720
[4,7,1,6,3,2,5]=>[7]=>720
[4,7,1,6,3,5,2]=>[5,2]=>504
[4,7,1,6,5,2,3]=>[6,1]=>840
[4,7,1,6,5,3,2]=>[4,2,1]=>630
[4,7,2,1,3,5,6]=>[5,2]=>504
[4,7,2,1,3,6,5]=>[4,2,1]=>630
[4,7,2,1,5,3,6]=>[4,2,1]=>630
[4,7,2,1,5,6,3]=>[3,2,1,1]=>420
[4,7,2,1,6,3,5]=>[5,2]=>504
[4,7,2,1,6,5,3]=>[3,2,2]=>210
[4,7,2,3,1,5,6]=>[7]=>720
[4,7,2,3,1,6,5]=>[6,1]=>840
[4,7,2,3,5,1,6]=>[6,1]=>840
[4,7,2,3,5,6,1]=>[5,1,1]=>504
[4,7,2,3,6,1,5]=>[7]=>720
[4,7,2,3,6,5,1]=>[5,2]=>504
[4,7,2,5,1,3,6]=>[4,3]=>420
[4,7,2,5,1,6,3]=>[3,3,1]=>280
[4,7,2,5,3,1,6]=>[7]=>720
[4,7,2,5,3,6,1]=>[6,1]=>840
[4,7,2,5,6,1,3]=>[4,3]=>420
[4,7,2,5,6,3,1]=>[7]=>720
[4,7,2,6,1,3,5]=>[7]=>720
[4,7,2,6,1,5,3]=>[4,3]=>420
[4,7,2,6,3,1,5]=>[4,3]=>420
[4,7,2,6,3,5,1]=>[7]=>720
[4,7,2,6,5,1,3]=>[3,3,1]=>280
[4,7,2,6,5,3,1]=>[6,1]=>840
[4,7,3,1,2,5,6]=>[4,2,1]=>630
[4,7,3,1,2,6,5]=>[3,2,1,1]=>420
[4,7,3,1,5,2,6]=>[3,2,1,1]=>420
[4,7,3,1,5,6,2]=>[2,2,1,1,1]=>105
[4,7,3,1,6,2,5]=>[4,2,1]=>630
[4,7,3,1,6,5,2]=>[2,2,2,1]=>105
[4,7,3,2,1,5,6]=>[6,1]=>840
[4,7,3,2,1,6,5]=>[5,1,1]=>504
[4,7,3,2,5,1,6]=>[5,1,1]=>504
[4,7,3,2,5,6,1]=>[4,1,1,1]=>210
[4,7,3,2,6,1,5]=>[6,1]=>840
[4,7,3,2,6,5,1]=>[4,2,1]=>630
[4,7,3,5,1,2,6]=>[3,3,1]=>280
[4,7,3,5,1,6,2]=>[3,2,1,1]=>420
[4,7,3,5,2,1,6]=>[6,1]=>840
[4,7,3,5,2,6,1]=>[5,1,1]=>504
[4,7,3,5,6,1,2]=>[4,2,1]=>630
[4,7,3,5,6,2,1]=>[6,1]=>840
[4,7,3,6,1,2,5]=>[6,1]=>840
[4,7,3,6,1,5,2]=>[4,2,1]=>630
[4,7,3,6,2,1,5]=>[3,3,1]=>280
[4,7,3,6,2,5,1]=>[6,1]=>840
[4,7,3,6,5,1,2]=>[3,2,1,1]=>420
[4,7,3,6,5,2,1]=>[5,1,1]=>504
[4,7,5,1,2,3,6]=>[5,2]=>504
[4,7,5,1,2,6,3]=>[4,2,1]=>630
[4,7,5,1,3,2,6]=>[3,2,2]=>210
[4,7,5,1,3,6,2]=>[2,2,2,1]=>105
[4,7,5,1,6,2,3]=>[5,2]=>504
[4,7,5,1,6,3,2]=>[3,2,2]=>210
[4,7,5,2,1,3,6]=>[7]=>720
[4,7,5,2,1,6,3]=>[6,1]=>840
[4,7,5,2,3,1,6]=>[5,2]=>504
[4,7,5,2,3,6,1]=>[4,2,1]=>630
[4,7,5,2,6,1,3]=>[7]=>720
[4,7,5,2,6,3,1]=>[4,3]=>420
[4,7,5,3,1,2,6]=>[4,3]=>420
[4,7,5,3,1,6,2]=>[4,2,1]=>630
[4,7,5,3,2,1,6]=>[7]=>720
[4,7,5,3,2,6,1]=>[6,1]=>840
[4,7,5,3,6,1,2]=>[5,2]=>504
[4,7,5,3,6,2,1]=>[7]=>720
[4,7,5,6,1,2,3]=>[7]=>720
[4,7,5,6,1,3,2]=>[5,2]=>504
[4,7,5,6,2,1,3]=>[4,3]=>420
[4,7,5,6,2,3,1]=>[7]=>720
[4,7,5,6,3,1,2]=>[3,2,2]=>210
[4,7,5,6,3,2,1]=>[5,2]=>504
[4,7,6,1,2,3,5]=>[3,2,2]=>210
[4,7,6,1,2,5,3]=>[5,2]=>504
[4,7,6,1,3,2,5]=>[5,2]=>504
[4,7,6,1,3,5,2]=>[3,2,2]=>210
[4,7,6,1,5,2,3]=>[4,2,1]=>630
[4,7,6,1,5,3,2]=>[2,2,2,1]=>105
[4,7,6,2,1,3,5]=>[5,2]=>504
[4,7,6,2,1,5,3]=>[7]=>720
[4,7,6,2,3,1,5]=>[7]=>720
[4,7,6,2,3,5,1]=>[4,3]=>420
[4,7,6,2,5,1,3]=>[6,1]=>840
[4,7,6,2,5,3,1]=>[4,2,1]=>630
[4,7,6,3,1,2,5]=>[7]=>720
[4,7,6,3,1,5,2]=>[5,2]=>504
[4,7,6,3,2,1,5]=>[4,3]=>420
[4,7,6,3,2,5,1]=>[7]=>720
[4,7,6,3,5,1,2]=>[4,2,1]=>630
[4,7,6,3,5,2,1]=>[6,1]=>840
[4,7,6,5,1,2,3]=>[4,3]=>420
[4,7,6,5,1,3,2]=>[3,2,2]=>210
[4,7,6,5,2,1,3]=>[7]=>720
[4,7,6,5,2,3,1]=>[5,2]=>504
[4,7,6,5,3,1,2]=>[5,2]=>504
[4,7,6,5,3,2,1]=>[7]=>720
[5,1,2,3,4,6,7]=>[5,1,1]=>504
[5,1,2,3,4,7,6]=>[5,2]=>504
[5,1,2,3,6,4,7]=>[6,1]=>840
[5,1,2,3,6,7,4]=>[7]=>720
[5,1,2,3,7,4,6]=>[7]=>720
[5,1,2,3,7,6,4]=>[6,1]=>840
[5,1,2,4,3,6,7]=>[4,1,1,1]=>210
[5,1,2,4,3,7,6]=>[4,2,1]=>630
[5,1,2,4,6,3,7]=>[5,1,1]=>504
[5,1,2,4,6,7,3]=>[6,1]=>840
[5,1,2,4,7,3,6]=>[6,1]=>840
[5,1,2,4,7,6,3]=>[5,1,1]=>504
[5,1,2,6,3,4,7]=>[4,2,1]=>630
[5,1,2,6,3,7,4]=>[4,3]=>420
[5,1,2,6,4,3,7]=>[6,1]=>840
[5,1,2,6,4,7,3]=>[7]=>720
[5,1,2,6,7,3,4]=>[7]=>720
[5,1,2,6,7,4,3]=>[5,2]=>504
[5,1,2,7,3,4,6]=>[4,3]=>420
[5,1,2,7,3,6,4]=>[4,2,1]=>630
[5,1,2,7,4,3,6]=>[7]=>720
[5,1,2,7,4,6,3]=>[6,1]=>840
[5,1,2,7,6,3,4]=>[5,2]=>504
[5,1,2,7,6,4,3]=>[7]=>720
[5,1,3,2,4,6,7]=>[4,1,1,1]=>210
[5,1,3,2,4,7,6]=>[4,2,1]=>630
[5,1,3,2,6,4,7]=>[5,1,1]=>504
[5,1,3,2,6,7,4]=>[6,1]=>840
[5,1,3,2,7,4,6]=>[6,1]=>840
[5,1,3,2,7,6,4]=>[5,1,1]=>504
[5,1,3,4,2,6,7]=>[3,1,1,1,1]=>70
[5,1,3,4,2,7,6]=>[3,2,1,1]=>420
[5,1,3,4,6,2,7]=>[4,1,1,1]=>210
[5,1,3,4,6,7,2]=>[5,1,1]=>504
[5,1,3,4,7,2,6]=>[5,1,1]=>504
[5,1,3,4,7,6,2]=>[4,1,1,1]=>210
[5,1,3,6,2,4,7]=>[3,2,1,1]=>420
[5,1,3,6,2,7,4]=>[3,3,1]=>280
[5,1,3,6,4,2,7]=>[5,1,1]=>504
[5,1,3,6,4,7,2]=>[6,1]=>840
[5,1,3,6,7,2,4]=>[6,1]=>840
[5,1,3,6,7,4,2]=>[4,2,1]=>630
[5,1,3,7,2,4,6]=>[3,3,1]=>280
[5,1,3,7,2,6,4]=>[3,2,1,1]=>420
[5,1,3,7,4,2,6]=>[6,1]=>840
[5,1,3,7,4,6,2]=>[5,1,1]=>504
[5,1,3,7,6,2,4]=>[4,2,1]=>630
[5,1,3,7,6,4,2]=>[6,1]=>840
[5,1,4,2,3,6,7]=>[5,1,1]=>504
[5,1,4,2,3,7,6]=>[5,2]=>504
[5,1,4,2,6,3,7]=>[6,1]=>840
[5,1,4,2,6,7,3]=>[7]=>720
[5,1,4,2,7,3,6]=>[7]=>720
[5,1,4,2,7,6,3]=>[6,1]=>840
[5,1,4,3,2,6,7]=>[3,2,1,1]=>420
[5,1,4,3,2,7,6]=>[3,2,2]=>210
[5,1,4,3,6,2,7]=>[4,2,1]=>630
[5,1,4,3,6,7,2]=>[5,2]=>504
[5,1,4,3,7,2,6]=>[5,2]=>504
[5,1,4,3,7,6,2]=>[4,2,1]=>630
[5,1,4,6,2,3,7]=>[3,3,1]=>280
[5,1,4,6,2,7,3]=>[4,3]=>420
[5,1,4,6,3,2,7]=>[6,1]=>840
[5,1,4,6,3,7,2]=>[7]=>720
[5,1,4,6,7,2,3]=>[7]=>720
[5,1,4,6,7,3,2]=>[4,3]=>420
[5,1,4,7,2,3,6]=>[4,3]=>420
[5,1,4,7,2,6,3]=>[3,3,1]=>280
[5,1,4,7,3,2,6]=>[7]=>720
[5,1,4,7,3,6,2]=>[6,1]=>840
[5,1,4,7,6,2,3]=>[4,3]=>420
[5,1,4,7,6,3,2]=>[7]=>720
[5,1,6,2,3,4,7]=>[6,1]=>840
[5,1,6,2,3,7,4]=>[7]=>720
[5,1,6,2,4,3,7]=>[4,2,1]=>630
[5,1,6,2,4,7,3]=>[4,3]=>420
[5,1,6,2,7,3,4]=>[5,2]=>504
[5,1,6,2,7,4,3]=>[7]=>720
[5,1,6,3,2,4,7]=>[3,3,1]=>280
[5,1,6,3,2,7,4]=>[4,3]=>420
[5,1,6,3,4,2,7]=>[6,1]=>840
[5,1,6,3,4,7,2]=>[7]=>720
[5,1,6,3,7,2,4]=>[7]=>720
[5,1,6,3,7,4,2]=>[4,3]=>420
[5,1,6,4,2,3,7]=>[3,2,1,1]=>420
[5,1,6,4,2,7,3]=>[3,3,1]=>280
[5,1,6,4,3,2,7]=>[5,1,1]=>504
[5,1,6,4,3,7,2]=>[6,1]=>840
[5,1,6,4,7,2,3]=>[6,1]=>840
[5,1,6,4,7,3,2]=>[4,2,1]=>630
[5,1,6,7,2,3,4]=>[3,2,2]=>210
[5,1,6,7,2,4,3]=>[4,3]=>420
[5,1,6,7,3,2,4]=>[5,2]=>504
[5,1,6,7,3,4,2]=>[7]=>720
[5,1,6,7,4,2,3]=>[7]=>720
[5,1,6,7,4,3,2]=>[5,2]=>504
[5,1,7,2,3,4,6]=>[7]=>720
[5,1,7,2,3,6,4]=>[6,1]=>840
[5,1,7,2,4,3,6]=>[4,3]=>420
[5,1,7,2,4,6,3]=>[4,2,1]=>630
[5,1,7,2,6,3,4]=>[7]=>720
[5,1,7,2,6,4,3]=>[5,2]=>504
[5,1,7,3,2,4,6]=>[4,3]=>420
[5,1,7,3,2,6,4]=>[3,3,1]=>280
[5,1,7,3,4,2,6]=>[7]=>720
[5,1,7,3,4,6,2]=>[6,1]=>840
[5,1,7,3,6,2,4]=>[4,3]=>420
[5,1,7,3,6,4,2]=>[7]=>720
[5,1,7,4,2,3,6]=>[3,3,1]=>280
[5,1,7,4,2,6,3]=>[3,2,1,1]=>420
[5,1,7,4,3,2,6]=>[6,1]=>840
[5,1,7,4,3,6,2]=>[5,1,1]=>504
[5,1,7,4,6,2,3]=>[4,2,1]=>630
[5,1,7,4,6,3,2]=>[6,1]=>840
[5,1,7,6,2,3,4]=>[4,3]=>420
[5,1,7,6,2,4,3]=>[3,2,2]=>210
[5,1,7,6,3,2,4]=>[7]=>720
[5,1,7,6,3,4,2]=>[5,2]=>504
[5,1,7,6,4,2,3]=>[5,2]=>504
[5,1,7,6,4,3,2]=>[7]=>720
[5,2,1,3,4,6,7]=>[4,1,1,1]=>210
[5,2,1,3,4,7,6]=>[4,2,1]=>630
[5,2,1,3,6,4,7]=>[5,1,1]=>504
[5,2,1,3,6,7,4]=>[6,1]=>840
[5,2,1,3,7,4,6]=>[6,1]=>840
[5,2,1,3,7,6,4]=>[5,1,1]=>504
[5,2,1,4,3,6,7]=>[3,1,1,1,1]=>70
[5,2,1,4,3,7,6]=>[3,2,1,1]=>420
[5,2,1,4,6,3,7]=>[4,1,1,1]=>210
[5,2,1,4,6,7,3]=>[5,1,1]=>504
[5,2,1,4,7,3,6]=>[5,1,1]=>504
[5,2,1,4,7,6,3]=>[4,1,1,1]=>210
[5,2,1,6,3,4,7]=>[3,2,1,1]=>420
[5,2,1,6,3,7,4]=>[3,3,1]=>280
[5,2,1,6,4,3,7]=>[5,1,1]=>504
[5,2,1,6,4,7,3]=>[6,1]=>840
[5,2,1,6,7,3,4]=>[6,1]=>840
[5,2,1,6,7,4,3]=>[4,2,1]=>630
[5,2,1,7,3,4,6]=>[3,3,1]=>280
[5,2,1,7,3,6,4]=>[3,2,1,1]=>420
[5,2,1,7,4,3,6]=>[6,1]=>840
[5,2,1,7,4,6,3]=>[5,1,1]=>504
[5,2,1,7,6,3,4]=>[4,2,1]=>630
[5,2,1,7,6,4,3]=>[6,1]=>840
[5,2,3,1,4,6,7]=>[3,1,1,1,1]=>70
[5,2,3,1,4,7,6]=>[3,2,1,1]=>420
[5,2,3,1,6,4,7]=>[4,1,1,1]=>210
[5,2,3,1,6,7,4]=>[5,1,1]=>504
[5,2,3,1,7,4,6]=>[5,1,1]=>504
[5,2,3,1,7,6,4]=>[4,1,1,1]=>210
[5,2,3,4,1,6,7]=>[2,1,1,1,1,1]=>21
[5,2,3,4,1,7,6]=>[2,2,1,1,1]=>105
[5,2,3,4,6,1,7]=>[3,1,1,1,1]=>70
[5,2,3,4,6,7,1]=>[4,1,1,1]=>210
[5,2,3,4,7,1,6]=>[4,1,1,1]=>210
[5,2,3,4,7,6,1]=>[3,1,1,1,1]=>70
[5,2,3,6,1,4,7]=>[2,2,1,1,1]=>105
[5,2,3,6,1,7,4]=>[3,2,1,1]=>420
[5,2,3,6,4,1,7]=>[4,1,1,1]=>210
[5,2,3,6,4,7,1]=>[5,1,1]=>504
[5,2,3,6,7,1,4]=>[5,1,1]=>504
[5,2,3,6,7,4,1]=>[3,2,1,1]=>420
[5,2,3,7,1,4,6]=>[3,2,1,1]=>420
[5,2,3,7,1,6,4]=>[2,2,1,1,1]=>105
[5,2,3,7,4,1,6]=>[5,1,1]=>504
[5,2,3,7,4,6,1]=>[4,1,1,1]=>210
[5,2,3,7,6,1,4]=>[3,2,1,1]=>420
[5,2,3,7,6,4,1]=>[5,1,1]=>504
[5,2,4,1,3,6,7]=>[4,1,1,1]=>210
[5,2,4,1,3,7,6]=>[4,2,1]=>630
[5,2,4,1,6,3,7]=>[5,1,1]=>504
[5,2,4,1,6,7,3]=>[6,1]=>840
[5,2,4,1,7,3,6]=>[6,1]=>840
[5,2,4,1,7,6,3]=>[5,1,1]=>504
[5,2,4,3,1,6,7]=>[2,2,1,1,1]=>105
[5,2,4,3,1,7,6]=>[2,2,2,1]=>105
[5,2,4,3,6,1,7]=>[3,2,1,1]=>420
[5,2,4,3,6,7,1]=>[4,2,1]=>630
[5,2,4,3,7,1,6]=>[4,2,1]=>630
[5,2,4,3,7,6,1]=>[3,2,1,1]=>420
[5,2,4,6,1,3,7]=>[3,2,1,1]=>420
[5,2,4,6,1,7,3]=>[4,2,1]=>630
[5,2,4,6,3,1,7]=>[5,1,1]=>504
[5,2,4,6,3,7,1]=>[6,1]=>840
[5,2,4,6,7,1,3]=>[6,1]=>840
[5,2,4,6,7,3,1]=>[3,3,1]=>280
[5,2,4,7,1,3,6]=>[4,2,1]=>630
[5,2,4,7,1,6,3]=>[3,2,1,1]=>420
[5,2,4,7,3,1,6]=>[6,1]=>840
[5,2,4,7,3,6,1]=>[5,1,1]=>504
[5,2,4,7,6,1,3]=>[3,3,1]=>280
[5,2,4,7,6,3,1]=>[6,1]=>840
[5,2,6,1,3,4,7]=>[5,1,1]=>504
[5,2,6,1,3,7,4]=>[6,1]=>840
[5,2,6,1,4,3,7]=>[3,2,1,1]=>420
[5,2,6,1,4,7,3]=>[3,3,1]=>280
[5,2,6,1,7,3,4]=>[4,2,1]=>630
[5,2,6,1,7,4,3]=>[6,1]=>840
[5,2,6,3,1,4,7]=>[3,2,1,1]=>420
[5,2,6,3,1,7,4]=>[4,2,1]=>630
[5,2,6,3,4,1,7]=>[5,1,1]=>504
[5,2,6,3,4,7,1]=>[6,1]=>840
[5,2,6,3,7,1,4]=>[6,1]=>840
[5,2,6,3,7,4,1]=>[3,3,1]=>280
[5,2,6,4,1,3,7]=>[2,2,1,1,1]=>105
[5,2,6,4,1,7,3]=>[3,2,1,1]=>420
[5,2,6,4,3,1,7]=>[4,1,1,1]=>210
[5,2,6,4,3,7,1]=>[5,1,1]=>504
[5,2,6,4,7,1,3]=>[5,1,1]=>504
[5,2,6,4,7,3,1]=>[3,2,1,1]=>420
[5,2,6,7,1,3,4]=>[2,2,2,1]=>105
[5,2,6,7,1,4,3]=>[4,2,1]=>630
[5,2,6,7,3,1,4]=>[4,2,1]=>630
[5,2,6,7,3,4,1]=>[6,1]=>840
[5,2,6,7,4,1,3]=>[6,1]=>840
[5,2,6,7,4,3,1]=>[4,2,1]=>630
[5,2,7,1,3,4,6]=>[6,1]=>840
[5,2,7,1,3,6,4]=>[5,1,1]=>504
[5,2,7,1,4,3,6]=>[3,3,1]=>280
[5,2,7,1,4,6,3]=>[3,2,1,1]=>420
[5,2,7,1,6,3,4]=>[6,1]=>840
[5,2,7,1,6,4,3]=>[4,2,1]=>630
[5,2,7,3,1,4,6]=>[4,2,1]=>630
[5,2,7,3,1,6,4]=>[3,2,1,1]=>420
[5,2,7,3,4,1,6]=>[6,1]=>840
[5,2,7,3,4,6,1]=>[5,1,1]=>504
[5,2,7,3,6,1,4]=>[3,3,1]=>280
[5,2,7,3,6,4,1]=>[6,1]=>840
[5,2,7,4,1,3,6]=>[3,2,1,1]=>420
[5,2,7,4,1,6,3]=>[2,2,1,1,1]=>105
[5,2,7,4,3,1,6]=>[5,1,1]=>504
[5,2,7,4,3,6,1]=>[4,1,1,1]=>210
[5,2,7,4,6,1,3]=>[3,2,1,1]=>420
[5,2,7,4,6,3,1]=>[5,1,1]=>504
[5,2,7,6,1,3,4]=>[4,2,1]=>630
[5,2,7,6,1,4,3]=>[2,2,2,1]=>105
[5,2,7,6,3,1,4]=>[6,1]=>840
[5,2,7,6,3,4,1]=>[4,2,1]=>630
[5,2,7,6,4,1,3]=>[4,2,1]=>630
[5,2,7,6,4,3,1]=>[6,1]=>840
[5,3,1,2,4,6,7]=>[5,1,1]=>504
[5,3,1,2,4,7,6]=>[5,2]=>504
[5,3,1,2,6,4,7]=>[6,1]=>840
[5,3,1,2,6,7,4]=>[7]=>720
[5,3,1,2,7,4,6]=>[7]=>720
[5,3,1,2,7,6,4]=>[6,1]=>840
[5,3,1,4,2,6,7]=>[4,1,1,1]=>210
[5,3,1,4,2,7,6]=>[4,2,1]=>630
[5,3,1,4,6,2,7]=>[5,1,1]=>504
[5,3,1,4,6,7,2]=>[6,1]=>840
[5,3,1,4,7,2,6]=>[6,1]=>840
[5,3,1,4,7,6,2]=>[5,1,1]=>504
[5,3,1,6,2,4,7]=>[4,2,1]=>630
[5,3,1,6,2,7,4]=>[4,3]=>420
[5,3,1,6,4,2,7]=>[6,1]=>840
[5,3,1,6,4,7,2]=>[7]=>720
[5,3,1,6,7,2,4]=>[7]=>720
[5,3,1,6,7,4,2]=>[5,2]=>504
[5,3,1,7,2,4,6]=>[4,3]=>420
[5,3,1,7,2,6,4]=>[4,2,1]=>630
[5,3,1,7,4,2,6]=>[7]=>720
[5,3,1,7,4,6,2]=>[6,1]=>840
[5,3,1,7,6,2,4]=>[5,2]=>504
[5,3,1,7,6,4,2]=>[7]=>720
[5,3,2,1,4,6,7]=>[3,2,1,1]=>420
[5,3,2,1,4,7,6]=>[3,2,2]=>210
[5,3,2,1,6,4,7]=>[4,2,1]=>630
[5,3,2,1,6,7,4]=>[5,2]=>504
[5,3,2,1,7,4,6]=>[5,2]=>504
[5,3,2,1,7,6,4]=>[4,2,1]=>630
[5,3,2,4,1,6,7]=>[2,2,1,1,1]=>105
[5,3,2,4,1,7,6]=>[2,2,2,1]=>105
[5,3,2,4,6,1,7]=>[3,2,1,1]=>420
[5,3,2,4,6,7,1]=>[4,2,1]=>630
[5,3,2,4,7,1,6]=>[4,2,1]=>630
[5,3,2,4,7,6,1]=>[3,2,1,1]=>420
[5,3,2,6,1,4,7]=>[2,2,2,1]=>105
[5,3,2,6,1,7,4]=>[3,2,2]=>210
[5,3,2,6,4,1,7]=>[4,2,1]=>630
[5,3,2,6,4,7,1]=>[5,2]=>504
[5,3,2,6,7,1,4]=>[5,2]=>504
[5,3,2,6,7,4,1]=>[3,2,2]=>210
[5,3,2,7,1,4,6]=>[3,2,2]=>210
[5,3,2,7,1,6,4]=>[2,2,2,1]=>105
[5,3,2,7,4,1,6]=>[5,2]=>504
[5,3,2,7,4,6,1]=>[4,2,1]=>630
[5,3,2,7,6,1,4]=>[3,2,2]=>210
[5,3,2,7,6,4,1]=>[5,2]=>504
[5,3,4,1,2,6,7]=>[5,1,1]=>504
[5,3,4,1,2,7,6]=>[5,2]=>504
[5,3,4,1,6,2,7]=>[6,1]=>840
[5,3,4,1,6,7,2]=>[7]=>720
[5,3,4,1,7,2,6]=>[7]=>720
[5,3,4,1,7,6,2]=>[6,1]=>840
[5,3,4,2,1,6,7]=>[3,2,1,1]=>420
[5,3,4,2,1,7,6]=>[3,2,2]=>210
[5,3,4,2,6,1,7]=>[3,3,1]=>280
[5,3,4,2,6,7,1]=>[4,3]=>420
[5,3,4,2,7,1,6]=>[4,3]=>420
[5,3,4,2,7,6,1]=>[3,3,1]=>280
[5,3,4,6,1,2,7]=>[4,2,1]=>630
[5,3,4,6,1,7,2]=>[5,2]=>504
[5,3,4,6,2,1,7]=>[6,1]=>840
[5,3,4,6,2,7,1]=>[7]=>720
[5,3,4,6,7,1,2]=>[7]=>720
[5,3,4,6,7,2,1]=>[4,3]=>420
[5,3,4,7,1,2,6]=>[5,2]=>504
[5,3,4,7,1,6,2]=>[4,2,1]=>630
[5,3,4,7,2,1,6]=>[7]=>720
[5,3,4,7,2,6,1]=>[6,1]=>840
[5,3,4,7,6,1,2]=>[4,3]=>420
[5,3,4,7,6,2,1]=>[7]=>720
[5,3,6,1,2,4,7]=>[6,1]=>840
[5,3,6,1,2,7,4]=>[7]=>720
[5,3,6,1,4,2,7]=>[3,3,1]=>280
[5,3,6,1,4,7,2]=>[4,3]=>420
[5,3,6,1,7,2,4]=>[4,3]=>420
[5,3,6,1,7,4,2]=>[7]=>720
[5,3,6,2,1,4,7]=>[4,2,1]=>630
[5,3,6,2,1,7,4]=>[5,2]=>504
[5,3,6,2,4,1,7]=>[6,1]=>840
[5,3,6,2,4,7,1]=>[7]=>720
[5,3,6,2,7,1,4]=>[7]=>720
[5,3,6,2,7,4,1]=>[4,3]=>420
[5,3,6,4,1,2,7]=>[3,2,1,1]=>420
[5,3,6,4,1,7,2]=>[4,2,1]=>630
[5,3,6,4,2,1,7]=>[5,1,1]=>504
[5,3,6,4,2,7,1]=>[6,1]=>840
[5,3,6,4,7,1,2]=>[6,1]=>840
[5,3,6,4,7,2,1]=>[3,3,1]=>280
[5,3,6,7,1,2,4]=>[3,2,2]=>210
[5,3,6,7,1,4,2]=>[5,2]=>504
[5,3,6,7,2,1,4]=>[5,2]=>504
[5,3,6,7,2,4,1]=>[7]=>720
[5,3,6,7,4,1,2]=>[7]=>720
[5,3,6,7,4,2,1]=>[4,3]=>420
[5,3,7,1,2,4,6]=>[7]=>720
[5,3,7,1,2,6,4]=>[6,1]=>840
[5,3,7,1,4,2,6]=>[4,3]=>420
[5,3,7,1,4,6,2]=>[3,3,1]=>280
[5,3,7,1,6,2,4]=>[7]=>720
[5,3,7,1,6,4,2]=>[4,3]=>420
[5,3,7,2,1,4,6]=>[5,2]=>504
[5,3,7,2,1,6,4]=>[4,2,1]=>630
[5,3,7,2,4,1,6]=>[7]=>720
[5,3,7,2,4,6,1]=>[6,1]=>840
[5,3,7,2,6,1,4]=>[4,3]=>420
[5,3,7,2,6,4,1]=>[7]=>720
[5,3,7,4,1,2,6]=>[4,2,1]=>630
[5,3,7,4,1,6,2]=>[3,2,1,1]=>420
[5,3,7,4,2,1,6]=>[6,1]=>840
[5,3,7,4,2,6,1]=>[5,1,1]=>504
[5,3,7,4,6,1,2]=>[3,3,1]=>280
[5,3,7,4,6,2,1]=>[6,1]=>840
[5,3,7,6,1,2,4]=>[5,2]=>504
[5,3,7,6,1,4,2]=>[3,2,2]=>210
[5,3,7,6,2,1,4]=>[7]=>720
[5,3,7,6,2,4,1]=>[5,2]=>504
[5,3,7,6,4,1,2]=>[4,3]=>420
[5,3,7,6,4,2,1]=>[7]=>720
[5,4,1,2,3,6,7]=>[3,2,1,1]=>420
[5,4,1,2,3,7,6]=>[3,2,2]=>210
[5,4,1,2,6,3,7]=>[4,2,1]=>630
[5,4,1,2,6,7,3]=>[5,2]=>504
[5,4,1,2,7,3,6]=>[5,2]=>504
[5,4,1,2,7,6,3]=>[4,2,1]=>630
[5,4,1,3,2,6,7]=>[5,1,1]=>504
[5,4,1,3,2,7,6]=>[5,2]=>504
[5,4,1,3,6,2,7]=>[6,1]=>840
[5,4,1,3,6,7,2]=>[7]=>720
[5,4,1,3,7,2,6]=>[7]=>720
[5,4,1,3,7,6,2]=>[6,1]=>840
[5,4,1,6,2,3,7]=>[6,1]=>840
[5,4,1,6,2,7,3]=>[7]=>720
[5,4,1,6,3,2,7]=>[3,3,1]=>280
[5,4,1,6,3,7,2]=>[4,3]=>420
[5,4,1,6,7,2,3]=>[4,3]=>420
[5,4,1,6,7,3,2]=>[7]=>720
[5,4,1,7,2,3,6]=>[7]=>720
[5,4,1,7,2,6,3]=>[6,1]=>840
[5,4,1,7,3,2,6]=>[4,3]=>420
[5,4,1,7,3,6,2]=>[3,3,1]=>280
[5,4,1,7,6,2,3]=>[7]=>720
[5,4,1,7,6,3,2]=>[4,3]=>420
[5,4,2,1,3,6,7]=>[5,1,1]=>504
[5,4,2,1,3,7,6]=>[5,2]=>504
[5,4,2,1,6,3,7]=>[6,1]=>840
[5,4,2,1,6,7,3]=>[7]=>720
[5,4,2,1,7,3,6]=>[7]=>720
[5,4,2,1,7,6,3]=>[6,1]=>840
[5,4,2,3,1,6,7]=>[3,2,1,1]=>420
[5,4,2,3,1,7,6]=>[3,2,2]=>210
[5,4,2,3,6,1,7]=>[3,3,1]=>280
[5,4,2,3,6,7,1]=>[4,3]=>420
[5,4,2,3,7,1,6]=>[4,3]=>420
[5,4,2,3,7,6,1]=>[3,3,1]=>280
[5,4,2,6,1,3,7]=>[4,2,1]=>630
[5,4,2,6,1,7,3]=>[5,2]=>504
[5,4,2,6,3,1,7]=>[6,1]=>840
[5,4,2,6,3,7,1]=>[7]=>720
[5,4,2,6,7,1,3]=>[7]=>720
[5,4,2,6,7,3,1]=>[4,3]=>420
[5,4,2,7,1,3,6]=>[5,2]=>504
[5,4,2,7,1,6,3]=>[4,2,1]=>630
[5,4,2,7,3,1,6]=>[7]=>720
[5,4,2,7,3,6,1]=>[6,1]=>840
[5,4,2,7,6,1,3]=>[4,3]=>420
[5,4,2,7,6,3,1]=>[7]=>720
[5,4,3,1,2,6,7]=>[4,1,1,1]=>210
[5,4,3,1,2,7,6]=>[4,2,1]=>630
[5,4,3,1,6,2,7]=>[5,1,1]=>504
[5,4,3,1,6,7,2]=>[6,1]=>840
[5,4,3,1,7,2,6]=>[6,1]=>840
[5,4,3,1,7,6,2]=>[5,1,1]=>504
[5,4,3,2,1,6,7]=>[2,2,1,1,1]=>105
[5,4,3,2,1,7,6]=>[2,2,2,1]=>105
[5,4,3,2,6,1,7]=>[3,2,1,1]=>420
[5,4,3,2,6,7,1]=>[4,2,1]=>630
[5,4,3,2,7,1,6]=>[4,2,1]=>630
[5,4,3,2,7,6,1]=>[3,2,1,1]=>420
[5,4,3,6,1,2,7]=>[3,2,1,1]=>420
[5,4,3,6,1,7,2]=>[4,2,1]=>630
[5,4,3,6,2,1,7]=>[5,1,1]=>504
[5,4,3,6,2,7,1]=>[6,1]=>840
[5,4,3,6,7,1,2]=>[6,1]=>840
[5,4,3,6,7,2,1]=>[3,3,1]=>280
[5,4,3,7,1,2,6]=>[4,2,1]=>630
[5,4,3,7,1,6,2]=>[3,2,1,1]=>420
[5,4,3,7,2,1,6]=>[6,1]=>840
[5,4,3,7,2,6,1]=>[5,1,1]=>504
[5,4,3,7,6,1,2]=>[3,3,1]=>280
[5,4,3,7,6,2,1]=>[6,1]=>840
[5,4,6,1,2,3,7]=>[4,2,1]=>630
[5,4,6,1,2,7,3]=>[4,3]=>420
[5,4,6,1,3,2,7]=>[6,1]=>840
[5,4,6,1,3,7,2]=>[7]=>720
[5,4,6,1,7,2,3]=>[7]=>720
[5,4,6,1,7,3,2]=>[5,2]=>504
[5,4,6,2,1,3,7]=>[2,2,2,1]=>105
[5,4,6,2,1,7,3]=>[3,2,2]=>210
[5,4,6,2,3,1,7]=>[4,2,1]=>630
[5,4,6,2,3,7,1]=>[5,2]=>504
[5,4,6,2,7,1,3]=>[5,2]=>504
[5,4,6,2,7,3,1]=>[3,2,2]=>210
[5,4,6,3,1,2,7]=>[4,2,1]=>630
[5,4,6,3,1,7,2]=>[5,2]=>504
[5,4,6,3,2,1,7]=>[6,1]=>840
[5,4,6,3,2,7,1]=>[7]=>720
[5,4,6,3,7,1,2]=>[7]=>720
[5,4,6,3,7,2,1]=>[4,3]=>420
[5,4,6,7,1,2,3]=>[5,2]=>504
[5,4,6,7,1,3,2]=>[3,2,2]=>210
[5,4,6,7,2,1,3]=>[7]=>720
[5,4,6,7,2,3,1]=>[5,2]=>504
[5,4,6,7,3,1,2]=>[4,3]=>420
[5,4,6,7,3,2,1]=>[7]=>720
[5,4,7,1,2,3,6]=>[4,3]=>420
[5,4,7,1,2,6,3]=>[4,2,1]=>630
[5,4,7,1,3,2,6]=>[7]=>720
[5,4,7,1,3,6,2]=>[6,1]=>840
[5,4,7,1,6,2,3]=>[5,2]=>504
[5,4,7,1,6,3,2]=>[7]=>720
[5,4,7,2,1,3,6]=>[3,2,2]=>210
[5,4,7,2,1,6,3]=>[2,2,2,1]=>105
[5,4,7,2,3,1,6]=>[5,2]=>504
[5,4,7,2,3,6,1]=>[4,2,1]=>630
[5,4,7,2,6,1,3]=>[3,2,2]=>210
[5,4,7,2,6,3,1]=>[5,2]=>504
[5,4,7,3,1,2,6]=>[5,2]=>504
[5,4,7,3,1,6,2]=>[4,2,1]=>630
[5,4,7,3,2,1,6]=>[7]=>720
[5,4,7,3,2,6,1]=>[6,1]=>840
[5,4,7,3,6,1,2]=>[4,3]=>420
[5,4,7,3,6,2,1]=>[7]=>720
[5,4,7,6,1,2,3]=>[3,2,2]=>210
[5,4,7,6,1,3,2]=>[5,2]=>504
[5,4,7,6,2,1,3]=>[5,2]=>504
[5,4,7,6,2,3,1]=>[7]=>720
[5,4,7,6,3,1,2]=>[7]=>720
[5,4,7,6,3,2,1]=>[4,3]=>420
[5,6,1,2,3,4,7]=>[3,3,1]=>280
[5,6,1,2,3,7,4]=>[4,3]=>420
[5,6,1,2,4,3,7]=>[6,1]=>840
[5,6,1,2,4,7,3]=>[7]=>720
[5,6,1,2,7,3,4]=>[7]=>720
[5,6,1,2,7,4,3]=>[4,3]=>420
[5,6,1,3,2,4,7]=>[6,1]=>840
[5,6,1,3,2,7,4]=>[7]=>720
[5,6,1,3,4,2,7]=>[4,2,1]=>630
[5,6,1,3,4,7,2]=>[4,3]=>420
[5,6,1,3,7,2,4]=>[5,2]=>504
[5,6,1,3,7,4,2]=>[7]=>720
[5,6,1,4,2,3,7]=>[5,1,1]=>504
[5,6,1,4,2,7,3]=>[6,1]=>840
[5,6,1,4,3,2,7]=>[3,2,1,1]=>420
[5,6,1,4,3,7,2]=>[3,3,1]=>280
[5,6,1,4,7,2,3]=>[4,2,1]=>630
[5,6,1,4,7,3,2]=>[6,1]=>840
[5,6,1,7,2,3,4]=>[5,2]=>504
[5,6,1,7,2,4,3]=>[7]=>720
[5,6,1,7,3,2,4]=>[3,2,2]=>210
[5,6,1,7,3,4,2]=>[4,3]=>420
[5,6,1,7,4,2,3]=>[5,2]=>504
[5,6,1,7,4,3,2]=>[7]=>720
[5,6,2,1,3,4,7]=>[6,1]=>840
[5,6,2,1,3,7,4]=>[7]=>720
[5,6,2,1,4,3,7]=>[3,3,1]=>280
[5,6,2,1,4,7,3]=>[4,3]=>420
[5,6,2,1,7,3,4]=>[4,3]=>420
[5,6,2,1,7,4,3]=>[7]=>720
[5,6,2,3,1,4,7]=>[4,2,1]=>630
[5,6,2,3,1,7,4]=>[5,2]=>504
[5,6,2,3,4,1,7]=>[6,1]=>840
[5,6,2,3,4,7,1]=>[7]=>720
[5,6,2,3,7,1,4]=>[7]=>720
[5,6,2,3,7,4,1]=>[4,3]=>420
[5,6,2,4,1,3,7]=>[3,2,1,1]=>420
[5,6,2,4,1,7,3]=>[4,2,1]=>630
[5,6,2,4,3,1,7]=>[5,1,1]=>504
[5,6,2,4,3,7,1]=>[6,1]=>840
[5,6,2,4,7,1,3]=>[6,1]=>840
[5,6,2,4,7,3,1]=>[3,3,1]=>280
[5,6,2,7,1,3,4]=>[3,2,2]=>210
[5,6,2,7,1,4,3]=>[5,2]=>504
[5,6,2,7,3,1,4]=>[5,2]=>504
[5,6,2,7,3,4,1]=>[7]=>720
[5,6,2,7,4,1,3]=>[7]=>720
[5,6,2,7,4,3,1]=>[4,3]=>420
[5,6,3,1,2,4,7]=>[5,1,1]=>504
[5,6,3,1,2,7,4]=>[6,1]=>840
[5,6,3,1,4,2,7]=>[3,2,1,1]=>420
[5,6,3,1,4,7,2]=>[3,3,1]=>280
[5,6,3,1,7,2,4]=>[4,2,1]=>630
[5,6,3,1,7,4,2]=>[6,1]=>840
[5,6,3,2,1,4,7]=>[3,2,1,1]=>420
[5,6,3,2,1,7,4]=>[4,2,1]=>630
[5,6,3,2,4,1,7]=>[5,1,1]=>504
[5,6,3,2,4,7,1]=>[6,1]=>840
[5,6,3,2,7,1,4]=>[6,1]=>840
[5,6,3,2,7,4,1]=>[3,3,1]=>280
[5,6,3,4,1,2,7]=>[2,2,1,1,1]=>105
[5,6,3,4,1,7,2]=>[3,2,1,1]=>420
[5,6,3,4,2,1,7]=>[4,1,1,1]=>210
[5,6,3,4,2,7,1]=>[5,1,1]=>504
[5,6,3,4,7,1,2]=>[5,1,1]=>504
[5,6,3,4,7,2,1]=>[3,2,1,1]=>420
[5,6,3,7,1,2,4]=>[2,2,2,1]=>105
[5,6,3,7,1,4,2]=>[4,2,1]=>630
[5,6,3,7,2,1,4]=>[4,2,1]=>630
[5,6,3,7,2,4,1]=>[6,1]=>840
[5,6,3,7,4,1,2]=>[6,1]=>840
[5,6,3,7,4,2,1]=>[4,2,1]=>630
[5,6,4,1,2,3,7]=>[6,1]=>840
[5,6,4,1,2,7,3]=>[7]=>720
[5,6,4,1,3,2,7]=>[4,2,1]=>630
[5,6,4,1,3,7,2]=>[4,3]=>420
[5,6,4,1,7,2,3]=>[5,2]=>504
[5,6,4,1,7,3,2]=>[7]=>720
[5,6,4,2,1,3,7]=>[4,2,1]=>630
[5,6,4,2,1,7,3]=>[5,2]=>504
[5,6,4,2,3,1,7]=>[6,1]=>840
[5,6,4,2,3,7,1]=>[7]=>720
[5,6,4,2,7,1,3]=>[7]=>720
[5,6,4,2,7,3,1]=>[4,3]=>420
[5,6,4,3,1,2,7]=>[2,2,2,1]=>105
[5,6,4,3,1,7,2]=>[3,2,2]=>210
[5,6,4,3,2,1,7]=>[4,2,1]=>630
[5,6,4,3,2,7,1]=>[5,2]=>504
[5,6,4,3,7,1,2]=>[5,2]=>504
[5,6,4,3,7,2,1]=>[3,2,2]=>210
[5,6,4,7,1,2,3]=>[3,2,2]=>210
[5,6,4,7,1,3,2]=>[5,2]=>504
[5,6,4,7,2,1,3]=>[4,3]=>420
[5,6,4,7,2,3,1]=>[7]=>720
[5,6,4,7,3,1,2]=>[7]=>720
[5,6,4,7,3,2,1]=>[5,2]=>504
[5,6,7,1,2,3,4]=>[7]=>720
[5,6,7,1,2,4,3]=>[5,2]=>504
[5,6,7,1,3,2,4]=>[5,2]=>504
[5,6,7,1,3,4,2]=>[7]=>720
[5,6,7,1,4,2,3]=>[3,2,2]=>210
[5,6,7,1,4,3,2]=>[4,3]=>420
[5,6,7,2,1,3,4]=>[5,2]=>504
[5,6,7,2,1,4,3]=>[3,2,2]=>210
[5,6,7,2,3,1,4]=>[7]=>720
[5,6,7,2,3,4,1]=>[4,3]=>420
[5,6,7,2,4,1,3]=>[5,2]=>504
[5,6,7,2,4,3,1]=>[7]=>720
[5,6,7,3,1,2,4]=>[3,2,2]=>210
[5,6,7,3,1,4,2]=>[5,2]=>504
[5,6,7,3,2,1,4]=>[4,3]=>420
[5,6,7,3,2,4,1]=>[7]=>720
[5,6,7,3,4,1,2]=>[7]=>720
[5,6,7,3,4,2,1]=>[5,2]=>504
[5,6,7,4,1,2,3]=>[2,2,2,1]=>105
[5,6,7,4,1,3,2]=>[4,2,1]=>630
[5,6,7,4,2,1,3]=>[4,2,1]=>630
[5,6,7,4,2,3,1]=>[6,1]=>840
[5,6,7,4,3,1,2]=>[6,1]=>840
[5,6,7,4,3,2,1]=>[4,2,1]=>630
[5,7,1,2,3,4,6]=>[4,3]=>420
[5,7,1,2,3,6,4]=>[3,3,1]=>280
[5,7,1,2,4,3,6]=>[7]=>720
[5,7,1,2,4,6,3]=>[6,1]=>840
[5,7,1,2,6,3,4]=>[4,3]=>420
[5,7,1,2,6,4,3]=>[7]=>720
[5,7,1,3,2,4,6]=>[7]=>720
[5,7,1,3,2,6,4]=>[6,1]=>840
[5,7,1,3,4,2,6]=>[4,3]=>420
[5,7,1,3,4,6,2]=>[4,2,1]=>630
[5,7,1,3,6,2,4]=>[7]=>720
[5,7,1,3,6,4,2]=>[5,2]=>504
[5,7,1,4,2,3,6]=>[6,1]=>840
[5,7,1,4,2,6,3]=>[5,1,1]=>504
[5,7,1,4,3,2,6]=>[3,3,1]=>280
[5,7,1,4,3,6,2]=>[3,2,1,1]=>420
[5,7,1,4,6,2,3]=>[6,1]=>840
[5,7,1,4,6,3,2]=>[4,2,1]=>630
[5,7,1,6,2,3,4]=>[7]=>720
[5,7,1,6,2,4,3]=>[5,2]=>504
[5,7,1,6,3,2,4]=>[4,3]=>420
[5,7,1,6,3,4,2]=>[3,2,2]=>210
[5,7,1,6,4,2,3]=>[7]=>720
[5,7,1,6,4,3,2]=>[5,2]=>504
[5,7,2,1,3,4,6]=>[7]=>720
[5,7,2,1,3,6,4]=>[6,1]=>840
[5,7,2,1,4,3,6]=>[4,3]=>420
[5,7,2,1,4,6,3]=>[3,3,1]=>280
[5,7,2,1,6,3,4]=>[7]=>720
[5,7,2,1,6,4,3]=>[4,3]=>420
[5,7,2,3,1,4,6]=>[5,2]=>504
[5,7,2,3,1,6,4]=>[4,2,1]=>630
[5,7,2,3,4,1,6]=>[7]=>720
[5,7,2,3,4,6,1]=>[6,1]=>840
[5,7,2,3,6,1,4]=>[4,3]=>420
[5,7,2,3,6,4,1]=>[7]=>720
[5,7,2,4,1,3,6]=>[4,2,1]=>630
[5,7,2,4,1,6,3]=>[3,2,1,1]=>420
[5,7,2,4,3,1,6]=>[6,1]=>840
[5,7,2,4,3,6,1]=>[5,1,1]=>504
[5,7,2,4,6,1,3]=>[3,3,1]=>280
[5,7,2,4,6,3,1]=>[6,1]=>840
[5,7,2,6,1,3,4]=>[5,2]=>504
[5,7,2,6,1,4,3]=>[3,2,2]=>210
[5,7,2,6,3,1,4]=>[7]=>720
[5,7,2,6,3,4,1]=>[5,2]=>504
[5,7,2,6,4,1,3]=>[4,3]=>420
[5,7,2,6,4,3,1]=>[7]=>720
[5,7,3,1,2,4,6]=>[6,1]=>840
[5,7,3,1,2,6,4]=>[5,1,1]=>504
[5,7,3,1,4,2,6]=>[3,3,1]=>280
[5,7,3,1,4,6,2]=>[3,2,1,1]=>420
[5,7,3,1,6,2,4]=>[6,1]=>840
[5,7,3,1,6,4,2]=>[4,2,1]=>630
[5,7,3,2,1,4,6]=>[4,2,1]=>630
[5,7,3,2,1,6,4]=>[3,2,1,1]=>420
[5,7,3,2,4,1,6]=>[6,1]=>840
[5,7,3,2,4,6,1]=>[5,1,1]=>504
[5,7,3,2,6,1,4]=>[3,3,1]=>280
[5,7,3,2,6,4,1]=>[6,1]=>840
[5,7,3,4,1,2,6]=>[3,2,1,1]=>420
[5,7,3,4,1,6,2]=>[2,2,1,1,1]=>105
[5,7,3,4,2,1,6]=>[5,1,1]=>504
[5,7,3,4,2,6,1]=>[4,1,1,1]=>210
[5,7,3,4,6,1,2]=>[3,2,1,1]=>420
[5,7,3,4,6,2,1]=>[5,1,1]=>504
[5,7,3,6,1,2,4]=>[4,2,1]=>630
[5,7,3,6,1,4,2]=>[2,2,2,1]=>105
[5,7,3,6,2,1,4]=>[6,1]=>840
[5,7,3,6,2,4,1]=>[4,2,1]=>630
[5,7,3,6,4,1,2]=>[4,2,1]=>630
[5,7,3,6,4,2,1]=>[6,1]=>840
[5,7,4,1,2,3,6]=>[7]=>720
[5,7,4,1,2,6,3]=>[6,1]=>840
[5,7,4,1,3,2,6]=>[4,3]=>420
[5,7,4,1,3,6,2]=>[4,2,1]=>630
[5,7,4,1,6,2,3]=>[7]=>720
[5,7,4,1,6,3,2]=>[5,2]=>504
[5,7,4,2,1,3,6]=>[5,2]=>504
[5,7,4,2,1,6,3]=>[4,2,1]=>630
[5,7,4,2,3,1,6]=>[7]=>720
[5,7,4,2,3,6,1]=>[6,1]=>840
[5,7,4,2,6,1,3]=>[4,3]=>420
[5,7,4,2,6,3,1]=>[7]=>720
[5,7,4,3,1,2,6]=>[3,2,2]=>210
[5,7,4,3,1,6,2]=>[2,2,2,1]=>105
[5,7,4,3,2,1,6]=>[5,2]=>504
[5,7,4,3,2,6,1]=>[4,2,1]=>630
[5,7,4,3,6,1,2]=>[3,2,2]=>210
[5,7,4,3,6,2,1]=>[5,2]=>504
[5,7,4,6,1,2,3]=>[5,2]=>504
[5,7,4,6,1,3,2]=>[3,2,2]=>210
[5,7,4,6,2,1,3]=>[7]=>720
[5,7,4,6,2,3,1]=>[4,3]=>420
[5,7,4,6,3,1,2]=>[5,2]=>504
[5,7,4,6,3,2,1]=>[7]=>720
[5,7,6,1,2,3,4]=>[5,2]=>504
[5,7,6,1,2,4,3]=>[7]=>720
[5,7,6,1,3,2,4]=>[7]=>720
[5,7,6,1,3,4,2]=>[5,2]=>504
[5,7,6,1,4,2,3]=>[4,3]=>420
[5,7,6,1,4,3,2]=>[3,2,2]=>210
[5,7,6,2,1,3,4]=>[3,2,2]=>210
[5,7,6,2,1,4,3]=>[5,2]=>504
[5,7,6,2,3,1,4]=>[4,3]=>420
[5,7,6,2,3,4,1]=>[7]=>720
[5,7,6,2,4,1,3]=>[7]=>720
[5,7,6,2,4,3,1]=>[5,2]=>504
[5,7,6,3,1,2,4]=>[5,2]=>504
[5,7,6,3,1,4,2]=>[3,2,2]=>210
[5,7,6,3,2,1,4]=>[7]=>720
[5,7,6,3,2,4,1]=>[4,3]=>420
[5,7,6,3,4,1,2]=>[5,2]=>504
[5,7,6,3,4,2,1]=>[7]=>720
[5,7,6,4,1,2,3]=>[4,2,1]=>630
[5,7,6,4,1,3,2]=>[2,2,2,1]=>105
[5,7,6,4,2,1,3]=>[6,1]=>840
[5,7,6,4,2,3,1]=>[4,2,1]=>630
[5,7,6,4,3,1,2]=>[4,2,1]=>630
[5,7,6,4,3,2,1]=>[6,1]=>840
[6,1,2,3,4,5,7]=>[6,1]=>840
[6,1,2,3,4,7,5]=>[7]=>720
[6,1,2,3,5,4,7]=>[5,1,1]=>504
[6,1,2,3,5,7,4]=>[6,1]=>840
[6,1,2,3,7,4,5]=>[5,2]=>504
[6,1,2,3,7,5,4]=>[7]=>720
[6,1,2,4,3,5,7]=>[5,1,1]=>504
[6,1,2,4,3,7,5]=>[6,1]=>840
[6,1,2,4,5,3,7]=>[4,1,1,1]=>210
[6,1,2,4,5,7,3]=>[5,1,1]=>504
[6,1,2,4,7,3,5]=>[4,2,1]=>630
[6,1,2,4,7,5,3]=>[6,1]=>840
[6,1,2,5,3,4,7]=>[6,1]=>840
[6,1,2,5,3,7,4]=>[7]=>720
[6,1,2,5,4,3,7]=>[4,2,1]=>630
[6,1,2,5,4,7,3]=>[5,2]=>504
[6,1,2,5,7,3,4]=>[4,3]=>420
[6,1,2,5,7,4,3]=>[7]=>720
[6,1,2,7,3,4,5]=>[7]=>720
[6,1,2,7,3,5,4]=>[5,2]=>504
[6,1,2,7,4,3,5]=>[4,3]=>420
[6,1,2,7,4,5,3]=>[7]=>720
[6,1,2,7,5,3,4]=>[4,2,1]=>630
[6,1,2,7,5,4,3]=>[6,1]=>840
[6,1,3,2,4,5,7]=>[5,1,1]=>504
[6,1,3,2,4,7,5]=>[6,1]=>840
[6,1,3,2,5,4,7]=>[4,1,1,1]=>210
[6,1,3,2,5,7,4]=>[5,1,1]=>504
[6,1,3,2,7,4,5]=>[4,2,1]=>630
[6,1,3,2,7,5,4]=>[6,1]=>840
[6,1,3,4,2,5,7]=>[4,1,1,1]=>210
[6,1,3,4,2,7,5]=>[5,1,1]=>504
[6,1,3,4,5,2,7]=>[3,1,1,1,1]=>70
[6,1,3,4,5,7,2]=>[4,1,1,1]=>210
[6,1,3,4,7,2,5]=>[3,2,1,1]=>420
[6,1,3,4,7,5,2]=>[5,1,1]=>504
[6,1,3,5,2,4,7]=>[5,1,1]=>504
[6,1,3,5,2,7,4]=>[6,1]=>840
[6,1,3,5,4,2,7]=>[3,2,1,1]=>420
[6,1,3,5,4,7,2]=>[4,2,1]=>630
[6,1,3,5,7,2,4]=>[3,3,1]=>280
[6,1,3,5,7,4,2]=>[6,1]=>840
[6,1,3,7,2,4,5]=>[6,1]=>840
[6,1,3,7,2,5,4]=>[4,2,1]=>630
[6,1,3,7,4,2,5]=>[3,3,1]=>280
[6,1,3,7,4,5,2]=>[6,1]=>840
[6,1,3,7,5,2,4]=>[3,2,1,1]=>420
[6,1,3,7,5,4,2]=>[5,1,1]=>504
[6,1,4,2,3,5,7]=>[6,1]=>840
[6,1,4,2,3,7,5]=>[7]=>720
[6,1,4,2,5,3,7]=>[5,1,1]=>504
[6,1,4,2,5,7,3]=>[6,1]=>840
[6,1,4,2,7,3,5]=>[5,2]=>504
[6,1,4,2,7,5,3]=>[7]=>720
[6,1,4,3,2,5,7]=>[4,2,1]=>630
[6,1,4,3,2,7,5]=>[5,2]=>504
[6,1,4,3,5,2,7]=>[3,2,1,1]=>420
[6,1,4,3,5,7,2]=>[4,2,1]=>630
[6,1,4,3,7,2,5]=>[3,2,2]=>210
[6,1,4,3,7,5,2]=>[5,2]=>504
[6,1,4,5,2,3,7]=>[6,1]=>840
[6,1,4,5,2,7,3]=>[7]=>720
[6,1,4,5,3,2,7]=>[3,3,1]=>280
[6,1,4,5,3,7,2]=>[4,3]=>420
[6,1,4,5,7,2,3]=>[4,3]=>420
[6,1,4,5,7,3,2]=>[7]=>720
[6,1,4,7,2,3,5]=>[7]=>720
[6,1,4,7,2,5,3]=>[4,3]=>420
[6,1,4,7,3,2,5]=>[4,3]=>420
[6,1,4,7,3,5,2]=>[7]=>720
[6,1,4,7,5,2,3]=>[3,3,1]=>280
[6,1,4,7,5,3,2]=>[6,1]=>840
[6,1,5,2,3,4,7]=>[4,2,1]=>630
[6,1,5,2,3,7,4]=>[5,2]=>504
[6,1,5,2,4,3,7]=>[6,1]=>840
[6,1,5,2,4,7,3]=>[7]=>720
[6,1,5,2,7,3,4]=>[7]=>720
[6,1,5,2,7,4,3]=>[4,3]=>420
[6,1,5,3,2,4,7]=>[6,1]=>840
[6,1,5,3,2,7,4]=>[7]=>720
[6,1,5,3,4,2,7]=>[3,3,1]=>280
[6,1,5,3,4,7,2]=>[4,3]=>420
[6,1,5,3,7,2,4]=>[4,3]=>420
[6,1,5,3,7,4,2]=>[7]=>720
[6,1,5,4,2,3,7]=>[5,1,1]=>504
[6,1,5,4,2,7,3]=>[6,1]=>840
[6,1,5,4,3,2,7]=>[3,2,1,1]=>420
[6,1,5,4,3,7,2]=>[4,2,1]=>630
[6,1,5,4,7,2,3]=>[3,3,1]=>280
[6,1,5,4,7,3,2]=>[6,1]=>840
[6,1,5,7,2,3,4]=>[5,2]=>504
[6,1,5,7,2,4,3]=>[7]=>720
[6,1,5,7,3,2,4]=>[3,2,2]=>210
[6,1,5,7,3,4,2]=>[5,2]=>504
[6,1,5,7,4,2,3]=>[4,3]=>420
[6,1,5,7,4,3,2]=>[7]=>720
[6,1,7,2,3,4,5]=>[4,3]=>420
[6,1,7,2,3,5,4]=>[7]=>720
[6,1,7,2,4,3,5]=>[7]=>720
[6,1,7,2,4,5,3]=>[5,2]=>504
[6,1,7,2,5,3,4]=>[6,1]=>840
[6,1,7,2,5,4,3]=>[4,2,1]=>630
[6,1,7,3,2,4,5]=>[7]=>720
[6,1,7,3,2,5,4]=>[4,3]=>420
[6,1,7,3,4,2,5]=>[4,3]=>420
[6,1,7,3,4,5,2]=>[7]=>720
[6,1,7,3,5,2,4]=>[3,3,1]=>280
[6,1,7,3,5,4,2]=>[6,1]=>840
[6,1,7,4,2,3,5]=>[6,1]=>840
[6,1,7,4,2,5,3]=>[4,2,1]=>630
[6,1,7,4,3,2,5]=>[3,3,1]=>280
[6,1,7,4,3,5,2]=>[6,1]=>840
[6,1,7,4,5,2,3]=>[3,2,1,1]=>420
[6,1,7,4,5,3,2]=>[5,1,1]=>504
[6,1,7,5,2,3,4]=>[7]=>720
[6,1,7,5,2,4,3]=>[5,2]=>504
[6,1,7,5,3,2,4]=>[4,3]=>420
[6,1,7,5,3,4,2]=>[7]=>720
[6,1,7,5,4,2,3]=>[3,2,2]=>210
[6,1,7,5,4,3,2]=>[5,2]=>504
[6,2,1,3,4,5,7]=>[5,1,1]=>504
[6,2,1,3,4,7,5]=>[6,1]=>840
[6,2,1,3,5,4,7]=>[4,1,1,1]=>210
[6,2,1,3,5,7,4]=>[5,1,1]=>504
[6,2,1,3,7,4,5]=>[4,2,1]=>630
[6,2,1,3,7,5,4]=>[6,1]=>840
[6,2,1,4,3,5,7]=>[4,1,1,1]=>210
[6,2,1,4,3,7,5]=>[5,1,1]=>504
[6,2,1,4,5,3,7]=>[3,1,1,1,1]=>70
[6,2,1,4,5,7,3]=>[4,1,1,1]=>210
[6,2,1,4,7,3,5]=>[3,2,1,1]=>420
[6,2,1,4,7,5,3]=>[5,1,1]=>504
[6,2,1,5,3,4,7]=>[5,1,1]=>504
[6,2,1,5,3,7,4]=>[6,1]=>840
[6,2,1,5,4,3,7]=>[3,2,1,1]=>420
[6,2,1,5,4,7,3]=>[4,2,1]=>630
[6,2,1,5,7,3,4]=>[3,3,1]=>280
[6,2,1,5,7,4,3]=>[6,1]=>840
[6,2,1,7,3,4,5]=>[6,1]=>840
[6,2,1,7,3,5,4]=>[4,2,1]=>630
[6,2,1,7,4,3,5]=>[3,3,1]=>280
[6,2,1,7,4,5,3]=>[6,1]=>840
[6,2,1,7,5,3,4]=>[3,2,1,1]=>420
[6,2,1,7,5,4,3]=>[5,1,1]=>504
[6,2,3,1,4,5,7]=>[4,1,1,1]=>210
[6,2,3,1,4,7,5]=>[5,1,1]=>504
[6,2,3,1,5,4,7]=>[3,1,1,1,1]=>70
[6,2,3,1,5,7,4]=>[4,1,1,1]=>210
[6,2,3,1,7,4,5]=>[3,2,1,1]=>420
[6,2,3,1,7,5,4]=>[5,1,1]=>504
[6,2,3,4,1,5,7]=>[3,1,1,1,1]=>70
[6,2,3,4,1,7,5]=>[4,1,1,1]=>210
[6,2,3,4,5,1,7]=>[2,1,1,1,1,1]=>21
[6,2,3,4,5,7,1]=>[3,1,1,1,1]=>70
[6,2,3,4,7,1,5]=>[2,2,1,1,1]=>105
[6,2,3,4,7,5,1]=>[4,1,1,1]=>210
[6,2,3,5,1,4,7]=>[4,1,1,1]=>210
[6,2,3,5,1,7,4]=>[5,1,1]=>504
[6,2,3,5,4,1,7]=>[2,2,1,1,1]=>105
[6,2,3,5,4,7,1]=>[3,2,1,1]=>420
[6,2,3,5,7,1,4]=>[3,2,1,1]=>420
[6,2,3,5,7,4,1]=>[5,1,1]=>504
[6,2,3,7,1,4,5]=>[5,1,1]=>504
[6,2,3,7,1,5,4]=>[3,2,1,1]=>420
[6,2,3,7,4,1,5]=>[3,2,1,1]=>420
[6,2,3,7,4,5,1]=>[5,1,1]=>504
[6,2,3,7,5,1,4]=>[2,2,1,1,1]=>105
[6,2,3,7,5,4,1]=>[4,1,1,1]=>210
[6,2,4,1,3,5,7]=>[5,1,1]=>504
[6,2,4,1,3,7,5]=>[6,1]=>840
[6,2,4,1,5,3,7]=>[4,1,1,1]=>210
[6,2,4,1,5,7,3]=>[5,1,1]=>504
[6,2,4,1,7,3,5]=>[4,2,1]=>630
[6,2,4,1,7,5,3]=>[6,1]=>840
[6,2,4,3,1,5,7]=>[3,2,1,1]=>420
[6,2,4,3,1,7,5]=>[4,2,1]=>630
[6,2,4,3,5,1,7]=>[2,2,1,1,1]=>105
[6,2,4,3,5,7,1]=>[3,2,1,1]=>420
[6,2,4,3,7,1,5]=>[2,2,2,1]=>105
[6,2,4,3,7,5,1]=>[4,2,1]=>630
[6,2,4,5,1,3,7]=>[5,1,1]=>504
[6,2,4,5,1,7,3]=>[6,1]=>840
[6,2,4,5,3,1,7]=>[3,2,1,1]=>420
[6,2,4,5,3,7,1]=>[3,3,1]=>280
[6,2,4,5,7,1,3]=>[4,2,1]=>630
[6,2,4,5,7,3,1]=>[6,1]=>840
[6,2,4,7,1,3,5]=>[6,1]=>840
[6,2,4,7,1,5,3]=>[3,3,1]=>280
[6,2,4,7,3,1,5]=>[4,2,1]=>630
[6,2,4,7,3,5,1]=>[6,1]=>840
[6,2,4,7,5,1,3]=>[3,2,1,1]=>420
[6,2,4,7,5,3,1]=>[5,1,1]=>504
[6,2,5,1,3,4,7]=>[3,2,1,1]=>420
[6,2,5,1,3,7,4]=>[4,2,1]=>630
[6,2,5,1,4,3,7]=>[5,1,1]=>504
[6,2,5,1,4,7,3]=>[6,1]=>840
[6,2,5,1,7,3,4]=>[6,1]=>840
[6,2,5,1,7,4,3]=>[3,3,1]=>280
[6,2,5,3,1,4,7]=>[5,1,1]=>504
[6,2,5,3,1,7,4]=>[6,1]=>840
[6,2,5,3,4,1,7]=>[3,2,1,1]=>420
[6,2,5,3,4,7,1]=>[3,3,1]=>280
[6,2,5,3,7,1,4]=>[4,2,1]=>630
[6,2,5,3,7,4,1]=>[6,1]=>840
[6,2,5,4,1,3,7]=>[4,1,1,1]=>210
[6,2,5,4,1,7,3]=>[5,1,1]=>504
[6,2,5,4,3,1,7]=>[2,2,1,1,1]=>105
[6,2,5,4,3,7,1]=>[3,2,1,1]=>420
[6,2,5,4,7,1,3]=>[3,2,1,1]=>420
[6,2,5,4,7,3,1]=>[5,1,1]=>504
[6,2,5,7,1,3,4]=>[4,2,1]=>630
[6,2,5,7,1,4,3]=>[6,1]=>840
[6,2,5,7,3,1,4]=>[2,2,2,1]=>105
[6,2,5,7,3,4,1]=>[4,2,1]=>630
[6,2,5,7,4,1,3]=>[4,2,1]=>630
[6,2,5,7,4,3,1]=>[6,1]=>840
[6,2,7,1,3,4,5]=>[3,3,1]=>280
[6,2,7,1,3,5,4]=>[6,1]=>840
[6,2,7,1,4,3,5]=>[6,1]=>840
[6,2,7,1,4,5,3]=>[4,2,1]=>630
[6,2,7,1,5,3,4]=>[5,1,1]=>504
[6,2,7,1,5,4,3]=>[3,2,1,1]=>420
[6,2,7,3,1,4,5]=>[6,1]=>840
[6,2,7,3,1,5,4]=>[3,3,1]=>280
[6,2,7,3,4,1,5]=>[4,2,1]=>630
[6,2,7,3,4,5,1]=>[6,1]=>840
[6,2,7,3,5,1,4]=>[3,2,1,1]=>420
[6,2,7,3,5,4,1]=>[5,1,1]=>504
[6,2,7,4,1,3,5]=>[5,1,1]=>504
[6,2,7,4,1,5,3]=>[3,2,1,1]=>420
[6,2,7,4,3,1,5]=>[3,2,1,1]=>420
[6,2,7,4,3,5,1]=>[5,1,1]=>504
[6,2,7,4,5,1,3]=>[2,2,1,1,1]=>105
[6,2,7,4,5,3,1]=>[4,1,1,1]=>210
[6,2,7,5,1,3,4]=>[6,1]=>840
[6,2,7,5,1,4,3]=>[4,2,1]=>630
[6,2,7,5,3,1,4]=>[4,2,1]=>630
[6,2,7,5,3,4,1]=>[6,1]=>840
[6,2,7,5,4,1,3]=>[2,2,2,1]=>105
[6,2,7,5,4,3,1]=>[4,2,1]=>630
[6,3,1,2,4,5,7]=>[6,1]=>840
[6,3,1,2,4,7,5]=>[7]=>720
[6,3,1,2,5,4,7]=>[5,1,1]=>504
[6,3,1,2,5,7,4]=>[6,1]=>840
[6,3,1,2,7,4,5]=>[5,2]=>504
[6,3,1,2,7,5,4]=>[7]=>720
[6,3,1,4,2,5,7]=>[5,1,1]=>504
[6,3,1,4,2,7,5]=>[6,1]=>840
[6,3,1,4,5,2,7]=>[4,1,1,1]=>210
[6,3,1,4,5,7,2]=>[5,1,1]=>504
[6,3,1,4,7,2,5]=>[4,2,1]=>630
[6,3,1,4,7,5,2]=>[6,1]=>840
[6,3,1,5,2,4,7]=>[6,1]=>840
[6,3,1,5,2,7,4]=>[7]=>720
[6,3,1,5,4,2,7]=>[4,2,1]=>630
[6,3,1,5,4,7,2]=>[5,2]=>504
[6,3,1,5,7,2,4]=>[4,3]=>420
[6,3,1,5,7,4,2]=>[7]=>720
[6,3,1,7,2,4,5]=>[7]=>720
[6,3,1,7,2,5,4]=>[5,2]=>504
[6,3,1,7,4,2,5]=>[4,3]=>420
[6,3,1,7,4,5,2]=>[7]=>720
[6,3,1,7,5,2,4]=>[4,2,1]=>630
[6,3,1,7,5,4,2]=>[6,1]=>840
[6,3,2,1,4,5,7]=>[4,2,1]=>630
[6,3,2,1,4,7,5]=>[5,2]=>504
[6,3,2,1,5,4,7]=>[3,2,1,1]=>420
[6,3,2,1,5,7,4]=>[4,2,1]=>630
[6,3,2,1,7,4,5]=>[3,2,2]=>210
[6,3,2,1,7,5,4]=>[5,2]=>504
[6,3,2,4,1,5,7]=>[3,2,1,1]=>420
[6,3,2,4,1,7,5]=>[4,2,1]=>630
[6,3,2,4,5,1,7]=>[2,2,1,1,1]=>105
[6,3,2,4,5,7,1]=>[3,2,1,1]=>420
[6,3,2,4,7,1,5]=>[2,2,2,1]=>105
[6,3,2,4,7,5,1]=>[4,2,1]=>630
[6,3,2,5,1,4,7]=>[4,2,1]=>630
[6,3,2,5,1,7,4]=>[5,2]=>504
[6,3,2,5,4,1,7]=>[2,2,2,1]=>105
[6,3,2,5,4,7,1]=>[3,2,2]=>210
[6,3,2,5,7,1,4]=>[3,2,2]=>210
[6,3,2,5,7,4,1]=>[5,2]=>504
[6,3,2,7,1,4,5]=>[5,2]=>504
[6,3,2,7,1,5,4]=>[3,2,2]=>210
[6,3,2,7,4,1,5]=>[3,2,2]=>210
[6,3,2,7,4,5,1]=>[5,2]=>504
[6,3,2,7,5,1,4]=>[2,2,2,1]=>105
[6,3,2,7,5,4,1]=>[4,2,1]=>630
[6,3,4,1,2,5,7]=>[6,1]=>840
[6,3,4,1,2,7,5]=>[7]=>720
[6,3,4,1,5,2,7]=>[5,1,1]=>504
[6,3,4,1,5,7,2]=>[6,1]=>840
[6,3,4,1,7,2,5]=>[5,2]=>504
[6,3,4,1,7,5,2]=>[7]=>720
[6,3,4,2,1,5,7]=>[3,3,1]=>280
[6,3,4,2,1,7,5]=>[4,3]=>420
[6,3,4,2,5,1,7]=>[3,2,1,1]=>420
[6,3,4,2,5,7,1]=>[3,3,1]=>280
[6,3,4,2,7,1,5]=>[3,2,2]=>210
[6,3,4,2,7,5,1]=>[4,3]=>420
[6,3,4,5,1,2,7]=>[6,1]=>840
[6,3,4,5,1,7,2]=>[7]=>720
[6,3,4,5,2,1,7]=>[4,2,1]=>630
[6,3,4,5,2,7,1]=>[4,3]=>420
[6,3,4,5,7,1,2]=>[5,2]=>504
[6,3,4,5,7,2,1]=>[7]=>720
[6,3,4,7,1,2,5]=>[7]=>720
[6,3,4,7,1,5,2]=>[4,3]=>420
[6,3,4,7,2,1,5]=>[5,2]=>504
[6,3,4,7,2,5,1]=>[7]=>720
[6,3,4,7,5,1,2]=>[4,2,1]=>630
[6,3,4,7,5,2,1]=>[6,1]=>840
[6,3,5,1,2,4,7]=>[3,3,1]=>280
[6,3,5,1,2,7,4]=>[4,3]=>420
[6,3,5,1,4,2,7]=>[6,1]=>840
[6,3,5,1,4,7,2]=>[7]=>720
[6,3,5,1,7,2,4]=>[7]=>720
[6,3,5,1,7,4,2]=>[4,3]=>420
[6,3,5,2,1,4,7]=>[6,1]=>840
[6,3,5,2,1,7,4]=>[7]=>720
[6,3,5,2,4,1,7]=>[4,2,1]=>630
[6,3,5,2,4,7,1]=>[4,3]=>420
[6,3,5,2,7,1,4]=>[5,2]=>504
[6,3,5,2,7,4,1]=>[7]=>720
[6,3,5,4,1,2,7]=>[5,1,1]=>504
[6,3,5,4,1,7,2]=>[6,1]=>840
[6,3,5,4,2,1,7]=>[3,2,1,1]=>420
[6,3,5,4,2,7,1]=>[3,3,1]=>280
[6,3,5,4,7,1,2]=>[4,2,1]=>630
[6,3,5,4,7,2,1]=>[6,1]=>840
[6,3,5,7,1,2,4]=>[5,2]=>504
[6,3,5,7,1,4,2]=>[7]=>720
[6,3,5,7,2,1,4]=>[3,2,2]=>210
[6,3,5,7,2,4,1]=>[4,3]=>420
[6,3,5,7,4,1,2]=>[5,2]=>504
[6,3,5,7,4,2,1]=>[7]=>720
[6,3,7,1,2,4,5]=>[4,3]=>420
[6,3,7,1,2,5,4]=>[7]=>720
[6,3,7,1,4,2,5]=>[7]=>720
[6,3,7,1,4,5,2]=>[4,3]=>420
[6,3,7,1,5,2,4]=>[6,1]=>840
[6,3,7,1,5,4,2]=>[3,3,1]=>280
[6,3,7,2,1,4,5]=>[7]=>720
[6,3,7,2,1,5,4]=>[4,3]=>420
[6,3,7,2,4,1,5]=>[5,2]=>504
[6,3,7,2,4,5,1]=>[7]=>720
[6,3,7,2,5,1,4]=>[4,2,1]=>630
[6,3,7,2,5,4,1]=>[6,1]=>840
[6,3,7,4,1,2,5]=>[6,1]=>840
[6,3,7,4,1,5,2]=>[3,3,1]=>280
[6,3,7,4,2,1,5]=>[4,2,1]=>630
[6,3,7,4,2,5,1]=>[6,1]=>840
[6,3,7,4,5,1,2]=>[3,2,1,1]=>420
[6,3,7,4,5,2,1]=>[5,1,1]=>504
[6,3,7,5,1,2,4]=>[7]=>720
[6,3,7,5,1,4,2]=>[4,3]=>420
[6,3,7,5,2,1,4]=>[5,2]=>504
[6,3,7,5,2,4,1]=>[7]=>720
[6,3,7,5,4,1,2]=>[3,2,2]=>210
[6,3,7,5,4,2,1]=>[5,2]=>504
[6,4,1,2,3,5,7]=>[4,2,1]=>630
[6,4,1,2,3,7,5]=>[5,2]=>504
[6,4,1,2,5,3,7]=>[3,2,1,1]=>420
[6,4,1,2,5,7,3]=>[4,2,1]=>630
[6,4,1,2,7,3,5]=>[3,2,2]=>210
[6,4,1,2,7,5,3]=>[5,2]=>504
[6,4,1,3,2,5,7]=>[6,1]=>840
[6,4,1,3,2,7,5]=>[7]=>720
[6,4,1,3,5,2,7]=>[5,1,1]=>504
[6,4,1,3,5,7,2]=>[6,1]=>840
[6,4,1,3,7,2,5]=>[5,2]=>504
[6,4,1,3,7,5,2]=>[7]=>720
[6,4,1,5,2,3,7]=>[3,3,1]=>280
[6,4,1,5,2,7,3]=>[4,3]=>420
[6,4,1,5,3,2,7]=>[6,1]=>840
[6,4,1,5,3,7,2]=>[7]=>720
[6,4,1,5,7,2,3]=>[7]=>720
[6,4,1,5,7,3,2]=>[4,3]=>420
[6,4,1,7,2,3,5]=>[4,3]=>420
[6,4,1,7,2,5,3]=>[7]=>720
[6,4,1,7,3,2,5]=>[7]=>720
[6,4,1,7,3,5,2]=>[4,3]=>420
[6,4,1,7,5,2,3]=>[6,1]=>840
[6,4,1,7,5,3,2]=>[3,3,1]=>280
[6,4,2,1,3,5,7]=>[6,1]=>840
[6,4,2,1,3,7,5]=>[7]=>720
[6,4,2,1,5,3,7]=>[5,1,1]=>504
[6,4,2,1,5,7,3]=>[6,1]=>840
[6,4,2,1,7,3,5]=>[5,2]=>504
[6,4,2,1,7,5,3]=>[7]=>720
[6,4,2,3,1,5,7]=>[3,3,1]=>280
[6,4,2,3,1,7,5]=>[4,3]=>420
[6,4,2,3,5,1,7]=>[3,2,1,1]=>420
[6,4,2,3,5,7,1]=>[3,3,1]=>280
[6,4,2,3,7,1,5]=>[3,2,2]=>210
[6,4,2,3,7,5,1]=>[4,3]=>420
[6,4,2,5,1,3,7]=>[6,1]=>840
[6,4,2,5,1,7,3]=>[7]=>720
[6,4,2,5,3,1,7]=>[4,2,1]=>630
[6,4,2,5,3,7,1]=>[4,3]=>420
[6,4,2,5,7,1,3]=>[5,2]=>504
[6,4,2,5,7,3,1]=>[7]=>720
[6,4,2,7,1,3,5]=>[7]=>720
[6,4,2,7,1,5,3]=>[4,3]=>420
[6,4,2,7,3,1,5]=>[5,2]=>504
[6,4,2,7,3,5,1]=>[7]=>720
[6,4,2,7,5,1,3]=>[4,2,1]=>630
[6,4,2,7,5,3,1]=>[6,1]=>840
[6,4,3,1,2,5,7]=>[5,1,1]=>504
[6,4,3,1,2,7,5]=>[6,1]=>840
[6,4,3,1,5,2,7]=>[4,1,1,1]=>210
[6,4,3,1,5,7,2]=>[5,1,1]=>504
[6,4,3,1,7,2,5]=>[4,2,1]=>630
[6,4,3,1,7,5,2]=>[6,1]=>840
[6,4,3,2,1,5,7]=>[3,2,1,1]=>420
[6,4,3,2,1,7,5]=>[4,2,1]=>630
[6,4,3,2,5,1,7]=>[2,2,1,1,1]=>105
[6,4,3,2,5,7,1]=>[3,2,1,1]=>420
[6,4,3,2,7,1,5]=>[2,2,2,1]=>105
[6,4,3,2,7,5,1]=>[4,2,1]=>630
[6,4,3,5,1,2,7]=>[5,1,1]=>504
[6,4,3,5,1,7,2]=>[6,1]=>840
[6,4,3,5,2,1,7]=>[3,2,1,1]=>420
[6,4,3,5,2,7,1]=>[3,3,1]=>280
[6,4,3,5,7,1,2]=>[4,2,1]=>630
[6,4,3,5,7,2,1]=>[6,1]=>840
[6,4,3,7,1,2,5]=>[6,1]=>840
[6,4,3,7,1,5,2]=>[3,3,1]=>280
[6,4,3,7,2,1,5]=>[4,2,1]=>630
[6,4,3,7,2,5,1]=>[6,1]=>840
[6,4,3,7,5,1,2]=>[3,2,1,1]=>420
[6,4,3,7,5,2,1]=>[5,1,1]=>504
[6,4,5,1,2,3,7]=>[6,1]=>840
[6,4,5,1,2,7,3]=>[7]=>720
[6,4,5,1,3,2,7]=>[4,2,1]=>630
[6,4,5,1,3,7,2]=>[5,2]=>504
[6,4,5,1,7,2,3]=>[4,3]=>420
[6,4,5,1,7,3,2]=>[7]=>720
[6,4,5,2,1,3,7]=>[4,2,1]=>630
[6,4,5,2,1,7,3]=>[5,2]=>504
[6,4,5,2,3,1,7]=>[2,2,2,1]=>105
[6,4,5,2,3,7,1]=>[3,2,2]=>210
[6,4,5,2,7,1,3]=>[3,2,2]=>210
[6,4,5,2,7,3,1]=>[5,2]=>504
[6,4,5,3,1,2,7]=>[6,1]=>840
[6,4,5,3,1,7,2]=>[7]=>720
[6,4,5,3,2,1,7]=>[4,2,1]=>630
[6,4,5,3,2,7,1]=>[4,3]=>420
[6,4,5,3,7,1,2]=>[5,2]=>504
[6,4,5,3,7,2,1]=>[7]=>720
[6,4,5,7,1,2,3]=>[7]=>720
[6,4,5,7,1,3,2]=>[4,3]=>420
[6,4,5,7,2,1,3]=>[5,2]=>504
[6,4,5,7,2,3,1]=>[7]=>720
[6,4,5,7,3,1,2]=>[3,2,2]=>210
[6,4,5,7,3,2,1]=>[5,2]=>504
[6,4,7,1,2,3,5]=>[7]=>720
[6,4,7,1,2,5,3]=>[5,2]=>504
[6,4,7,1,3,2,5]=>[4,3]=>420
[6,4,7,1,3,5,2]=>[7]=>720
[6,4,7,1,5,2,3]=>[4,2,1]=>630
[6,4,7,1,5,3,2]=>[6,1]=>840
[6,4,7,2,1,3,5]=>[5,2]=>504
[6,4,7,2,1,5,3]=>[3,2,2]=>210
[6,4,7,2,3,1,5]=>[3,2,2]=>210
[6,4,7,2,3,5,1]=>[5,2]=>504
[6,4,7,2,5,1,3]=>[2,2,2,1]=>105
[6,4,7,2,5,3,1]=>[4,2,1]=>630
[6,4,7,3,1,2,5]=>[7]=>720
[6,4,7,3,1,5,2]=>[4,3]=>420
[6,4,7,3,2,1,5]=>[5,2]=>504
[6,4,7,3,2,5,1]=>[7]=>720
[6,4,7,3,5,1,2]=>[4,2,1]=>630
[6,4,7,3,5,2,1]=>[6,1]=>840
[6,4,7,5,1,2,3]=>[5,2]=>504
[6,4,7,5,1,3,2]=>[7]=>720
[6,4,7,5,2,1,3]=>[3,2,2]=>210
[6,4,7,5,2,3,1]=>[4,3]=>420
[6,4,7,5,3,1,2]=>[5,2]=>504
[6,4,7,5,3,2,1]=>[7]=>720
[6,5,1,2,3,4,7]=>[6,1]=>840
[6,5,1,2,3,7,4]=>[7]=>720
[6,5,1,2,4,3,7]=>[3,3,1]=>280
[6,5,1,2,4,7,3]=>[4,3]=>420
[6,5,1,2,7,3,4]=>[4,3]=>420
[6,5,1,2,7,4,3]=>[7]=>720
[6,5,1,3,2,4,7]=>[4,2,1]=>630
[6,5,1,3,2,7,4]=>[5,2]=>504
[6,5,1,3,4,2,7]=>[6,1]=>840
[6,5,1,3,4,7,2]=>[7]=>720
[6,5,1,3,7,2,4]=>[7]=>720
[6,5,1,3,7,4,2]=>[4,3]=>420
[6,5,1,4,2,3,7]=>[3,2,1,1]=>420
[6,5,1,4,2,7,3]=>[4,2,1]=>630
[6,5,1,4,3,2,7]=>[5,1,1]=>504
[6,5,1,4,3,7,2]=>[6,1]=>840
[6,5,1,4,7,2,3]=>[6,1]=>840
[6,5,1,4,7,3,2]=>[3,3,1]=>280
[6,5,1,7,2,3,4]=>[3,2,2]=>210
[6,5,1,7,2,4,3]=>[5,2]=>504
[6,5,1,7,3,2,4]=>[5,2]=>504
[6,5,1,7,3,4,2]=>[7]=>720
[6,5,1,7,4,2,3]=>[7]=>720
[6,5,1,7,4,3,2]=>[4,3]=>420
[6,5,2,1,3,4,7]=>[3,3,1]=>280
[6,5,2,1,3,7,4]=>[4,3]=>420
[6,5,2,1,4,3,7]=>[6,1]=>840
[6,5,2,1,4,7,3]=>[7]=>720
[6,5,2,1,7,3,4]=>[7]=>720
[6,5,2,1,7,4,3]=>[4,3]=>420
[6,5,2,3,1,4,7]=>[6,1]=>840
[6,5,2,3,1,7,4]=>[7]=>720
[6,5,2,3,4,1,7]=>[4,2,1]=>630
[6,5,2,3,4,7,1]=>[4,3]=>420
[6,5,2,3,7,1,4]=>[5,2]=>504
[6,5,2,3,7,4,1]=>[7]=>720
[6,5,2,4,1,3,7]=>[5,1,1]=>504
[6,5,2,4,1,7,3]=>[6,1]=>840
[6,5,2,4,3,1,7]=>[3,2,1,1]=>420
[6,5,2,4,3,7,1]=>[3,3,1]=>280
[6,5,2,4,7,1,3]=>[4,2,1]=>630
[6,5,2,4,7,3,1]=>[6,1]=>840
[6,5,2,7,1,3,4]=>[5,2]=>504
[6,5,2,7,1,4,3]=>[7]=>720
[6,5,2,7,3,1,4]=>[3,2,2]=>210
[6,5,2,7,3,4,1]=>[4,3]=>420
[6,5,2,7,4,1,3]=>[5,2]=>504
[6,5,2,7,4,3,1]=>[7]=>720
[6,5,3,1,2,4,7]=>[3,2,1,1]=>420
[6,5,3,1,2,7,4]=>[4,2,1]=>630
[6,5,3,1,4,2,7]=>[5,1,1]=>504
[6,5,3,1,4,7,2]=>[6,1]=>840
[6,5,3,1,7,2,4]=>[6,1]=>840
[6,5,3,1,7,4,2]=>[3,3,1]=>280
[6,5,3,2,1,4,7]=>[5,1,1]=>504
[6,5,3,2,1,7,4]=>[6,1]=>840
[6,5,3,2,4,1,7]=>[3,2,1,1]=>420
[6,5,3,2,4,7,1]=>[3,3,1]=>280
[6,5,3,2,7,1,4]=>[4,2,1]=>630
[6,5,3,2,7,4,1]=>[6,1]=>840
[6,5,3,4,1,2,7]=>[4,1,1,1]=>210
[6,5,3,4,1,7,2]=>[5,1,1]=>504
[6,5,3,4,2,1,7]=>[2,2,1,1,1]=>105
[6,5,3,4,2,7,1]=>[3,2,1,1]=>420
[6,5,3,4,7,1,2]=>[3,2,1,1]=>420
[6,5,3,4,7,2,1]=>[5,1,1]=>504
[6,5,3,7,1,2,4]=>[4,2,1]=>630
[6,5,3,7,1,4,2]=>[6,1]=>840
[6,5,3,7,2,1,4]=>[2,2,2,1]=>105
[6,5,3,7,2,4,1]=>[4,2,1]=>630
[6,5,3,7,4,1,2]=>[4,2,1]=>630
[6,5,3,7,4,2,1]=>[6,1]=>840
[6,5,4,1,2,3,7]=>[4,2,1]=>630
[6,5,4,1,2,7,3]=>[5,2]=>504
[6,5,4,1,3,2,7]=>[6,1]=>840
[6,5,4,1,3,7,2]=>[7]=>720
[6,5,4,1,7,2,3]=>[7]=>720
[6,5,4,1,7,3,2]=>[4,3]=>420
[6,5,4,2,1,3,7]=>[6,1]=>840
[6,5,4,2,1,7,3]=>[7]=>720
[6,5,4,2,3,1,7]=>[4,2,1]=>630
[6,5,4,2,3,7,1]=>[4,3]=>420
[6,5,4,2,7,1,3]=>[5,2]=>504
[6,5,4,2,7,3,1]=>[7]=>720
[6,5,4,3,1,2,7]=>[4,2,1]=>630
[6,5,4,3,1,7,2]=>[5,2]=>504
[6,5,4,3,2,1,7]=>[2,2,2,1]=>105
[6,5,4,3,2,7,1]=>[3,2,2]=>210
[6,5,4,3,7,1,2]=>[3,2,2]=>210
[6,5,4,3,7,2,1]=>[5,2]=>504
[6,5,4,7,1,2,3]=>[4,3]=>420
[6,5,4,7,1,3,2]=>[7]=>720
[6,5,4,7,2,1,3]=>[3,2,2]=>210
[6,5,4,7,2,3,1]=>[5,2]=>504
[6,5,4,7,3,1,2]=>[5,2]=>504
[6,5,4,7,3,2,1]=>[7]=>720
[6,5,7,1,2,3,4]=>[5,2]=>504
[6,5,7,1,2,4,3]=>[3,2,2]=>210
[6,5,7,1,3,2,4]=>[7]=>720
[6,5,7,1,3,4,2]=>[4,3]=>420
[6,5,7,1,4,2,3]=>[5,2]=>504
[6,5,7,1,4,3,2]=>[7]=>720
[6,5,7,2,1,3,4]=>[7]=>720
[6,5,7,2,1,4,3]=>[5,2]=>504
[6,5,7,2,3,1,4]=>[5,2]=>504
[6,5,7,2,3,4,1]=>[7]=>720
[6,5,7,2,4,1,3]=>[3,2,2]=>210
[6,5,7,2,4,3,1]=>[4,3]=>420
[6,5,7,3,1,2,4]=>[4,3]=>420
[6,5,7,3,1,4,2]=>[7]=>720
[6,5,7,3,2,1,4]=>[3,2,2]=>210
[6,5,7,3,2,4,1]=>[5,2]=>504
[6,5,7,3,4,1,2]=>[5,2]=>504
[6,5,7,3,4,2,1]=>[7]=>720
[6,5,7,4,1,2,3]=>[4,2,1]=>630
[6,5,7,4,1,3,2]=>[6,1]=>840
[6,5,7,4,2,1,3]=>[2,2,2,1]=>105
[6,5,7,4,2,3,1]=>[4,2,1]=>630
[6,5,7,4,3,1,2]=>[4,2,1]=>630
[6,5,7,4,3,2,1]=>[6,1]=>840
[6,7,1,2,3,4,5]=>[7]=>720
[6,7,1,2,3,5,4]=>[4,3]=>420
[6,7,1,2,4,3,5]=>[4,3]=>420
[6,7,1,2,4,5,3]=>[7]=>720
[6,7,1,2,5,3,4]=>[3,3,1]=>280
[6,7,1,2,5,4,3]=>[6,1]=>840
[6,7,1,3,2,4,5]=>[4,3]=>420
[6,7,1,3,2,5,4]=>[7]=>720
[6,7,1,3,4,2,5]=>[7]=>720
[6,7,1,3,4,5,2]=>[5,2]=>504
[6,7,1,3,5,2,4]=>[6,1]=>840
[6,7,1,3,5,4,2]=>[4,2,1]=>630
[6,7,1,4,2,3,5]=>[3,3,1]=>280
[6,7,1,4,2,5,3]=>[6,1]=>840
[6,7,1,4,3,2,5]=>[6,1]=>840
[6,7,1,4,3,5,2]=>[4,2,1]=>630
[6,7,1,4,5,2,3]=>[5,1,1]=>504
[6,7,1,4,5,3,2]=>[3,2,1,1]=>420
[6,7,1,5,2,3,4]=>[4,3]=>420
[6,7,1,5,2,4,3]=>[7]=>720
[6,7,1,5,3,2,4]=>[7]=>720
[6,7,1,5,3,4,2]=>[5,2]=>504
[6,7,1,5,4,2,3]=>[5,2]=>504
[6,7,1,5,4,3,2]=>[3,2,2]=>210
[6,7,2,1,3,4,5]=>[4,3]=>420
[6,7,2,1,3,5,4]=>[7]=>720
[6,7,2,1,4,3,5]=>[7]=>720
[6,7,2,1,4,5,3]=>[4,3]=>420
[6,7,2,1,5,3,4]=>[6,1]=>840
[6,7,2,1,5,4,3]=>[3,3,1]=>280
[6,7,2,3,1,4,5]=>[7]=>720
[6,7,2,3,1,5,4]=>[4,3]=>420
[6,7,2,3,4,1,5]=>[5,2]=>504
[6,7,2,3,4,5,1]=>[7]=>720
[6,7,2,3,5,1,4]=>[4,2,1]=>630
[6,7,2,3,5,4,1]=>[6,1]=>840
[6,7,2,4,1,3,5]=>[6,1]=>840
[6,7,2,4,1,5,3]=>[3,3,1]=>280
[6,7,2,4,3,1,5]=>[4,2,1]=>630
[6,7,2,4,3,5,1]=>[6,1]=>840
[6,7,2,4,5,1,3]=>[3,2,1,1]=>420
[6,7,2,4,5,3,1]=>[5,1,1]=>504
[6,7,2,5,1,3,4]=>[7]=>720
[6,7,2,5,1,4,3]=>[4,3]=>420
[6,7,2,5,3,1,4]=>[5,2]=>504
[6,7,2,5,3,4,1]=>[7]=>720
[6,7,2,5,4,1,3]=>[3,2,2]=>210
[6,7,2,5,4,3,1]=>[5,2]=>504
[6,7,3,1,2,4,5]=>[3,3,1]=>280
[6,7,3,1,2,5,4]=>[6,1]=>840
[6,7,3,1,4,2,5]=>[6,1]=>840
[6,7,3,1,4,5,2]=>[4,2,1]=>630
[6,7,3,1,5,2,4]=>[5,1,1]=>504
[6,7,3,1,5,4,2]=>[3,2,1,1]=>420
[6,7,3,2,1,4,5]=>[6,1]=>840
[6,7,3,2,1,5,4]=>[3,3,1]=>280
[6,7,3,2,4,1,5]=>[4,2,1]=>630
[6,7,3,2,4,5,1]=>[6,1]=>840
[6,7,3,2,5,1,4]=>[3,2,1,1]=>420
[6,7,3,2,5,4,1]=>[5,1,1]=>504
[6,7,3,4,1,2,5]=>[5,1,1]=>504
[6,7,3,4,1,5,2]=>[3,2,1,1]=>420
[6,7,3,4,2,1,5]=>[3,2,1,1]=>420
[6,7,3,4,2,5,1]=>[5,1,1]=>504
[6,7,3,4,5,1,2]=>[2,2,1,1,1]=>105
[6,7,3,4,5,2,1]=>[4,1,1,1]=>210
[6,7,3,5,1,2,4]=>[6,1]=>840
[6,7,3,5,1,4,2]=>[4,2,1]=>630
[6,7,3,5,2,1,4]=>[4,2,1]=>630
[6,7,3,5,2,4,1]=>[6,1]=>840
[6,7,3,5,4,1,2]=>[2,2,2,1]=>105
[6,7,3,5,4,2,1]=>[4,2,1]=>630
[6,7,4,1,2,3,5]=>[4,3]=>420
[6,7,4,1,2,5,3]=>[7]=>720
[6,7,4,1,3,2,5]=>[7]=>720
[6,7,4,1,3,5,2]=>[5,2]=>504
[6,7,4,1,5,2,3]=>[6,1]=>840
[6,7,4,1,5,3,2]=>[4,2,1]=>630
[6,7,4,2,1,3,5]=>[7]=>720
[6,7,4,2,1,5,3]=>[4,3]=>420
[6,7,4,2,3,1,5]=>[5,2]=>504
[6,7,4,2,3,5,1]=>[7]=>720
[6,7,4,2,5,1,3]=>[4,2,1]=>630
[6,7,4,2,5,3,1]=>[6,1]=>840
[6,7,4,3,1,2,5]=>[5,2]=>504
[6,7,4,3,1,5,2]=>[3,2,2]=>210
[6,7,4,3,2,1,5]=>[3,2,2]=>210
[6,7,4,3,2,5,1]=>[5,2]=>504
[6,7,4,3,5,1,2]=>[2,2,2,1]=>105
[6,7,4,3,5,2,1]=>[4,2,1]=>630
[6,7,4,5,1,2,3]=>[7]=>720
[6,7,4,5,1,3,2]=>[5,2]=>504
[6,7,4,5,2,1,3]=>[5,2]=>504
[6,7,4,5,2,3,1]=>[7]=>720
[6,7,4,5,3,1,2]=>[3,2,2]=>210
[6,7,4,5,3,2,1]=>[4,3]=>420
[6,7,5,1,2,3,4]=>[7]=>720
[6,7,5,1,2,4,3]=>[4,3]=>420
[6,7,5,1,3,2,4]=>[5,2]=>504
[6,7,5,1,3,4,2]=>[3,2,2]=>210
[6,7,5,1,4,2,3]=>[7]=>720
[6,7,5,1,4,3,2]=>[5,2]=>504
[6,7,5,2,1,3,4]=>[4,3]=>420
[6,7,5,2,1,4,3]=>[7]=>720
[6,7,5,2,3,1,4]=>[3,2,2]=>210
[6,7,5,2,3,4,1]=>[5,2]=>504
[6,7,5,2,4,1,3]=>[5,2]=>504
[6,7,5,2,4,3,1]=>[7]=>720
[6,7,5,3,1,2,4]=>[7]=>720
[6,7,5,3,1,4,2]=>[5,2]=>504
[6,7,5,3,2,1,4]=>[5,2]=>504
[6,7,5,3,2,4,1]=>[7]=>720
[6,7,5,3,4,1,2]=>[3,2,2]=>210
[6,7,5,3,4,2,1]=>[4,3]=>420
[6,7,5,4,1,2,3]=>[6,1]=>840
[6,7,5,4,1,3,2]=>[4,2,1]=>630
[6,7,5,4,2,1,3]=>[4,2,1]=>630
[6,7,5,4,2,3,1]=>[6,1]=>840
[6,7,5,4,3,1,2]=>[2,2,2,1]=>105
[6,7,5,4,3,2,1]=>[4,2,1]=>630
[7,1,2,3,4,5,6]=>[7]=>720
[7,1,2,3,4,6,5]=>[6,1]=>840
[7,1,2,3,5,4,6]=>[6,1]=>840
[7,1,2,3,5,6,4]=>[5,1,1]=>504
[7,1,2,3,6,4,5]=>[7]=>720
[7,1,2,3,6,5,4]=>[5,2]=>504
[7,1,2,4,3,5,6]=>[6,1]=>840
[7,1,2,4,3,6,5]=>[5,1,1]=>504
[7,1,2,4,5,3,6]=>[5,1,1]=>504
[7,1,2,4,5,6,3]=>[4,1,1,1]=>210
[7,1,2,4,6,3,5]=>[6,1]=>840
[7,1,2,4,6,5,3]=>[4,2,1]=>630
[7,1,2,5,3,4,6]=>[7]=>720
[7,1,2,5,3,6,4]=>[6,1]=>840
[7,1,2,5,4,3,6]=>[5,2]=>504
[7,1,2,5,4,6,3]=>[4,2,1]=>630
[7,1,2,5,6,3,4]=>[7]=>720
[7,1,2,5,6,4,3]=>[4,3]=>420
[7,1,2,6,3,4,5]=>[5,2]=>504
[7,1,2,6,3,5,4]=>[7]=>720
[7,1,2,6,4,3,5]=>[7]=>720
[7,1,2,6,4,5,3]=>[4,3]=>420
[7,1,2,6,5,3,4]=>[6,1]=>840
[7,1,2,6,5,4,3]=>[4,2,1]=>630
[7,1,3,2,4,5,6]=>[6,1]=>840
[7,1,3,2,4,6,5]=>[5,1,1]=>504
[7,1,3,2,5,4,6]=>[5,1,1]=>504
[7,1,3,2,5,6,4]=>[4,1,1,1]=>210
[7,1,3,2,6,4,5]=>[6,1]=>840
[7,1,3,2,6,5,4]=>[4,2,1]=>630
[7,1,3,4,2,5,6]=>[5,1,1]=>504
[7,1,3,4,2,6,5]=>[4,1,1,1]=>210
[7,1,3,4,5,2,6]=>[4,1,1,1]=>210
[7,1,3,4,5,6,2]=>[3,1,1,1,1]=>70
[7,1,3,4,6,2,5]=>[5,1,1]=>504
[7,1,3,4,6,5,2]=>[3,2,1,1]=>420
[7,1,3,5,2,4,6]=>[6,1]=>840
[7,1,3,5,2,6,4]=>[5,1,1]=>504
[7,1,3,5,4,2,6]=>[4,2,1]=>630
[7,1,3,5,4,6,2]=>[3,2,1,1]=>420
[7,1,3,5,6,2,4]=>[6,1]=>840
[7,1,3,5,6,4,2]=>[3,3,1]=>280
[7,1,3,6,2,4,5]=>[4,2,1]=>630
[7,1,3,6,2,5,4]=>[6,1]=>840
[7,1,3,6,4,2,5]=>[6,1]=>840
[7,1,3,6,4,5,2]=>[3,3,1]=>280
[7,1,3,6,5,2,4]=>[5,1,1]=>504
[7,1,3,6,5,4,2]=>[3,2,1,1]=>420
[7,1,4,2,3,5,6]=>[7]=>720
[7,1,4,2,3,6,5]=>[6,1]=>840
[7,1,4,2,5,3,6]=>[6,1]=>840
[7,1,4,2,5,6,3]=>[5,1,1]=>504
[7,1,4,2,6,3,5]=>[7]=>720
[7,1,4,2,6,5,3]=>[5,2]=>504
[7,1,4,3,2,5,6]=>[5,2]=>504
[7,1,4,3,2,6,5]=>[4,2,1]=>630
[7,1,4,3,5,2,6]=>[4,2,1]=>630
[7,1,4,3,5,6,2]=>[3,2,1,1]=>420
[7,1,4,3,6,2,5]=>[5,2]=>504
[7,1,4,3,6,5,2]=>[3,2,2]=>210
[7,1,4,5,2,3,6]=>[7]=>720
[7,1,4,5,2,6,3]=>[6,1]=>840
[7,1,4,5,3,2,6]=>[4,3]=>420
[7,1,4,5,3,6,2]=>[3,3,1]=>280
[7,1,4,5,6,2,3]=>[7]=>720
[7,1,4,5,6,3,2]=>[4,3]=>420
[7,1,4,6,2,3,5]=>[4,3]=>420
[7,1,4,6,2,5,3]=>[7]=>720
[7,1,4,6,3,2,5]=>[7]=>720
[7,1,4,6,3,5,2]=>[4,3]=>420
[7,1,4,6,5,2,3]=>[6,1]=>840
[7,1,4,6,5,3,2]=>[3,3,1]=>280
[7,1,5,2,3,4,6]=>[5,2]=>504
[7,1,5,2,3,6,4]=>[4,2,1]=>630
[7,1,5,2,4,3,6]=>[7]=>720
[7,1,5,2,4,6,3]=>[6,1]=>840
[7,1,5,2,6,3,4]=>[4,3]=>420
[7,1,5,2,6,4,3]=>[7]=>720
[7,1,5,3,2,4,6]=>[7]=>720
[7,1,5,3,2,6,4]=>[6,1]=>840
[7,1,5,3,4,2,6]=>[4,3]=>420
[7,1,5,3,4,6,2]=>[3,3,1]=>280
[7,1,5,3,6,2,4]=>[7]=>720
[7,1,5,3,6,4,2]=>[4,3]=>420
[7,1,5,4,2,3,6]=>[6,1]=>840
[7,1,5,4,2,6,3]=>[5,1,1]=>504
[7,1,5,4,3,2,6]=>[4,2,1]=>630
[7,1,5,4,3,6,2]=>[3,2,1,1]=>420
[7,1,5,4,6,2,3]=>[6,1]=>840
[7,1,5,4,6,3,2]=>[3,3,1]=>280
[7,1,5,6,2,3,4]=>[7]=>720
[7,1,5,6,2,4,3]=>[5,2]=>504
[7,1,5,6,3,2,4]=>[5,2]=>504
[7,1,5,6,3,4,2]=>[3,2,2]=>210
[7,1,5,6,4,2,3]=>[7]=>720
[7,1,5,6,4,3,2]=>[4,3]=>420
[7,1,6,2,3,4,5]=>[7]=>720
[7,1,6,2,3,5,4]=>[4,3]=>420
[7,1,6,2,4,3,5]=>[5,2]=>504
[7,1,6,2,4,5,3]=>[7]=>720
[7,1,6,2,5,3,4]=>[4,2,1]=>630
[7,1,6,2,5,4,3]=>[6,1]=>840
[7,1,6,3,2,4,5]=>[4,3]=>420
[7,1,6,3,2,5,4]=>[7]=>720
[7,1,6,3,4,2,5]=>[7]=>720
[7,1,6,3,4,5,2]=>[4,3]=>420
[7,1,6,3,5,2,4]=>[6,1]=>840
[7,1,6,3,5,4,2]=>[3,3,1]=>280
[7,1,6,4,2,3,5]=>[4,2,1]=>630
[7,1,6,4,2,5,3]=>[6,1]=>840
[7,1,6,4,3,2,5]=>[6,1]=>840
[7,1,6,4,3,5,2]=>[3,3,1]=>280
[7,1,6,4,5,2,3]=>[5,1,1]=>504
[7,1,6,4,5,3,2]=>[3,2,1,1]=>420
[7,1,6,5,2,3,4]=>[5,2]=>504
[7,1,6,5,2,4,3]=>[7]=>720
[7,1,6,5,3,2,4]=>[7]=>720
[7,1,6,5,3,4,2]=>[4,3]=>420
[7,1,6,5,4,2,3]=>[5,2]=>504
[7,1,6,5,4,3,2]=>[3,2,2]=>210
[7,2,1,3,4,5,6]=>[6,1]=>840
[7,2,1,3,4,6,5]=>[5,1,1]=>504
[7,2,1,3,5,4,6]=>[5,1,1]=>504
[7,2,1,3,5,6,4]=>[4,1,1,1]=>210
[7,2,1,3,6,4,5]=>[6,1]=>840
[7,2,1,3,6,5,4]=>[4,2,1]=>630
[7,2,1,4,3,5,6]=>[5,1,1]=>504
[7,2,1,4,3,6,5]=>[4,1,1,1]=>210
[7,2,1,4,5,3,6]=>[4,1,1,1]=>210
[7,2,1,4,5,6,3]=>[3,1,1,1,1]=>70
[7,2,1,4,6,3,5]=>[5,1,1]=>504
[7,2,1,4,6,5,3]=>[3,2,1,1]=>420
[7,2,1,5,3,4,6]=>[6,1]=>840
[7,2,1,5,3,6,4]=>[5,1,1]=>504
[7,2,1,5,4,3,6]=>[4,2,1]=>630
[7,2,1,5,4,6,3]=>[3,2,1,1]=>420
[7,2,1,5,6,3,4]=>[6,1]=>840
[7,2,1,5,6,4,3]=>[3,3,1]=>280
[7,2,1,6,3,4,5]=>[4,2,1]=>630
[7,2,1,6,3,5,4]=>[6,1]=>840
[7,2,1,6,4,3,5]=>[6,1]=>840
[7,2,1,6,4,5,3]=>[3,3,1]=>280
[7,2,1,6,5,3,4]=>[5,1,1]=>504
[7,2,1,6,5,4,3]=>[3,2,1,1]=>420
[7,2,3,1,4,5,6]=>[5,1,1]=>504
[7,2,3,1,4,6,5]=>[4,1,1,1]=>210
[7,2,3,1,5,4,6]=>[4,1,1,1]=>210
[7,2,3,1,5,6,4]=>[3,1,1,1,1]=>70
[7,2,3,1,6,4,5]=>[5,1,1]=>504
[7,2,3,1,6,5,4]=>[3,2,1,1]=>420
[7,2,3,4,1,5,6]=>[4,1,1,1]=>210
[7,2,3,4,1,6,5]=>[3,1,1,1,1]=>70
[7,2,3,4,5,1,6]=>[3,1,1,1,1]=>70
[7,2,3,4,5,6,1]=>[2,1,1,1,1,1]=>21
[7,2,3,4,6,1,5]=>[4,1,1,1]=>210
[7,2,3,4,6,5,1]=>[2,2,1,1,1]=>105
[7,2,3,5,1,4,6]=>[5,1,1]=>504
[7,2,3,5,1,6,4]=>[4,1,1,1]=>210
[7,2,3,5,4,1,6]=>[3,2,1,1]=>420
[7,2,3,5,4,6,1]=>[2,2,1,1,1]=>105
[7,2,3,5,6,1,4]=>[5,1,1]=>504
[7,2,3,5,6,4,1]=>[3,2,1,1]=>420
[7,2,3,6,1,4,5]=>[3,2,1,1]=>420
[7,2,3,6,1,5,4]=>[5,1,1]=>504
[7,2,3,6,4,1,5]=>[5,1,1]=>504
[7,2,3,6,4,5,1]=>[3,2,1,1]=>420
[7,2,3,6,5,1,4]=>[4,1,1,1]=>210
[7,2,3,6,5,4,1]=>[2,2,1,1,1]=>105
[7,2,4,1,3,5,6]=>[6,1]=>840
[7,2,4,1,3,6,5]=>[5,1,1]=>504
[7,2,4,1,5,3,6]=>[5,1,1]=>504
[7,2,4,1,5,6,3]=>[4,1,1,1]=>210
[7,2,4,1,6,3,5]=>[6,1]=>840
[7,2,4,1,6,5,3]=>[4,2,1]=>630
[7,2,4,3,1,5,6]=>[4,2,1]=>630
[7,2,4,3,1,6,5]=>[3,2,1,1]=>420
[7,2,4,3,5,1,6]=>[3,2,1,1]=>420
[7,2,4,3,5,6,1]=>[2,2,1,1,1]=>105
[7,2,4,3,6,1,5]=>[4,2,1]=>630
[7,2,4,3,6,5,1]=>[2,2,2,1]=>105
[7,2,4,5,1,3,6]=>[6,1]=>840
[7,2,4,5,1,6,3]=>[5,1,1]=>504
[7,2,4,5,3,1,6]=>[3,3,1]=>280
[7,2,4,5,3,6,1]=>[3,2,1,1]=>420
[7,2,4,5,6,1,3]=>[6,1]=>840
[7,2,4,5,6,3,1]=>[4,2,1]=>630
[7,2,4,6,1,3,5]=>[3,3,1]=>280
[7,2,4,6,1,5,3]=>[6,1]=>840
[7,2,4,6,3,1,5]=>[6,1]=>840
[7,2,4,6,3,5,1]=>[4,2,1]=>630
[7,2,4,6,5,1,3]=>[5,1,1]=>504
[7,2,4,6,5,3,1]=>[3,2,1,1]=>420
[7,2,5,1,3,4,6]=>[4,2,1]=>630
[7,2,5,1,3,6,4]=>[3,2,1,1]=>420
[7,2,5,1,4,3,6]=>[6,1]=>840
[7,2,5,1,4,6,3]=>[5,1,1]=>504
[7,2,5,1,6,3,4]=>[3,3,1]=>280
[7,2,5,1,6,4,3]=>[6,1]=>840
[7,2,5,3,1,4,6]=>[6,1]=>840
[7,2,5,3,1,6,4]=>[5,1,1]=>504
[7,2,5,3,4,1,6]=>[3,3,1]=>280
[7,2,5,3,4,6,1]=>[3,2,1,1]=>420
[7,2,5,3,6,1,4]=>[6,1]=>840
[7,2,5,3,6,4,1]=>[4,2,1]=>630
[7,2,5,4,1,3,6]=>[5,1,1]=>504
[7,2,5,4,1,6,3]=>[4,1,1,1]=>210
[7,2,5,4,3,1,6]=>[3,2,1,1]=>420
[7,2,5,4,3,6,1]=>[2,2,1,1,1]=>105
[7,2,5,4,6,1,3]=>[5,1,1]=>504
[7,2,5,4,6,3,1]=>[3,2,1,1]=>420
[7,2,5,6,1,3,4]=>[6,1]=>840
[7,2,5,6,1,4,3]=>[4,2,1]=>630
[7,2,5,6,3,1,4]=>[4,2,1]=>630
[7,2,5,6,3,4,1]=>[2,2,2,1]=>105
[7,2,5,6,4,1,3]=>[6,1]=>840
[7,2,5,6,4,3,1]=>[4,2,1]=>630
[7,2,6,1,3,4,5]=>[6,1]=>840
[7,2,6,1,3,5,4]=>[3,3,1]=>280
[7,2,6,1,4,3,5]=>[4,2,1]=>630
[7,2,6,1,4,5,3]=>[6,1]=>840
[7,2,6,1,5,3,4]=>[3,2,1,1]=>420
[7,2,6,1,5,4,3]=>[5,1,1]=>504
[7,2,6,3,1,4,5]=>[3,3,1]=>280
[7,2,6,3,1,5,4]=>[6,1]=>840
[7,2,6,3,4,1,5]=>[6,1]=>840
[7,2,6,3,4,5,1]=>[4,2,1]=>630
[7,2,6,3,5,1,4]=>[5,1,1]=>504
[7,2,6,3,5,4,1]=>[3,2,1,1]=>420
[7,2,6,4,1,3,5]=>[3,2,1,1]=>420
[7,2,6,4,1,5,3]=>[5,1,1]=>504
[7,2,6,4,3,1,5]=>[5,1,1]=>504
[7,2,6,4,3,5,1]=>[3,2,1,1]=>420
[7,2,6,4,5,1,3]=>[4,1,1,1]=>210
[7,2,6,4,5,3,1]=>[2,2,1,1,1]=>105
[7,2,6,5,1,3,4]=>[4,2,1]=>630
[7,2,6,5,1,4,3]=>[6,1]=>840
[7,2,6,5,3,1,4]=>[6,1]=>840
[7,2,6,5,3,4,1]=>[4,2,1]=>630
[7,2,6,5,4,1,3]=>[4,2,1]=>630
[7,2,6,5,4,3,1]=>[2,2,2,1]=>105
[7,3,1,2,4,5,6]=>[7]=>720
[7,3,1,2,4,6,5]=>[6,1]=>840
[7,3,1,2,5,4,6]=>[6,1]=>840
[7,3,1,2,5,6,4]=>[5,1,1]=>504
[7,3,1,2,6,4,5]=>[7]=>720
[7,3,1,2,6,5,4]=>[5,2]=>504
[7,3,1,4,2,5,6]=>[6,1]=>840
[7,3,1,4,2,6,5]=>[5,1,1]=>504
[7,3,1,4,5,2,6]=>[5,1,1]=>504
[7,3,1,4,5,6,2]=>[4,1,1,1]=>210
[7,3,1,4,6,2,5]=>[6,1]=>840
[7,3,1,4,6,5,2]=>[4,2,1]=>630
[7,3,1,5,2,4,6]=>[7]=>720
[7,3,1,5,2,6,4]=>[6,1]=>840
[7,3,1,5,4,2,6]=>[5,2]=>504
[7,3,1,5,4,6,2]=>[4,2,1]=>630
[7,3,1,5,6,2,4]=>[7]=>720
[7,3,1,5,6,4,2]=>[4,3]=>420
[7,3,1,6,2,4,5]=>[5,2]=>504
[7,3,1,6,2,5,4]=>[7]=>720
[7,3,1,6,4,2,5]=>[7]=>720
[7,3,1,6,4,5,2]=>[4,3]=>420
[7,3,1,6,5,2,4]=>[6,1]=>840
[7,3,1,6,5,4,2]=>[4,2,1]=>630
[7,3,2,1,4,5,6]=>[5,2]=>504
[7,3,2,1,4,6,5]=>[4,2,1]=>630
[7,3,2,1,5,4,6]=>[4,2,1]=>630
[7,3,2,1,5,6,4]=>[3,2,1,1]=>420
[7,3,2,1,6,4,5]=>[5,2]=>504
[7,3,2,1,6,5,4]=>[3,2,2]=>210
[7,3,2,4,1,5,6]=>[4,2,1]=>630
[7,3,2,4,1,6,5]=>[3,2,1,1]=>420
[7,3,2,4,5,1,6]=>[3,2,1,1]=>420
[7,3,2,4,5,6,1]=>[2,2,1,1,1]=>105
[7,3,2,4,6,1,5]=>[4,2,1]=>630
[7,3,2,4,6,5,1]=>[2,2,2,1]=>105
[7,3,2,5,1,4,6]=>[5,2]=>504
[7,3,2,5,1,6,4]=>[4,2,1]=>630
[7,3,2,5,4,1,6]=>[3,2,2]=>210
[7,3,2,5,4,6,1]=>[2,2,2,1]=>105
[7,3,2,5,6,1,4]=>[5,2]=>504
[7,3,2,5,6,4,1]=>[3,2,2]=>210
[7,3,2,6,1,4,5]=>[3,2,2]=>210
[7,3,2,6,1,5,4]=>[5,2]=>504
[7,3,2,6,4,1,5]=>[5,2]=>504
[7,3,2,6,4,5,1]=>[3,2,2]=>210
[7,3,2,6,5,1,4]=>[4,2,1]=>630
[7,3,2,6,5,4,1]=>[2,2,2,1]=>105
[7,3,4,1,2,5,6]=>[7]=>720
[7,3,4,1,2,6,5]=>[6,1]=>840
[7,3,4,1,5,2,6]=>[6,1]=>840
[7,3,4,1,5,6,2]=>[5,1,1]=>504
[7,3,4,1,6,2,5]=>[7]=>720
[7,3,4,1,6,5,2]=>[5,2]=>504
[7,3,4,2,1,5,6]=>[4,3]=>420
[7,3,4,2,1,6,5]=>[3,3,1]=>280
[7,3,4,2,5,1,6]=>[3,3,1]=>280
[7,3,4,2,5,6,1]=>[3,2,1,1]=>420
[7,3,4,2,6,1,5]=>[4,3]=>420
[7,3,4,2,6,5,1]=>[3,2,2]=>210
[7,3,4,5,1,2,6]=>[7]=>720
[7,3,4,5,1,6,2]=>[6,1]=>840
[7,3,4,5,2,1,6]=>[4,3]=>420
[7,3,4,5,2,6,1]=>[4,2,1]=>630
[7,3,4,5,6,1,2]=>[7]=>720
[7,3,4,5,6,2,1]=>[5,2]=>504
[7,3,4,6,1,2,5]=>[4,3]=>420
[7,3,4,6,1,5,2]=>[7]=>720
[7,3,4,6,2,1,5]=>[7]=>720
[7,3,4,6,2,5,1]=>[5,2]=>504
[7,3,4,6,5,1,2]=>[6,1]=>840
[7,3,4,6,5,2,1]=>[4,2,1]=>630
[7,3,5,1,2,4,6]=>[4,3]=>420
[7,3,5,1,2,6,4]=>[3,3,1]=>280
[7,3,5,1,4,2,6]=>[7]=>720
[7,3,5,1,4,6,2]=>[6,1]=>840
[7,3,5,1,6,2,4]=>[4,3]=>420
[7,3,5,1,6,4,2]=>[7]=>720
[7,3,5,2,1,4,6]=>[7]=>720
[7,3,5,2,1,6,4]=>[6,1]=>840
[7,3,5,2,4,1,6]=>[4,3]=>420
[7,3,5,2,4,6,1]=>[4,2,1]=>630
[7,3,5,2,6,1,4]=>[7]=>720
[7,3,5,2,6,4,1]=>[5,2]=>504
[7,3,5,4,1,2,6]=>[6,1]=>840
[7,3,5,4,1,6,2]=>[5,1,1]=>504
[7,3,5,4,2,1,6]=>[3,3,1]=>280
[7,3,5,4,2,6,1]=>[3,2,1,1]=>420
[7,3,5,4,6,1,2]=>[6,1]=>840
[7,3,5,4,6,2,1]=>[4,2,1]=>630
[7,3,5,6,1,2,4]=>[7]=>720
[7,3,5,6,1,4,2]=>[5,2]=>504
[7,3,5,6,2,1,4]=>[4,3]=>420
[7,3,5,6,2,4,1]=>[3,2,2]=>210
[7,3,5,6,4,1,2]=>[7]=>720
[7,3,5,6,4,2,1]=>[5,2]=>504
[7,3,6,1,2,4,5]=>[7]=>720
[7,3,6,1,2,5,4]=>[4,3]=>420
[7,3,6,1,4,2,5]=>[4,3]=>420
[7,3,6,1,4,5,2]=>[7]=>720
[7,3,6,1,5,2,4]=>[3,3,1]=>280
[7,3,6,1,5,4,2]=>[6,1]=>840
[7,3,6,2,1,4,5]=>[4,3]=>420
[7,3,6,2,1,5,4]=>[7]=>720
[7,3,6,2,4,1,5]=>[7]=>720
[7,3,6,2,4,5,1]=>[5,2]=>504
[7,3,6,2,5,1,4]=>[6,1]=>840
[7,3,6,2,5,4,1]=>[4,2,1]=>630
[7,3,6,4,1,2,5]=>[3,3,1]=>280
[7,3,6,4,1,5,2]=>[6,1]=>840
[7,3,6,4,2,1,5]=>[6,1]=>840
[7,3,6,4,2,5,1]=>[4,2,1]=>630
[7,3,6,4,5,1,2]=>[5,1,1]=>504
[7,3,6,4,5,2,1]=>[3,2,1,1]=>420
[7,3,6,5,1,2,4]=>[4,3]=>420
[7,3,6,5,1,4,2]=>[7]=>720
[7,3,6,5,2,1,4]=>[7]=>720
[7,3,6,5,2,4,1]=>[5,2]=>504
[7,3,6,5,4,1,2]=>[5,2]=>504
[7,3,6,5,4,2,1]=>[3,2,2]=>210
[7,4,1,2,3,5,6]=>[5,2]=>504
[7,4,1,2,3,6,5]=>[4,2,1]=>630
[7,4,1,2,5,3,6]=>[4,2,1]=>630
[7,4,1,2,5,6,3]=>[3,2,1,1]=>420
[7,4,1,2,6,3,5]=>[5,2]=>504
[7,4,1,2,6,5,3]=>[3,2,2]=>210
[7,4,1,3,2,5,6]=>[7]=>720
[7,4,1,3,2,6,5]=>[6,1]=>840
[7,4,1,3,5,2,6]=>[6,1]=>840
[7,4,1,3,5,6,2]=>[5,1,1]=>504
[7,4,1,3,6,2,5]=>[7]=>720
[7,4,1,3,6,5,2]=>[5,2]=>504
[7,4,1,5,2,3,6]=>[4,3]=>420
[7,4,1,5,2,6,3]=>[3,3,1]=>280
[7,4,1,5,3,2,6]=>[7]=>720
[7,4,1,5,3,6,2]=>[6,1]=>840
[7,4,1,5,6,2,3]=>[4,3]=>420
[7,4,1,5,6,3,2]=>[7]=>720
[7,4,1,6,2,3,5]=>[7]=>720
[7,4,1,6,2,5,3]=>[4,3]=>420
[7,4,1,6,3,2,5]=>[4,3]=>420
[7,4,1,6,3,5,2]=>[7]=>720
[7,4,1,6,5,2,3]=>[3,3,1]=>280
[7,4,1,6,5,3,2]=>[6,1]=>840
[7,4,2,1,3,5,6]=>[7]=>720
[7,4,2,1,3,6,5]=>[6,1]=>840
[7,4,2,1,5,3,6]=>[6,1]=>840
[7,4,2,1,5,6,3]=>[5,1,1]=>504
[7,4,2,1,6,3,5]=>[7]=>720
[7,4,2,1,6,5,3]=>[5,2]=>504
[7,4,2,3,1,5,6]=>[4,3]=>420
[7,4,2,3,1,6,5]=>[3,3,1]=>280
[7,4,2,3,5,1,6]=>[3,3,1]=>280
[7,4,2,3,5,6,1]=>[3,2,1,1]=>420
[7,4,2,3,6,1,5]=>[4,3]=>420
[7,4,2,3,6,5,1]=>[3,2,2]=>210
[7,4,2,5,1,3,6]=>[7]=>720
[7,4,2,5,1,6,3]=>[6,1]=>840
[7,4,2,5,3,1,6]=>[4,3]=>420
[7,4,2,5,3,6,1]=>[4,2,1]=>630
[7,4,2,5,6,1,3]=>[7]=>720
[7,4,2,5,6,3,1]=>[5,2]=>504
[7,4,2,6,1,3,5]=>[4,3]=>420
[7,4,2,6,1,5,3]=>[7]=>720
[7,4,2,6,3,1,5]=>[7]=>720
[7,4,2,6,3,5,1]=>[5,2]=>504
[7,4,2,6,5,1,3]=>[6,1]=>840
[7,4,2,6,5,3,1]=>[4,2,1]=>630
[7,4,3,1,2,5,6]=>[6,1]=>840
[7,4,3,1,2,6,5]=>[5,1,1]=>504
[7,4,3,1,5,2,6]=>[5,1,1]=>504
[7,4,3,1,5,6,2]=>[4,1,1,1]=>210
[7,4,3,1,6,2,5]=>[6,1]=>840
[7,4,3,1,6,5,2]=>[4,2,1]=>630
[7,4,3,2,1,5,6]=>[4,2,1]=>630
[7,4,3,2,1,6,5]=>[3,2,1,1]=>420
[7,4,3,2,5,1,6]=>[3,2,1,1]=>420
[7,4,3,2,5,6,1]=>[2,2,1,1,1]=>105
[7,4,3,2,6,1,5]=>[4,2,1]=>630
[7,4,3,2,6,5,1]=>[2,2,2,1]=>105
[7,4,3,5,1,2,6]=>[6,1]=>840
[7,4,3,5,1,6,2]=>[5,1,1]=>504
[7,4,3,5,2,1,6]=>[3,3,1]=>280
[7,4,3,5,2,6,1]=>[3,2,1,1]=>420
[7,4,3,5,6,1,2]=>[6,1]=>840
[7,4,3,5,6,2,1]=>[4,2,1]=>630
[7,4,3,6,1,2,5]=>[3,3,1]=>280
[7,4,3,6,1,5,2]=>[6,1]=>840
[7,4,3,6,2,1,5]=>[6,1]=>840
[7,4,3,6,2,5,1]=>[4,2,1]=>630
[7,4,3,6,5,1,2]=>[5,1,1]=>504
[7,4,3,6,5,2,1]=>[3,2,1,1]=>420
[7,4,5,1,2,3,6]=>[7]=>720
[7,4,5,1,2,6,3]=>[6,1]=>840
[7,4,5,1,3,2,6]=>[5,2]=>504
[7,4,5,1,3,6,2]=>[4,2,1]=>630
[7,4,5,1,6,2,3]=>[7]=>720
[7,4,5,1,6,3,2]=>[4,3]=>420
[7,4,5,2,1,3,6]=>[5,2]=>504
[7,4,5,2,1,6,3]=>[4,2,1]=>630
[7,4,5,2,3,1,6]=>[3,2,2]=>210
[7,4,5,2,3,6,1]=>[2,2,2,1]=>105
[7,4,5,2,6,1,3]=>[5,2]=>504
[7,4,5,2,6,3,1]=>[3,2,2]=>210
[7,4,5,3,1,2,6]=>[7]=>720
[7,4,5,3,1,6,2]=>[6,1]=>840
[7,4,5,3,2,1,6]=>[4,3]=>420
[7,4,5,3,2,6,1]=>[4,2,1]=>630
[7,4,5,3,6,1,2]=>[7]=>720
[7,4,5,3,6,2,1]=>[5,2]=>504
[7,4,5,6,1,2,3]=>[4,3]=>420
[7,4,5,6,1,3,2]=>[7]=>720
[7,4,5,6,2,1,3]=>[7]=>720
[7,4,5,6,2,3,1]=>[5,2]=>504
[7,4,5,6,3,1,2]=>[5,2]=>504
[7,4,5,6,3,2,1]=>[3,2,2]=>210
[7,4,6,1,2,3,5]=>[5,2]=>504
[7,4,6,1,2,5,3]=>[7]=>720
[7,4,6,1,3,2,5]=>[7]=>720
[7,4,6,1,3,5,2]=>[4,3]=>420
[7,4,6,1,5,2,3]=>[6,1]=>840
[7,4,6,1,5,3,2]=>[4,2,1]=>630
[7,4,6,2,1,3,5]=>[3,2,2]=>210
[7,4,6,2,1,5,3]=>[5,2]=>504
[7,4,6,2,3,1,5]=>[5,2]=>504
[7,4,6,2,3,5,1]=>[3,2,2]=>210
[7,4,6,2,5,1,3]=>[4,2,1]=>630
[7,4,6,2,5,3,1]=>[2,2,2,1]=>105
[7,4,6,3,1,2,5]=>[4,3]=>420
[7,4,6,3,1,5,2]=>[7]=>720
[7,4,6,3,2,1,5]=>[7]=>720
[7,4,6,3,2,5,1]=>[5,2]=>504
[7,4,6,3,5,1,2]=>[6,1]=>840
[7,4,6,3,5,2,1]=>[4,2,1]=>630
[7,4,6,5,1,2,3]=>[7]=>720
[7,4,6,5,1,3,2]=>[5,2]=>504
[7,4,6,5,2,1,3]=>[4,3]=>420
[7,4,6,5,2,3,1]=>[3,2,2]=>210
[7,4,6,5,3,1,2]=>[7]=>720
[7,4,6,5,3,2,1]=>[5,2]=>504
[7,5,1,2,3,4,6]=>[7]=>720
[7,5,1,2,3,6,4]=>[6,1]=>840
[7,5,1,2,4,3,6]=>[4,3]=>420
[7,5,1,2,4,6,3]=>[3,3,1]=>280
[7,5,1,2,6,3,4]=>[7]=>720
[7,5,1,2,6,4,3]=>[4,3]=>420
[7,5,1,3,2,4,6]=>[5,2]=>504
[7,5,1,3,2,6,4]=>[4,2,1]=>630
[7,5,1,3,4,2,6]=>[7]=>720
[7,5,1,3,4,6,2]=>[6,1]=>840
[7,5,1,3,6,2,4]=>[4,3]=>420
[7,5,1,3,6,4,2]=>[7]=>720
[7,5,1,4,2,3,6]=>[4,2,1]=>630
[7,5,1,4,2,6,3]=>[3,2,1,1]=>420
[7,5,1,4,3,2,6]=>[6,1]=>840
[7,5,1,4,3,6,2]=>[5,1,1]=>504
[7,5,1,4,6,2,3]=>[3,3,1]=>280
[7,5,1,4,6,3,2]=>[6,1]=>840
[7,5,1,6,2,3,4]=>[5,2]=>504
[7,5,1,6,2,4,3]=>[3,2,2]=>210
[7,5,1,6,3,2,4]=>[7]=>720
[7,5,1,6,3,4,2]=>[5,2]=>504
[7,5,1,6,4,2,3]=>[4,3]=>420
[7,5,1,6,4,3,2]=>[7]=>720
[7,5,2,1,3,4,6]=>[4,3]=>420
[7,5,2,1,3,6,4]=>[3,3,1]=>280
[7,5,2,1,4,3,6]=>[7]=>720
[7,5,2,1,4,6,3]=>[6,1]=>840
[7,5,2,1,6,3,4]=>[4,3]=>420
[7,5,2,1,6,4,3]=>[7]=>720
[7,5,2,3,1,4,6]=>[7]=>720
[7,5,2,3,1,6,4]=>[6,1]=>840
[7,5,2,3,4,1,6]=>[4,3]=>420
[7,5,2,3,4,6,1]=>[4,2,1]=>630
[7,5,2,3,6,1,4]=>[7]=>720
[7,5,2,3,6,4,1]=>[5,2]=>504
[7,5,2,4,1,3,6]=>[6,1]=>840
[7,5,2,4,1,6,3]=>[5,1,1]=>504
[7,5,2,4,3,1,6]=>[3,3,1]=>280
[7,5,2,4,3,6,1]=>[3,2,1,1]=>420
[7,5,2,4,6,1,3]=>[6,1]=>840
[7,5,2,4,6,3,1]=>[4,2,1]=>630
[7,5,2,6,1,3,4]=>[7]=>720
[7,5,2,6,1,4,3]=>[5,2]=>504
[7,5,2,6,3,1,4]=>[4,3]=>420
[7,5,2,6,3,4,1]=>[3,2,2]=>210
[7,5,2,6,4,1,3]=>[7]=>720
[7,5,2,6,4,3,1]=>[5,2]=>504
[7,5,3,1,2,4,6]=>[4,2,1]=>630
[7,5,3,1,2,6,4]=>[3,2,1,1]=>420
[7,5,3,1,4,2,6]=>[6,1]=>840
[7,5,3,1,4,6,2]=>[5,1,1]=>504
[7,5,3,1,6,2,4]=>[3,3,1]=>280
[7,5,3,1,6,4,2]=>[6,1]=>840
[7,5,3,2,1,4,6]=>[6,1]=>840
[7,5,3,2,1,6,4]=>[5,1,1]=>504
[7,5,3,2,4,1,6]=>[3,3,1]=>280
[7,5,3,2,4,6,1]=>[3,2,1,1]=>420
[7,5,3,2,6,1,4]=>[6,1]=>840
[7,5,3,2,6,4,1]=>[4,2,1]=>630
[7,5,3,4,1,2,6]=>[5,1,1]=>504
[7,5,3,4,1,6,2]=>[4,1,1,1]=>210
[7,5,3,4,2,1,6]=>[3,2,1,1]=>420
[7,5,3,4,2,6,1]=>[2,2,1,1,1]=>105
[7,5,3,4,6,1,2]=>[5,1,1]=>504
[7,5,3,4,6,2,1]=>[3,2,1,1]=>420
[7,5,3,6,1,2,4]=>[6,1]=>840
[7,5,3,6,1,4,2]=>[4,2,1]=>630
[7,5,3,6,2,1,4]=>[4,2,1]=>630
[7,5,3,6,2,4,1]=>[2,2,2,1]=>105
[7,5,3,6,4,1,2]=>[6,1]=>840
[7,5,3,6,4,2,1]=>[4,2,1]=>630
[7,5,4,1,2,3,6]=>[5,2]=>504
[7,5,4,1,2,6,3]=>[4,2,1]=>630
[7,5,4,1,3,2,6]=>[7]=>720
[7,5,4,1,3,6,2]=>[6,1]=>840
[7,5,4,1,6,2,3]=>[4,3]=>420
[7,5,4,1,6,3,2]=>[7]=>720
[7,5,4,2,1,3,6]=>[7]=>720
[7,5,4,2,1,6,3]=>[6,1]=>840
[7,5,4,2,3,1,6]=>[4,3]=>420
[7,5,4,2,3,6,1]=>[4,2,1]=>630
[7,5,4,2,6,1,3]=>[7]=>720
[7,5,4,2,6,3,1]=>[5,2]=>504
[7,5,4,3,1,2,6]=>[5,2]=>504
[7,5,4,3,1,6,2]=>[4,2,1]=>630
[7,5,4,3,2,1,6]=>[3,2,2]=>210
[7,5,4,3,2,6,1]=>[2,2,2,1]=>105
[7,5,4,3,6,1,2]=>[5,2]=>504
[7,5,4,3,6,2,1]=>[3,2,2]=>210
[7,5,4,6,1,2,3]=>[7]=>720
[7,5,4,6,1,3,2]=>[4,3]=>420
[7,5,4,6,2,1,3]=>[5,2]=>504
[7,5,4,6,2,3,1]=>[3,2,2]=>210
[7,5,4,6,3,1,2]=>[7]=>720
[7,5,4,6,3,2,1]=>[5,2]=>504
[7,5,6,1,2,3,4]=>[3,2,2]=>210
[7,5,6,1,2,4,3]=>[5,2]=>504
[7,5,6,1,3,2,4]=>[4,3]=>420
[7,5,6,1,3,4,2]=>[7]=>720
[7,5,6,1,4,2,3]=>[7]=>720
[7,5,6,1,4,3,2]=>[5,2]=>504
[7,5,6,2,1,3,4]=>[5,2]=>504
[7,5,6,2,1,4,3]=>[7]=>720
[7,5,6,2,3,1,4]=>[7]=>720
[7,5,6,2,3,4,1]=>[5,2]=>504
[7,5,6,2,4,1,3]=>[4,3]=>420
[7,5,6,2,4,3,1]=>[3,2,2]=>210
[7,5,6,3,1,2,4]=>[7]=>720
[7,5,6,3,1,4,2]=>[4,3]=>420
[7,5,6,3,2,1,4]=>[5,2]=>504
[7,5,6,3,2,4,1]=>[3,2,2]=>210
[7,5,6,3,4,1,2]=>[7]=>720
[7,5,6,3,4,2,1]=>[5,2]=>504
[7,5,6,4,1,2,3]=>[6,1]=>840
[7,5,6,4,1,3,2]=>[4,2,1]=>630
[7,5,6,4,2,1,3]=>[4,2,1]=>630
[7,5,6,4,2,3,1]=>[2,2,2,1]=>105
[7,5,6,4,3,1,2]=>[6,1]=>840
[7,5,6,4,3,2,1]=>[4,2,1]=>630
[7,6,1,2,3,4,5]=>[4,3]=>420
[7,6,1,2,3,5,4]=>[7]=>720
[7,6,1,2,4,3,5]=>[7]=>720
[7,6,1,2,4,5,3]=>[4,3]=>420
[7,6,1,2,5,3,4]=>[6,1]=>840
[7,6,1,2,5,4,3]=>[3,3,1]=>280
[7,6,1,3,2,4,5]=>[7]=>720
[7,6,1,3,2,5,4]=>[4,3]=>420
[7,6,1,3,4,2,5]=>[5,2]=>504
[7,6,1,3,4,5,2]=>[7]=>720
[7,6,1,3,5,2,4]=>[4,2,1]=>630
[7,6,1,3,5,4,2]=>[6,1]=>840
[7,6,1,4,2,3,5]=>[6,1]=>840
[7,6,1,4,2,5,3]=>[3,3,1]=>280
[7,6,1,4,3,2,5]=>[4,2,1]=>630
[7,6,1,4,3,5,2]=>[6,1]=>840
[7,6,1,4,5,2,3]=>[3,2,1,1]=>420
[7,6,1,4,5,3,2]=>[5,1,1]=>504
[7,6,1,5,2,3,4]=>[7]=>720
[7,6,1,5,2,4,3]=>[4,3]=>420
[7,6,1,5,3,2,4]=>[5,2]=>504
[7,6,1,5,3,4,2]=>[7]=>720
[7,6,1,5,4,2,3]=>[3,2,2]=>210
[7,6,1,5,4,3,2]=>[5,2]=>504
[7,6,2,1,3,4,5]=>[7]=>720
[7,6,2,1,3,5,4]=>[4,3]=>420
[7,6,2,1,4,3,5]=>[4,3]=>420
[7,6,2,1,4,5,3]=>[7]=>720
[7,6,2,1,5,3,4]=>[3,3,1]=>280
[7,6,2,1,5,4,3]=>[6,1]=>840
[7,6,2,3,1,4,5]=>[4,3]=>420
[7,6,2,3,1,5,4]=>[7]=>720
[7,6,2,3,4,1,5]=>[7]=>720
[7,6,2,3,4,5,1]=>[5,2]=>504
[7,6,2,3,5,1,4]=>[6,1]=>840
[7,6,2,3,5,4,1]=>[4,2,1]=>630
[7,6,2,4,1,3,5]=>[3,3,1]=>280
[7,6,2,4,1,5,3]=>[6,1]=>840
[7,6,2,4,3,1,5]=>[6,1]=>840
[7,6,2,4,3,5,1]=>[4,2,1]=>630
[7,6,2,4,5,1,3]=>[5,1,1]=>504
[7,6,2,4,5,3,1]=>[3,2,1,1]=>420
[7,6,2,5,1,3,4]=>[4,3]=>420
[7,6,2,5,1,4,3]=>[7]=>720
[7,6,2,5,3,1,4]=>[7]=>720
[7,6,2,5,3,4,1]=>[5,2]=>504
[7,6,2,5,4,1,3]=>[5,2]=>504
[7,6,2,5,4,3,1]=>[3,2,2]=>210
[7,6,3,1,2,4,5]=>[6,1]=>840
[7,6,3,1,2,5,4]=>[3,3,1]=>280
[7,6,3,1,4,2,5]=>[4,2,1]=>630
[7,6,3,1,4,5,2]=>[6,1]=>840
[7,6,3,1,5,2,4]=>[3,2,1,1]=>420
[7,6,3,1,5,4,2]=>[5,1,1]=>504
[7,6,3,2,1,4,5]=>[3,3,1]=>280
[7,6,3,2,1,5,4]=>[6,1]=>840
[7,6,3,2,4,1,5]=>[6,1]=>840
[7,6,3,2,4,5,1]=>[4,2,1]=>630
[7,6,3,2,5,1,4]=>[5,1,1]=>504
[7,6,3,2,5,4,1]=>[3,2,1,1]=>420
[7,6,3,4,1,2,5]=>[3,2,1,1]=>420
[7,6,3,4,1,5,2]=>[5,1,1]=>504
[7,6,3,4,2,1,5]=>[5,1,1]=>504
[7,6,3,4,2,5,1]=>[3,2,1,1]=>420
[7,6,3,4,5,1,2]=>[4,1,1,1]=>210
[7,6,3,4,5,2,1]=>[2,2,1,1,1]=>105
[7,6,3,5,1,2,4]=>[4,2,1]=>630
[7,6,3,5,1,4,2]=>[6,1]=>840
[7,6,3,5,2,1,4]=>[6,1]=>840
[7,6,3,5,2,4,1]=>[4,2,1]=>630
[7,6,3,5,4,1,2]=>[4,2,1]=>630
[7,6,3,5,4,2,1]=>[2,2,2,1]=>105
[7,6,4,1,2,3,5]=>[7]=>720
[7,6,4,1,2,5,3]=>[4,3]=>420
[7,6,4,1,3,2,5]=>[5,2]=>504
[7,6,4,1,3,5,2]=>[7]=>720
[7,6,4,1,5,2,3]=>[4,2,1]=>630
[7,6,4,1,5,3,2]=>[6,1]=>840
[7,6,4,2,1,3,5]=>[4,3]=>420
[7,6,4,2,1,5,3]=>[7]=>720
[7,6,4,2,3,1,5]=>[7]=>720
[7,6,4,2,3,5,1]=>[5,2]=>504
[7,6,4,2,5,1,3]=>[6,1]=>840
[7,6,4,2,5,3,1]=>[4,2,1]=>630
[7,6,4,3,1,2,5]=>[3,2,2]=>210
[7,6,4,3,1,5,2]=>[5,2]=>504
[7,6,4,3,2,1,5]=>[5,2]=>504
[7,6,4,3,2,5,1]=>[3,2,2]=>210
[7,6,4,3,5,1,2]=>[4,2,1]=>630
[7,6,4,3,5,2,1]=>[2,2,2,1]=>105
[7,6,4,5,1,2,3]=>[5,2]=>504
[7,6,4,5,1,3,2]=>[7]=>720
[7,6,4,5,2,1,3]=>[7]=>720
[7,6,4,5,2,3,1]=>[5,2]=>504
[7,6,4,5,3,1,2]=>[4,3]=>420
[7,6,4,5,3,2,1]=>[3,2,2]=>210
[7,6,5,1,2,3,4]=>[4,3]=>420
[7,6,5,1,2,4,3]=>[7]=>720
[7,6,5,1,3,2,4]=>[3,2,2]=>210
[7,6,5,1,3,4,2]=>[5,2]=>504
[7,6,5,1,4,2,3]=>[5,2]=>504
[7,6,5,1,4,3,2]=>[7]=>720
[7,6,5,2,1,3,4]=>[7]=>720
[7,6,5,2,1,4,3]=>[4,3]=>420
[7,6,5,2,3,1,4]=>[5,2]=>504
[7,6,5,2,3,4,1]=>[3,2,2]=>210
[7,6,5,2,4,1,3]=>[7]=>720
[7,6,5,2,4,3,1]=>[5,2]=>504
[7,6,5,3,1,2,4]=>[5,2]=>504
[7,6,5,3,1,4,2]=>[7]=>720
[7,6,5,3,2,1,4]=>[7]=>720
[7,6,5,3,2,4,1]=>[5,2]=>504
[7,6,5,3,4,1,2]=>[4,3]=>420
[7,6,5,3,4,2,1]=>[3,2,2]=>210
[7,6,5,4,1,2,3]=>[4,2,1]=>630
[7,6,5,4,1,3,2]=>[6,1]=>840
[7,6,5,4,2,1,3]=>[6,1]=>840
[7,6,5,4,2,3,1]=>[4,2,1]=>630
[7,6,5,4,3,1,2]=>[4,2,1]=>630
[7,6,5,4,3,2,1]=>[2,2,2,1]=>105
[8,7,6,5,4,3,2,1]=>[2,2,2,2]=>105
[7,8,6,5,4,3,2,1]=>[4,2,2]=>1260
[8,6,7,5,4,3,2,1]=>[4,2,2]=>1260
[7,6,8,5,4,3,2,1]=>[6,2]=>3360
[6,7,8,5,4,3,2,1]=>[4,2,2]=>1260
[8,7,5,6,4,3,2,1]=>[4,2,2]=>1260
[7,8,5,6,4,3,2,1]=>[4,4]=>1260
[8,6,5,7,4,3,2,1]=>[6,2]=>3360
[8,5,6,7,4,3,2,1]=>[4,2,2]=>1260
[7,6,5,8,4,3,2,1]=>[8]=>5040
[6,7,5,8,4,3,2,1]=>[6,2]=>3360
[7,5,6,8,4,3,2,1]=>[6,2]=>3360
[6,5,7,8,4,3,2,1]=>[8]=>5040
[5,6,7,8,4,3,2,1]=>[4,4]=>1260
[8,7,6,4,5,3,2,1]=>[2,2,2,1,1]=>420
[7,8,6,4,5,3,2,1]=>[4,2,1,1]=>2520
[8,6,7,4,5,3,2,1]=>[4,2,1,1]=>2520
[7,6,8,4,5,3,2,1]=>[6,1,1]=>3360
[8,7,5,4,6,3,2,1]=>[3,2,2,1]=>1680
[8,7,4,5,6,3,2,1]=>[4,2,2]=>1260
[8,6,5,4,7,3,2,1]=>[5,2,1]=>4032
[8,5,6,4,7,3,2,1]=>[3,2,2,1]=>1680
[8,6,4,5,7,3,2,1]=>[6,2]=>3360
[8,4,5,6,7,3,2,1]=>[6,2]=>3360
[7,6,5,4,8,3,2,1]=>[7,1]=>5760
[6,7,5,4,8,3,2,1]=>[5,2,1]=>4032
[7,5,6,4,8,3,2,1]=>[5,2,1]=>4032
[6,5,7,4,8,3,2,1]=>[7,1]=>5760
[5,6,7,4,8,3,2,1]=>[4,3,1]=>3360
[7,6,4,5,8,3,2,1]=>[8]=>5040
[6,7,4,5,8,3,2,1]=>[6,2]=>3360
[7,5,4,6,8,3,2,1]=>[5,3]=>2688
[7,4,5,6,8,3,2,1]=>[8]=>5040
[6,5,4,7,8,3,2,1]=>[8]=>5040
[5,6,4,7,8,3,2,1]=>[5,3]=>2688
[6,4,5,7,8,3,2,1]=>[5,3]=>2688
[5,4,6,7,8,3,2,1]=>[3,3,2]=>1120
[4,5,6,7,8,3,2,1]=>[6,2]=>3360
[8,7,6,5,3,4,2,1]=>[4,2,2]=>1260
[7,8,6,5,3,4,2,1]=>[4,4]=>1260
[8,6,7,5,3,4,2,1]=>[6,2]=>3360
[7,6,8,5,3,4,2,1]=>[8]=>5040
[8,7,5,6,3,4,2,1]=>[2,2,2,2]=>105
[7,8,5,6,3,4,2,1]=>[4,2,2]=>1260
[8,5,6,7,3,4,2,1]=>[6,2]=>3360
[7,6,5,8,3,4,2,1]=>[6,2]=>3360
[6,5,7,8,3,4,2,1]=>[4,4]=>1260
[5,6,7,8,3,4,2,1]=>[8]=>5040
[8,7,6,4,3,5,2,1]=>[3,2,2,1]=>1680
[7,8,6,4,3,5,2,1]=>[4,3,1]=>3360
[8,6,7,4,3,5,2,1]=>[5,2,1]=>4032
[7,6,8,4,3,5,2,1]=>[7,1]=>5760
[6,7,8,4,3,5,2,1]=>[5,2,1]=>4032
[8,7,6,3,4,5,2,1]=>[4,2,2]=>1260
[7,8,6,3,4,5,2,1]=>[4,4]=>1260
[8,6,7,3,4,5,2,1]=>[6,2]=>3360
[7,6,8,3,4,5,2,1]=>[8]=>5040
[6,7,8,3,4,5,2,1]=>[6,2]=>3360
[8,7,5,4,3,6,2,1]=>[2,2,2,1,1]=>420
[7,8,5,4,3,6,2,1]=>[4,2,1,1]=>2520
[8,7,4,5,3,6,2,1]=>[3,2,2,1]=>1680
[7,8,5,3,4,6,2,1]=>[4,3,1]=>3360
[8,7,4,3,5,6,2,1]=>[2,2,2,1,1]=>420
[8,7,3,4,5,6,2,1]=>[2,2,1,1,1,1]=>210
[7,8,3,4,5,6,2,1]=>[4,1,1,1,1]=>420
[8,6,5,4,3,7,2,1]=>[3,2,2,1]=>1680
[8,6,4,3,5,7,2,1]=>[3,2,2,1]=>1680
[8,5,4,3,6,7,2,1]=>[4,2,2]=>1260
[8,5,3,4,6,7,2,1]=>[4,2,1,1]=>2520
[8,4,3,5,6,7,2,1]=>[5,2,1]=>4032
[8,3,4,5,6,7,2,1]=>[6,2]=>3360
[7,6,5,4,3,8,2,1]=>[5,2,1]=>4032
[6,7,5,4,3,8,2,1]=>[3,2,2,1]=>1680
[7,5,6,4,3,8,2,1]=>[7,1]=>5760
[6,5,7,4,3,8,2,1]=>[4,3,1]=>3360
[5,6,7,4,3,8,2,1]=>[7,1]=>5760
[6,7,4,5,3,8,2,1]=>[3,3,2]=>1120
[7,5,4,6,3,8,2,1]=>[8]=>5040
[7,4,5,6,3,8,2,1]=>[6,2]=>3360
[6,5,4,7,3,8,2,1]=>[5,3]=>2688
[6,4,5,7,3,8,2,1]=>[3,3,2]=>1120
[5,4,6,7,3,8,2,1]=>[5,3]=>2688
[4,5,6,7,3,8,2,1]=>[8]=>5040
[7,6,5,3,4,8,2,1]=>[5,3]=>2688
[7,6,4,3,5,8,2,1]=>[5,2,1]=>4032
[7,6,3,4,5,8,2,1]=>[5,1,1,1]=>1344
[7,5,4,3,6,8,2,1]=>[6,2]=>3360
[7,5,3,4,6,8,2,1]=>[6,1,1]=>3360
[7,3,4,5,6,8,2,1]=>[8]=>5040
[6,5,4,3,7,8,2,1]=>[3,3,2]=>1120
[6,3,4,5,7,8,2,1]=>[5,3]=>2688
[5,4,3,6,7,8,2,1]=>[7,1]=>5760
[5,3,4,6,7,8,2,1]=>[8]=>5040
[4,3,5,6,7,8,2,1]=>[4,4]=>1260
[3,4,5,6,7,8,2,1]=>[8]=>5040
[8,7,6,5,4,2,3,1]=>[4,2,2]=>1260
[7,8,6,5,4,2,3,1]=>[6,2]=>3360
[8,6,7,5,4,2,3,1]=>[2,2,2,2]=>105
[7,6,8,5,4,2,3,1]=>[4,2,2]=>1260
[8,7,5,6,4,2,3,1]=>[6,2]=>3360
[8,6,5,7,4,2,3,1]=>[4,2,2]=>1260
[7,6,5,8,4,2,3,1]=>[6,2]=>3360
[7,5,6,8,4,2,3,1]=>[8]=>5040
[5,6,7,8,4,2,3,1]=>[4,2,2]=>1260
[8,7,6,4,5,2,3,1]=>[4,2,1,1]=>2520
[8,6,7,4,5,2,3,1]=>[2,2,2,1,1]=>420
[7,6,8,4,5,2,3,1]=>[4,2,1,1]=>2520
[8,7,5,4,6,2,3,1]=>[5,2,1]=>4032
[8,7,4,5,6,2,3,1]=>[6,2]=>3360
[7,8,4,5,6,2,3,1]=>[8]=>5040
[8,6,5,4,7,2,3,1]=>[3,2,2,1]=>1680
[8,5,6,4,7,2,3,1]=>[5,2,1]=>4032
[8,6,4,5,7,2,3,1]=>[4,2,2]=>1260
[8,4,5,6,7,2,3,1]=>[3,3,2]=>1120
[7,6,5,4,8,2,3,1]=>[5,2,1]=>4032
[7,5,6,4,8,2,3,1]=>[7,1]=>5760
[6,5,7,4,8,2,3,1]=>[5,2,1]=>4032
[4,5,6,7,8,2,3,1]=>[8]=>5040
[8,7,6,5,3,2,4,1]=>[6,2]=>3360
[7,8,6,5,3,2,4,1]=>[8]=>5040
[8,6,7,5,3,2,4,1]=>[4,2,2]=>1260
[7,6,8,5,3,2,4,1]=>[6,2]=>3360
[6,7,8,5,3,2,4,1]=>[8]=>5040
[8,7,5,6,3,2,4,1]=>[4,2,2]=>1260
[8,6,5,7,3,2,4,1]=>[2,2,2,2]=>105
[8,5,6,7,3,2,4,1]=>[4,2,2]=>1260
[7,6,5,8,3,2,4,1]=>[4,2,2]=>1260
[6,7,5,8,3,2,4,1]=>[6,2]=>3360
[5,6,7,8,3,2,4,1]=>[6,2]=>3360
[8,7,6,5,2,3,4,1]=>[4,2,2]=>1260
[8,6,7,5,2,3,4,1]=>[6,2]=>3360
[7,6,8,5,2,3,4,1]=>[8]=>5040
[6,7,8,5,2,3,4,1]=>[4,4]=>1260
[8,7,5,6,2,3,4,1]=>[6,2]=>3360
[7,8,5,6,2,3,4,1]=>[8]=>5040
[8,6,5,7,2,3,4,1]=>[4,2,2]=>1260
[8,5,6,7,2,3,4,1]=>[2,2,2,2]=>105
[7,6,5,8,2,3,4,1]=>[4,4]=>1260
[6,7,5,8,2,3,4,1]=>[8]=>5040
[6,5,7,8,2,3,4,1]=>[6,2]=>3360
[5,6,7,8,2,3,4,1]=>[8]=>5040
[8,7,6,4,3,2,5,1]=>[5,2,1]=>4032
[7,8,6,4,3,2,5,1]=>[7,1]=>5760
[8,6,7,4,3,2,5,1]=>[3,2,2,1]=>1680
[7,6,8,4,3,2,5,1]=>[5,2,1]=>4032
[6,7,8,4,3,2,5,1]=>[7,1]=>5760
[8,7,6,3,4,2,5,1]=>[6,2]=>3360
[7,8,6,3,4,2,5,1]=>[8]=>5040
[8,6,7,3,4,2,5,1]=>[4,2,2]=>1260
[7,6,8,3,4,2,5,1]=>[6,2]=>3360
[6,7,8,3,4,2,5,1]=>[8]=>5040
[7,6,8,4,2,3,5,1]=>[7,1]=>5760
[6,7,8,4,2,3,5,1]=>[4,3,1]=>3360
[8,7,6,3,2,4,5,1]=>[3,3,2]=>1120
[7,8,6,3,2,4,5,1]=>[5,3]=>2688
[8,6,7,3,2,4,5,1]=>[6,2]=>3360
[6,7,8,3,2,4,5,1]=>[5,3]=>2688
[8,7,6,2,3,4,5,1]=>[6,2]=>3360
[7,8,6,2,3,4,5,1]=>[8]=>5040
[8,6,7,2,3,4,5,1]=>[3,3,2]=>1120
[7,6,8,2,3,4,5,1]=>[5,3]=>2688
[6,7,8,2,3,4,5,1]=>[8]=>5040
[8,7,5,4,3,2,6,1]=>[3,2,2,1]=>1680
[8,7,5,3,4,2,6,1]=>[3,3,2]=>1120
[7,8,5,3,4,2,6,1]=>[5,3]=>2688
[8,7,4,3,5,2,6,1]=>[3,2,2,1]=>1680
[7,8,4,3,5,2,6,1]=>[5,2,1]=>4032
[8,7,5,4,2,3,6,1]=>[5,2,1]=>4032
[8,7,5,3,2,4,6,1]=>[6,2]=>3360
[8,7,4,3,2,5,6,1]=>[4,2,2]=>1260
[7,8,4,3,2,5,6,1]=>[6,2]=>3360
[7,8,3,4,2,5,6,1]=>[6,1,1]=>3360
[7,8,4,2,3,5,6,1]=>[8]=>5040
[7,8,3,2,4,5,6,1]=>[7,1]=>5760
[8,7,2,3,4,5,6,1]=>[6,2]=>3360
[7,8,2,3,4,5,6,1]=>[8]=>5040
[8,6,5,4,3,2,7,1]=>[2,2,2,1,1]=>420
[8,5,6,4,3,2,7,1]=>[4,2,1,1]=>2520
[8,6,4,5,3,2,7,1]=>[3,2,2,1]=>1680
[8,5,4,6,3,2,7,1]=>[5,2,1]=>4032
[8,6,5,3,4,2,7,1]=>[3,2,2,1]=>1680
[8,5,6,3,4,2,7,1]=>[5,2,1]=>4032
[8,6,4,3,5,2,7,1]=>[2,2,2,1,1]=>420
[8,6,3,4,5,2,7,1]=>[2,2,1,1,1,1]=>210
[8,5,4,3,6,2,7,1]=>[3,2,2,1]=>1680
[8,4,5,3,6,2,7,1]=>[5,2,1]=>4032
[8,4,3,5,6,2,7,1]=>[4,2,1,1]=>2520
[8,3,4,5,6,2,7,1]=>[5,2,1]=>4032
[8,6,5,3,2,4,7,1]=>[5,2,1]=>4032
[8,6,4,3,2,5,7,1]=>[3,2,2,1]=>1680
[8,6,4,2,3,5,7,1]=>[5,2,1]=>4032
[8,6,2,3,4,5,7,1]=>[5,2,1]=>4032
[8,5,4,3,2,6,7,1]=>[2,2,2,1,1]=>420
[8,5,3,4,2,6,7,1]=>[2,2,1,1,1,1]=>210
[8,3,4,5,2,6,7,1]=>[4,2,1,1]=>2520
[8,5,4,2,3,6,7,1]=>[4,2,1,1]=>2520
[8,4,5,2,3,6,7,1]=>[2,2,2,1,1]=>420
[8,4,3,2,5,6,7,1]=>[2,2,1,1,1,1]=>210
[8,3,4,2,5,6,7,1]=>[3,2,1,1,1]=>1120
[8,4,2,3,5,6,7,1]=>[3,2,1,1,1]=>1120
[8,3,2,4,5,6,7,1]=>[2,2,1,1,1,1]=>210
[8,2,3,4,5,6,7,1]=>[2,1,1,1,1,1,1]=>28
[7,6,5,4,3,2,8,1]=>[3,2,2,1]=>1680
[6,7,5,4,3,2,8,1]=>[5,2,1]=>4032
[7,5,6,4,3,2,8,1]=>[4,3,1]=>3360
[6,5,7,4,3,2,8,1]=>[7,1]=>5760
[5,6,7,4,3,2,8,1]=>[5,2,1]=>4032
[7,6,4,5,3,2,8,1]=>[3,3,2]=>1120
[6,7,4,5,3,2,8,1]=>[5,3]=>2688
[7,4,5,6,3,2,8,1]=>[3,3,2]=>1120
[6,5,4,7,3,2,8,1]=>[8]=>5040
[6,4,5,7,3,2,8,1]=>[6,2]=>3360
[4,5,6,7,3,2,8,1]=>[4,4]=>1260
[7,6,5,3,4,2,8,1]=>[3,3,2]=>1120
[7,5,6,3,4,2,8,1]=>[5,3]=>2688
[6,5,7,3,4,2,8,1]=>[8]=>5040
[7,6,4,3,5,2,8,1]=>[3,2,2,1]=>1680
[7,6,3,4,5,2,8,1]=>[3,2,1,1,1]=>1120
[7,5,4,3,6,2,8,1]=>[3,3,2]=>1120
[7,4,5,3,6,2,8,1]=>[5,3]=>2688
[7,3,4,5,6,2,8,1]=>[5,3]=>2688
[6,5,4,3,7,2,8,1]=>[6,2]=>3360
[6,4,5,3,7,2,8,1]=>[8]=>5040
[5,4,6,3,7,2,8,1]=>[4,4]=>1260
[4,5,6,3,7,2,8,1]=>[8]=>5040
[6,5,3,4,7,2,8,1]=>[6,1,1]=>3360
[5,6,3,4,7,2,8,1]=>[4,2,1,1]=>2520
[6,4,3,5,7,2,8,1]=>[7,1]=>5760
[6,3,4,5,7,2,8,1]=>[8]=>5040
[5,4,3,6,7,2,8,1]=>[4,3,1]=>3360
[4,5,3,6,7,2,8,1]=>[7,1]=>5760
[4,3,5,6,7,2,8,1]=>[8]=>5040
[3,4,5,6,7,2,8,1]=>[5,3]=>2688
[7,6,5,4,2,3,8,1]=>[4,3,1]=>3360
[6,7,5,4,2,3,8,1]=>[7,1]=>5760
[7,5,6,4,2,3,8,1]=>[3,2,2,1]=>1680
[6,5,7,4,2,3,8,1]=>[5,2,1]=>4032
[5,6,7,4,2,3,8,1]=>[7,1]=>5760
[7,6,4,5,2,3,8,1]=>[5,3]=>2688
[6,7,4,5,2,3,8,1]=>[8]=>5040
[7,5,4,6,2,3,8,1]=>[3,3,2]=>1120
[7,4,5,6,2,3,8,1]=>[5,3]=>2688
[6,5,4,7,2,3,8,1]=>[6,2]=>3360
[5,6,4,7,2,3,8,1]=>[8]=>5040
[5,4,6,7,2,3,8,1]=>[6,2]=>3360
[4,5,6,7,2,3,8,1]=>[4,2,2]=>1260
[7,6,5,3,2,4,8,1]=>[5,3]=>2688
[6,7,5,3,2,4,8,1]=>[8]=>5040
[6,5,7,3,2,4,8,1]=>[6,2]=>3360
[7,6,5,2,3,4,8,1]=>[3,3,2]=>1120
[7,5,6,2,3,4,8,1]=>[5,3]=>2688
[5,6,7,2,3,4,8,1]=>[5,3]=>2688
[6,7,4,3,2,5,8,1]=>[6,2]=>3360
[7,6,4,2,3,5,8,1]=>[5,3]=>2688
[7,6,3,2,4,5,8,1]=>[4,3,1]=>3360
[6,7,3,2,4,5,8,1]=>[7,1]=>5760
[7,6,2,3,4,5,8,1]=>[5,3]=>2688
[6,7,2,3,4,5,8,1]=>[8]=>5040
[7,5,4,3,2,6,8,1]=>[3,2,2,1]=>1680
[7,4,3,5,2,6,8,1]=>[3,3,1,1]=>1120
[7,5,4,2,3,6,8,1]=>[4,3,1]=>3360
[7,4,5,2,3,6,8,1]=>[3,2,2,1]=>1680
[7,5,3,2,4,6,8,1]=>[3,3,1,1]=>1120
[7,5,2,3,4,6,8,1]=>[4,3,1]=>3360
[7,4,3,2,5,6,8,1]=>[3,2,1,1,1]=>1120
[7,3,2,4,5,6,8,1]=>[3,2,1,1,1]=>1120
[7,2,3,4,5,6,8,1]=>[3,1,1,1,1,1]=>112
[6,5,4,3,2,7,8,1]=>[4,2,2]=>1260
[5,4,6,3,2,7,8,1]=>[8]=>5040
[4,5,6,3,2,7,8,1]=>[6,2]=>3360
[6,3,4,5,2,7,8,1]=>[4,4]=>1260
[5,4,3,6,2,7,8,1]=>[7,1]=>5760
[4,3,5,6,2,7,8,1]=>[5,3]=>2688
[3,4,5,6,2,7,8,1]=>[8]=>5040
[6,5,4,2,3,7,8,1]=>[4,4]=>1260
[6,4,5,2,3,7,8,1]=>[4,2,2]=>1260
[4,5,6,2,3,7,8,1]=>[8]=>5040
[6,5,3,2,4,7,8,1]=>[4,3,1]=>3360
[6,5,2,3,4,7,8,1]=>[4,4]=>1260
[6,2,3,4,5,7,8,1]=>[4,1,1,1,1]=>420
[5,4,3,2,6,7,8,1]=>[5,2,1]=>4032
[4,5,3,2,6,7,8,1]=>[7,1]=>5760
[5,3,4,2,6,7,8,1]=>[5,3]=>2688
[4,3,5,2,6,7,8,1]=>[8]=>5040
[3,4,5,2,6,7,8,1]=>[6,2]=>3360
[5,4,2,3,6,7,8,1]=>[5,3]=>2688
[4,5,2,3,6,7,8,1]=>[8]=>5040
[5,3,2,4,6,7,8,1]=>[5,2,1]=>4032
[5,2,3,4,6,7,8,1]=>[5,1,1,1]=>1344
[4,3,2,5,6,7,8,1]=>[6,2]=>3360
[3,4,2,5,6,7,8,1]=>[8]=>5040
[4,2,3,5,6,7,8,1]=>[6,1,1]=>3360
[3,2,4,5,6,7,8,1]=>[7,1]=>5760
[2,3,4,5,6,7,8,1]=>[8]=>5040
[8,7,6,5,4,3,1,2]=>[4,2,2]=>1260
[7,8,6,5,4,3,1,2]=>[2,2,2,2]=>105
[8,6,7,5,4,3,1,2]=>[6,2]=>3360
[7,6,8,5,4,3,1,2]=>[4,2,2]=>1260
[6,7,8,5,4,3,1,2]=>[6,2]=>3360
[8,7,5,6,4,3,1,2]=>[4,4]=>1260
[7,8,5,6,4,3,1,2]=>[4,2,2]=>1260
[8,6,5,7,4,3,1,2]=>[8]=>5040
[7,6,5,8,4,3,1,2]=>[6,2]=>3360
[6,7,5,8,4,3,1,2]=>[8]=>5040
[6,5,7,8,4,3,1,2]=>[4,4]=>1260
[5,6,7,8,4,3,1,2]=>[8]=>5040
[8,7,6,4,5,3,1,2]=>[4,2,1,1]=>2520
[7,8,6,4,5,3,1,2]=>[2,2,2,1,1]=>420
[6,7,8,4,5,3,1,2]=>[6,1,1]=>3360
[8,7,5,4,6,3,1,2]=>[4,3,1]=>3360
[8,5,6,4,7,3,1,2]=>[5,2,1]=>4032
[8,6,4,5,7,3,1,2]=>[8]=>5040
[8,5,4,6,7,3,1,2]=>[5,3]=>2688
[7,6,5,4,8,3,1,2]=>[5,2,1]=>4032
[7,5,6,4,8,3,1,2]=>[3,2,2,1]=>1680
[6,5,7,4,8,3,1,2]=>[4,3,1]=>3360
[7,6,4,5,8,3,1,2]=>[6,2]=>3360
[6,5,4,7,8,3,1,2]=>[5,3]=>2688
[5,6,4,7,8,3,1,2]=>[8]=>5040
[5,4,6,7,8,3,1,2]=>[6,2]=>3360
[4,5,6,7,8,3,1,2]=>[3,3,2]=>1120
[8,7,6,5,3,4,1,2]=>[4,4]=>1260
[7,8,6,5,3,4,1,2]=>[4,2,2]=>1260
[7,6,8,5,3,4,1,2]=>[6,2]=>3360
[6,7,8,5,3,4,1,2]=>[8]=>5040
[8,7,5,6,3,4,1,2]=>[4,2,2]=>1260
[7,8,5,6,3,4,1,2]=>[2,2,2,2]=>105
[8,6,5,7,3,4,1,2]=>[6,2]=>3360
[8,5,6,7,3,4,1,2]=>[8]=>5040
[7,6,5,8,3,4,1,2]=>[4,2,2]=>1260
[6,7,5,8,3,4,1,2]=>[6,2]=>3360
[7,5,6,8,3,4,1,2]=>[6,2]=>3360
[6,5,7,8,3,4,1,2]=>[8]=>5040
[5,6,7,8,3,4,1,2]=>[4,4]=>1260
[6,7,8,4,3,5,1,2]=>[7,1]=>5760
[8,7,6,3,4,5,1,2]=>[4,4]=>1260
[7,8,6,3,4,5,1,2]=>[4,2,2]=>1260
[8,6,7,3,4,5,1,2]=>[8]=>5040
[7,8,5,4,3,6,1,2]=>[2,2,2,1,1]=>420
[8,7,4,5,3,6,1,2]=>[4,3,1]=>3360
[7,8,4,5,3,6,1,2]=>[3,2,2,1]=>1680
[8,7,4,3,5,6,1,2]=>[4,2,1,1]=>2520
[7,8,4,3,5,6,1,2]=>[2,2,2,1,1]=>420
[8,7,3,4,5,6,1,2]=>[4,1,1,1,1]=>420
[7,8,3,4,5,6,1,2]=>[2,2,1,1,1,1]=>210
[8,6,5,4,3,7,1,2]=>[5,2,1]=>4032
[8,5,4,6,3,7,1,2]=>[8]=>5040
[8,5,4,3,6,7,1,2]=>[6,2]=>3360
[8,5,3,4,6,7,1,2]=>[6,1,1]=>3360
[8,4,3,5,6,7,1,2]=>[7,1]=>5760
[8,3,4,5,6,7,1,2]=>[8]=>5040
[7,6,5,4,3,8,1,2]=>[3,2,2,1]=>1680
[5,6,7,4,3,8,1,2]=>[4,3,1]=>3360
[6,7,4,5,3,8,1,2]=>[5,3]=>2688
[7,5,4,6,3,8,1,2]=>[6,2]=>3360
[6,5,4,7,3,8,1,2]=>[8]=>5040
[5,6,4,7,3,8,1,2]=>[5,3]=>2688
[4,5,6,7,3,8,1,2]=>[5,3]=>2688
[7,6,5,3,4,8,1,2]=>[3,3,2]=>1120
[7,5,4,3,6,8,1,2]=>[4,2,2]=>1260
[7,4,5,3,6,8,1,2]=>[6,2]=>3360
[7,5,3,4,6,8,1,2]=>[4,2,1,1]=>2520
[7,3,4,5,6,8,1,2]=>[6,2]=>3360
[6,5,4,3,7,8,1,2]=>[6,2]=>3360
[5,4,6,3,7,8,1,2]=>[5,3]=>2688
[4,5,6,3,7,8,1,2]=>[8]=>5040
[5,6,3,4,7,8,1,2]=>[3,3,1,1]=>1120
[6,4,3,5,7,8,1,2]=>[7,1]=>5760
[6,3,4,5,7,8,1,2]=>[8]=>5040
[5,4,3,6,7,8,1,2]=>[4,3,1]=>3360
[4,5,3,6,7,8,1,2]=>[7,1]=>5760
[5,3,4,6,7,8,1,2]=>[5,3]=>2688
[4,3,5,6,7,8,1,2]=>[8]=>5040
[3,4,5,6,7,8,1,2]=>[4,4]=>1260
[8,7,6,5,4,2,1,3]=>[6,2]=>3360
[7,8,6,5,4,2,1,3]=>[4,2,2]=>1260
[8,6,7,5,4,2,1,3]=>[4,2,2]=>1260
[7,6,8,5,4,2,1,3]=>[2,2,2,2]=>105
[6,7,8,5,4,2,1,3]=>[4,2,2]=>1260
[8,7,5,6,4,2,1,3]=>[8]=>5040
[7,8,5,6,4,2,1,3]=>[6,2]=>3360
[7,6,5,8,4,2,1,3]=>[4,2,2]=>1260
[6,7,5,8,4,2,1,3]=>[4,4]=>1260
[6,5,7,8,4,2,1,3]=>[8]=>5040
[5,6,7,8,4,2,1,3]=>[6,2]=>3360
[7,6,8,4,5,2,1,3]=>[2,2,2,1,1]=>420
[8,4,5,6,7,2,1,3]=>[5,3]=>2688
[6,7,5,4,8,2,1,3]=>[4,3,1]=>3360
[6,5,7,4,8,2,1,3]=>[7,1]=>5760
[7,4,5,6,8,2,1,3]=>[3,3,2]=>1120
[5,4,6,7,8,2,1,3]=>[8]=>5040
[4,5,6,7,8,2,1,3]=>[5,3]=>2688
[8,7,6,5,4,1,2,3]=>[4,2,2]=>1260
[7,8,6,5,4,1,2,3]=>[6,2]=>3360
[7,6,8,5,4,1,2,3]=>[4,2,2]=>1260
[6,7,8,5,4,1,2,3]=>[2,2,2,2]=>105
[7,8,5,6,4,1,2,3]=>[8]=>5040
[8,6,5,7,4,1,2,3]=>[8]=>5040
[8,5,6,7,4,1,2,3]=>[4,4]=>1260
[7,6,5,8,4,1,2,3]=>[4,4]=>1260
[6,7,5,8,4,1,2,3]=>[4,2,2]=>1260
[7,5,6,8,4,1,2,3]=>[8]=>5040
[6,5,7,8,4,1,2,3]=>[6,2]=>3360
[5,6,7,8,4,1,2,3]=>[8]=>5040
[8,7,6,4,5,1,2,3]=>[4,2,1,1]=>2520
[8,6,7,4,5,1,2,3]=>[6,1,1]=>3360
[6,7,8,4,5,1,2,3]=>[2,2,2,1,1]=>420
[8,7,5,4,6,1,2,3]=>[5,2,1]=>4032
[7,8,5,4,6,1,2,3]=>[7,1]=>5760
[8,7,4,5,6,1,2,3]=>[6,2]=>3360
[7,8,4,5,6,1,2,3]=>[8]=>5040
[8,6,5,4,7,1,2,3]=>[7,1]=>5760
[8,5,6,4,7,1,2,3]=>[4,3,1]=>3360
[8,5,4,6,7,1,2,3]=>[5,3]=>2688
[8,4,5,6,7,1,2,3]=>[8]=>5040
[7,6,5,4,8,1,2,3]=>[4,3,1]=>3360
[6,5,7,4,8,1,2,3]=>[5,2,1]=>4032
[5,6,7,4,8,1,2,3]=>[7,1]=>5760
[6,7,4,5,8,1,2,3]=>[4,2,2]=>1260
[7,5,4,6,8,1,2,3]=>[8]=>5040
[6,5,4,7,8,1,2,3]=>[6,2]=>3360
[5,6,4,7,8,1,2,3]=>[8]=>5040
[5,4,6,7,8,1,2,3]=>[5,3]=>2688
[4,5,6,7,8,1,2,3]=>[8]=>5040
[8,7,6,5,3,2,1,4]=>[8]=>5040
[7,8,6,5,3,2,1,4]=>[6,2]=>3360
[8,6,7,5,3,2,1,4]=>[6,2]=>3360
[7,6,8,5,3,2,1,4]=>[4,2,2]=>1260
[6,7,8,5,3,2,1,4]=>[4,4]=>1260
[8,7,5,6,3,2,1,4]=>[6,2]=>3360
[7,8,5,6,3,2,1,4]=>[4,2,2]=>1260
[8,6,5,7,3,2,1,4]=>[4,2,2]=>1260
[8,5,6,7,3,2,1,4]=>[4,4]=>1260
[7,6,5,8,3,2,1,4]=>[2,2,2,2]=>105
[6,7,5,8,3,2,1,4]=>[4,2,2]=>1260
[7,5,6,8,3,2,1,4]=>[4,2,2]=>1260
[6,5,7,8,3,2,1,4]=>[6,2]=>3360
[5,6,7,8,3,2,1,4]=>[4,2,2]=>1260
[8,7,6,5,2,3,1,4]=>[6,2]=>3360
[7,8,6,5,2,3,1,4]=>[4,2,2]=>1260
[8,6,7,5,2,3,1,4]=>[8]=>5040
[7,6,8,5,2,3,1,4]=>[6,2]=>3360
[7,8,5,6,2,3,1,4]=>[6,2]=>3360
[8,5,6,7,2,3,1,4]=>[4,2,2]=>1260
[7,6,5,8,2,3,1,4]=>[4,2,2]=>1260
[6,7,5,8,2,3,1,4]=>[6,2]=>3360
[7,5,6,8,2,3,1,4]=>[2,2,2,2]=>105
[5,6,7,8,2,3,1,4]=>[6,2]=>3360
[8,7,6,5,3,1,2,4]=>[6,2]=>3360
[7,8,6,5,3,1,2,4]=>[8]=>5040
[7,6,8,5,3,1,2,4]=>[4,4]=>1260
[8,7,5,6,3,1,2,4]=>[4,2,2]=>1260
[8,6,5,7,3,1,2,4]=>[6,2]=>3360
[7,6,5,8,3,1,2,4]=>[4,2,2]=>1260
[6,7,5,8,3,1,2,4]=>[2,2,2,2]=>105
[6,5,7,8,3,1,2,4]=>[4,2,2]=>1260
[5,6,7,8,3,1,2,4]=>[6,2]=>3360
[8,7,6,5,2,1,3,4]=>[8]=>5040
[7,8,6,5,2,1,3,4]=>[4,4]=>1260
[7,6,8,5,2,1,3,4]=>[8]=>5040
[6,7,8,5,2,1,3,4]=>[6,2]=>3360
[8,7,5,6,2,1,3,4]=>[4,4]=>1260
[7,8,5,6,2,1,3,4]=>[8]=>5040
[8,6,5,7,2,1,3,4]=>[8]=>5040
[8,5,6,7,2,1,3,4]=>[6,2]=>3360
[7,6,5,8,2,1,3,4]=>[6,2]=>3360
[6,7,5,8,2,1,3,4]=>[4,2,2]=>1260
[7,5,6,8,2,1,3,4]=>[4,2,2]=>1260
[6,5,7,8,2,1,3,4]=>[2,2,2,2]=>105
[5,6,7,8,2,1,3,4]=>[4,2,2]=>1260
[8,7,6,5,1,2,3,4]=>[4,4]=>1260
[7,8,6,5,1,2,3,4]=>[8]=>5040
[8,6,7,5,1,2,3,4]=>[4,2,2]=>1260
[7,6,8,5,1,2,3,4]=>[6,2]=>3360
[6,7,8,5,1,2,3,4]=>[8]=>5040
[8,7,5,6,1,2,3,4]=>[8]=>5040
[7,8,5,6,1,2,3,4]=>[4,4]=>1260
[8,6,5,7,1,2,3,4]=>[6,2]=>3360
[8,5,6,7,1,2,3,4]=>[8]=>5040
[7,6,5,8,1,2,3,4]=>[4,2,2]=>1260
[6,7,5,8,1,2,3,4]=>[6,2]=>3360
[7,5,6,8,1,2,3,4]=>[6,2]=>3360
[6,5,7,8,1,2,3,4]=>[4,2,2]=>1260
[5,6,7,8,1,2,3,4]=>[2,2,2,2]=>105
[8,7,6,4,3,2,1,5]=>[7,1]=>5760
[7,8,6,4,3,2,1,5]=>[5,2,1]=>4032
[8,6,7,4,3,2,1,5]=>[5,2,1]=>4032
[6,7,8,4,3,2,1,5]=>[4,3,1]=>3360
[8,7,6,3,4,2,1,5]=>[8]=>5040
[7,8,6,3,4,2,1,5]=>[6,2]=>3360
[8,7,6,4,2,3,1,5]=>[5,2,1]=>4032
[7,6,8,4,2,3,1,5]=>[5,2,1]=>4032
[8,7,6,3,2,4,1,5]=>[5,3]=>2688
[8,6,7,3,2,4,1,5]=>[8]=>5040
[6,7,8,3,2,4,1,5]=>[8]=>5040
[8,7,6,2,3,4,1,5]=>[8]=>5040
[8,6,7,2,3,4,1,5]=>[5,3]=>2688
[6,7,8,2,3,4,1,5]=>[5,3]=>2688
[8,7,6,4,3,1,2,5]=>[5,2,1]=>4032
[6,7,8,4,3,1,2,5]=>[3,2,2,1]=>1680
[8,7,6,3,4,1,2,5]=>[6,2]=>3360
[8,6,7,3,4,1,2,5]=>[8]=>5040
[6,7,8,3,4,1,2,5]=>[4,2,2]=>1260
[8,7,6,4,2,1,3,5]=>[7,1]=>5760
[7,8,6,4,2,1,3,5]=>[4,3,1]=>3360
[8,6,7,4,2,1,3,5]=>[5,2,1]=>4032
[6,7,8,4,2,1,3,5]=>[5,2,1]=>4032
[8,7,6,4,1,2,3,5]=>[4,3,1]=>3360
[7,8,6,4,1,2,3,5]=>[7,1]=>5760
[7,6,8,4,1,2,3,5]=>[5,2,1]=>4032
[6,7,8,4,1,2,3,5]=>[7,1]=>5760
[8,7,6,3,2,1,4,5]=>[8]=>5040
[7,8,6,3,2,1,4,5]=>[5,3]=>2688
[8,6,7,3,2,1,4,5]=>[5,3]=>2688
[7,6,8,3,2,1,4,5]=>[8]=>5040
[6,7,8,3,2,1,4,5]=>[6,2]=>3360
[8,7,6,2,3,1,4,5]=>[5,3]=>2688
[8,6,7,2,3,1,4,5]=>[8]=>5040
[6,7,8,2,3,1,4,5]=>[3,3,2]=>1120
[8,7,6,3,1,2,4,5]=>[5,3]=>2688
[7,8,6,3,1,2,4,5]=>[8]=>5040
[7,6,8,3,1,2,4,5]=>[6,2]=>3360
[6,7,8,3,1,2,4,5]=>[8]=>5040
[8,7,6,2,1,3,4,5]=>[3,3,2]=>1120
[8,6,7,2,1,3,4,5]=>[5,3]=>2688
[6,7,8,2,1,3,4,5]=>[5,3]=>2688
[8,7,6,1,2,3,4,5]=>[6,2]=>3360
[7,8,6,1,2,3,4,5]=>[3,3,2]=>1120
[8,6,7,1,2,3,4,5]=>[8]=>5040
[7,6,8,1,2,3,4,5]=>[5,3]=>2688
[6,7,8,1,2,3,4,5]=>[8]=>5040
[8,7,5,4,3,2,1,6]=>[5,2,1]=>4032
[7,8,5,4,3,2,1,6]=>[3,2,2,1]=>1680
[8,7,4,5,3,2,1,6]=>[5,3]=>2688
[8,7,5,3,4,2,1,6]=>[5,3]=>2688
[7,8,3,4,5,2,1,6]=>[3,2,1,1,1]=>1120
[7,8,4,5,2,3,1,6]=>[6,2]=>3360
[8,7,5,3,2,4,1,6]=>[8]=>5040
[8,7,4,3,2,5,1,6]=>[6,2]=>3360
[7,8,4,3,2,5,1,6]=>[4,2,2]=>1260
[8,7,3,4,2,5,1,6]=>[6,1,1]=>3360
[7,8,3,4,2,5,1,6]=>[4,2,1,1]=>2520
[8,7,2,3,4,5,1,6]=>[8]=>5040
[7,8,2,3,4,5,1,6]=>[6,2]=>3360
[8,7,5,4,3,1,2,6]=>[3,2,2,1]=>1680
[7,8,5,4,3,1,2,6]=>[5,2,1]=>4032
[8,7,5,3,4,1,2,6]=>[3,3,2]=>1120
[8,7,3,4,5,1,2,6]=>[3,2,1,1,1]=>1120
[7,8,3,4,5,1,2,6]=>[5,1,1,1]=>1344
[7,8,5,4,2,1,3,6]=>[7,1]=>5760
[8,7,5,4,1,2,3,6]=>[7,1]=>5760
[7,8,5,4,1,2,3,6]=>[4,3,1]=>3360
[8,7,4,5,1,2,3,6]=>[8]=>5040
[7,8,4,5,1,2,3,6]=>[5,3]=>2688
[8,7,5,3,2,1,4,6]=>[5,3]=>2688
[7,8,5,3,2,1,4,6]=>[8]=>5040
[8,7,5,3,1,2,4,6]=>[8]=>5040
[7,8,5,3,1,2,4,6]=>[5,3]=>2688
[8,7,5,2,1,3,4,6]=>[5,3]=>2688
[7,8,5,2,1,3,4,6]=>[8]=>5040
[8,7,5,1,2,3,4,6]=>[8]=>5040
[7,8,5,1,2,3,4,6]=>[5,3]=>2688
[8,7,4,3,2,1,5,6]=>[3,3,2]=>1120
[7,8,4,3,2,1,5,6]=>[6,2]=>3360
[8,7,3,4,2,1,5,6]=>[3,3,1,1]=>1120
[7,8,3,4,2,1,5,6]=>[6,1,1]=>3360
[7,8,4,2,3,1,5,6]=>[8]=>5040
[8,7,3,2,4,1,5,6]=>[4,3,1]=>3360
[7,8,3,2,4,1,5,6]=>[7,1]=>5760
[8,7,2,3,4,1,5,6]=>[5,3]=>2688
[7,8,2,3,4,1,5,6]=>[8]=>5040
[7,8,4,3,1,2,5,6]=>[3,3,2]=>1120
[8,7,3,4,1,2,5,6]=>[6,1,1]=>3360
[7,8,3,4,1,2,5,6]=>[3,3,1,1]=>1120
[7,8,4,2,1,3,5,6]=>[5,3]=>2688
[8,7,4,1,2,3,5,6]=>[5,3]=>2688
[7,8,4,1,2,3,5,6]=>[8]=>5040
[8,7,3,2,1,4,5,6]=>[7,1]=>5760
[7,8,3,2,1,4,5,6]=>[4,3,1]=>3360
[8,7,2,3,1,4,5,6]=>[8]=>5040
[7,8,2,3,1,4,5,6]=>[5,3]=>2688
[7,8,3,1,2,4,5,6]=>[7,1]=>5760
[8,7,2,1,3,4,5,6]=>[4,4]=>1260
[7,8,2,1,3,4,5,6]=>[8]=>5040
[8,7,1,2,3,4,5,6]=>[8]=>5040
[7,8,1,2,3,4,5,6]=>[4,4]=>1260
[8,6,5,4,3,2,1,7]=>[3,2,2,1]=>1680
[8,5,6,4,3,2,1,7]=>[4,3,1]=>3360
[8,4,5,6,3,2,1,7]=>[3,3,2]=>1120
[8,6,5,3,4,2,1,7]=>[3,3,2]=>1120
[8,5,6,3,4,2,1,7]=>[5,3]=>2688
[8,4,5,3,6,2,1,7]=>[5,3]=>2688
[8,4,3,5,6,2,1,7]=>[4,3,1]=>3360
[8,3,4,5,6,2,1,7]=>[5,3]=>2688
[8,6,5,4,2,3,1,7]=>[4,3,1]=>3360
[8,5,6,4,2,3,1,7]=>[3,2,2,1]=>1680
[8,4,5,6,2,3,1,7]=>[5,3]=>2688
[8,6,5,3,2,4,1,7]=>[5,3]=>2688
[8,6,5,2,3,4,1,7]=>[3,3,2]=>1120
[8,5,6,2,3,4,1,7]=>[5,3]=>2688
[8,6,4,2,3,5,1,7]=>[5,3]=>2688
[8,6,3,2,4,5,1,7]=>[4,3,1]=>3360
[8,5,4,3,2,6,1,7]=>[3,2,2,1]=>1680
[8,4,3,5,2,6,1,7]=>[3,3,1,1]=>1120
[8,5,4,2,3,6,1,7]=>[4,3,1]=>3360
[8,4,5,2,3,6,1,7]=>[3,2,2,1]=>1680
[8,5,3,2,4,6,1,7]=>[3,3,1,1]=>1120
[8,5,2,3,4,6,1,7]=>[4,3,1]=>3360
[8,3,4,2,5,6,1,7]=>[3,3,1,1]=>1120
[8,2,3,4,5,6,1,7]=>[3,1,1,1,1,1]=>112
[8,6,5,4,3,1,2,7]=>[5,2,1]=>4032
[8,6,5,3,4,1,2,7]=>[5,3]=>2688
[8,5,6,3,4,1,2,7]=>[8]=>5040
[8,6,3,4,5,1,2,7]=>[5,1,1,1]=>1344
[8,4,5,3,6,1,2,7]=>[8]=>5040
[8,5,3,4,6,1,2,7]=>[6,1,1]=>3360
[8,4,3,5,6,1,2,7]=>[7,1]=>5760
[8,3,4,5,6,1,2,7]=>[8]=>5040
[8,6,5,4,2,1,3,7]=>[7,1]=>5760
[8,5,6,4,2,1,3,7]=>[5,2,1]=>4032
[8,4,5,6,2,1,3,7]=>[8]=>5040
[8,6,5,4,1,2,3,7]=>[5,2,1]=>4032
[8,5,6,4,1,2,3,7]=>[7,1]=>5760
[8,6,4,5,1,2,3,7]=>[6,2]=>3360
[8,4,5,6,1,2,3,7]=>[5,3]=>2688
[8,6,5,3,2,1,4,7]=>[8]=>5040
[8,5,6,3,2,1,4,7]=>[6,2]=>3360
[8,6,5,2,3,1,4,7]=>[6,2]=>3360
[8,5,6,2,3,1,4,7]=>[8]=>5040
[8,5,6,3,1,2,4,7]=>[8]=>5040
[8,6,5,2,1,3,4,7]=>[8]=>5040
[8,5,6,2,1,3,4,7]=>[6,2]=>3360
[8,6,5,1,2,3,4,7]=>[4,4]=>1260
[8,5,6,1,2,3,4,7]=>[4,2,2]=>1260
[8,6,4,3,2,1,5,7]=>[6,2]=>3360
[8,6,3,4,2,1,5,7]=>[6,1,1]=>3360
[8,6,4,2,3,1,5,7]=>[8]=>5040
[8,6,3,2,4,1,5,7]=>[7,1]=>5760
[8,6,2,3,4,1,5,7]=>[8]=>5040
[8,6,4,3,1,2,5,7]=>[4,2,2]=>1260
[8,6,3,4,1,2,5,7]=>[4,2,1,1]=>2520
[8,6,4,2,1,3,5,7]=>[4,4]=>1260
[8,6,4,1,2,3,5,7]=>[8]=>5040
[8,6,3,2,1,4,5,7]=>[4,3,1]=>3360
[8,6,1,2,3,4,5,7]=>[5,3]=>2688
[8,5,4,3,2,1,6,7]=>[4,2,2]=>1260
[8,4,5,3,2,1,6,7]=>[4,4]=>1260
[8,4,3,5,2,1,6,7]=>[4,3,1]=>3360
[8,3,4,5,2,1,6,7]=>[4,4]=>1260
[8,4,5,2,3,1,6,7]=>[4,2,2]=>1260
[8,5,2,3,4,1,6,7]=>[4,4]=>1260
[8,4,2,3,5,1,6,7]=>[4,3,1]=>3360
[8,2,3,4,5,1,6,7]=>[4,1,1,1,1]=>420
[8,5,3,4,1,2,6,7]=>[6,1,1]=>3360
[8,3,4,5,1,2,6,7]=>[8]=>5040
[8,5,4,2,1,3,6,7]=>[8]=>5040
[8,5,4,1,2,3,6,7]=>[6,2]=>3360
[8,4,5,1,2,3,6,7]=>[8]=>5040
[8,5,3,2,1,4,6,7]=>[7,1]=>5760
[8,5,3,1,2,4,6,7]=>[5,2,1]=>4032
[8,5,2,1,3,4,6,7]=>[5,3]=>2688
[8,5,1,2,3,4,6,7]=>[8]=>5040
[8,4,3,2,1,5,6,7]=>[5,2,1]=>4032
[8,3,4,2,1,5,6,7]=>[5,3]=>2688
[8,4,2,3,1,5,6,7]=>[5,3]=>2688
[8,2,3,4,1,5,6,7]=>[5,1,1,1]=>1344
[8,3,4,1,2,5,6,7]=>[8]=>5040
[8,4,2,1,3,5,6,7]=>[8]=>5040
[8,4,1,2,3,5,6,7]=>[6,2]=>3360
[8,3,2,1,4,5,6,7]=>[6,2]=>3360
[8,2,3,1,4,5,6,7]=>[6,1,1]=>3360
[8,3,1,2,4,5,6,7]=>[8]=>5040
[8,2,1,3,4,5,6,7]=>[7,1]=>5760
[8,1,2,3,4,5,6,7]=>[8]=>5040
[7,6,5,4,3,2,1,8]=>[2,2,2,1,1]=>420
[6,7,5,4,3,2,1,8]=>[4,2,1,1]=>2520
[7,5,6,4,3,2,1,8]=>[4,2,1,1]=>2520
[6,5,7,4,3,2,1,8]=>[6,1,1]=>3360
[5,6,7,4,3,2,1,8]=>[4,2,1,1]=>2520
[7,6,4,5,3,2,1,8]=>[3,2,2,1]=>1680
[7,5,4,6,3,2,1,8]=>[5,2,1]=>4032
[6,5,4,7,3,2,1,8]=>[7,1]=>5760
[5,6,4,7,3,2,1,8]=>[5,2,1]=>4032
[5,4,6,7,3,2,1,8]=>[7,1]=>5760
[4,5,6,7,3,2,1,8]=>[4,3,1]=>3360
[7,6,5,3,4,2,1,8]=>[3,2,2,1]=>1680
[6,7,5,3,4,2,1,8]=>[4,3,1]=>3360
[7,5,6,3,4,2,1,8]=>[5,2,1]=>4032
[6,5,7,3,4,2,1,8]=>[7,1]=>5760
[5,6,7,3,4,2,1,8]=>[5,2,1]=>4032
[7,6,4,3,5,2,1,8]=>[2,2,2,1,1]=>420
[6,7,4,3,5,2,1,8]=>[4,2,1,1]=>2520
[7,6,3,4,5,2,1,8]=>[2,2,1,1,1,1]=>210
[7,5,4,3,6,2,1,8]=>[3,2,2,1]=>1680
[7,3,4,5,6,2,1,8]=>[5,2,1]=>4032
[6,5,4,3,7,2,1,8]=>[5,2,1]=>4032
[5,6,4,3,7,2,1,8]=>[3,2,2,1]=>1680
[5,4,6,3,7,2,1,8]=>[4,3,1]=>3360
[5,4,3,6,7,2,1,8]=>[3,3,1,1]=>1120
[3,4,5,6,7,2,1,8]=>[4,3,1]=>3360
[7,6,5,4,2,3,1,8]=>[4,2,1,1]=>2520
[6,7,5,4,2,3,1,8]=>[6,1,1]=>3360
[7,5,6,4,2,3,1,8]=>[2,2,2,1,1]=>420
[5,6,7,4,2,3,1,8]=>[6,1,1]=>3360
[7,6,4,5,2,3,1,8]=>[5,2,1]=>4032
[6,7,4,5,2,3,1,8]=>[7,1]=>5760
[7,5,4,6,2,3,1,8]=>[3,2,2,1]=>1680
[6,5,4,7,2,3,1,8]=>[5,2,1]=>4032
[5,6,4,7,2,3,1,8]=>[7,1]=>5760
[5,4,6,7,2,3,1,8]=>[5,2,1]=>4032
[4,5,6,7,2,3,1,8]=>[3,2,2,1]=>1680
[7,6,5,3,2,4,1,8]=>[5,2,1]=>4032
[6,5,7,3,2,4,1,8]=>[5,2,1]=>4032
[5,6,7,3,2,4,1,8]=>[7,1]=>5760
[7,6,5,2,3,4,1,8]=>[3,2,2,1]=>1680
[6,7,5,2,3,4,1,8]=>[5,2,1]=>4032
[7,5,6,2,3,4,1,8]=>[5,2,1]=>4032
[6,5,7,2,3,4,1,8]=>[7,1]=>5760
[5,6,7,2,3,4,1,8]=>[4,3,1]=>3360
[7,6,4,3,2,5,1,8]=>[3,2,2,1]=>1680
[6,7,4,3,2,5,1,8]=>[5,2,1]=>4032
[6,7,3,4,2,5,1,8]=>[5,1,1,1]=>1344
[7,6,4,2,3,5,1,8]=>[5,2,1]=>4032
[6,7,4,2,3,5,1,8]=>[7,1]=>5760
[7,6,3,2,4,5,1,8]=>[4,2,1,1]=>2520
[6,7,3,2,4,5,1,8]=>[6,1,1]=>3360
[7,6,2,3,4,5,1,8]=>[5,2,1]=>4032
[6,7,2,3,4,5,1,8]=>[7,1]=>5760
[7,5,4,3,2,6,1,8]=>[2,2,2,1,1]=>420
[7,4,5,3,2,6,1,8]=>[4,2,1,1]=>2520
[7,5,3,4,2,6,1,8]=>[2,2,1,1,1,1]=>210
[7,4,3,5,2,6,1,8]=>[3,2,1,1,1]=>1120
[7,4,5,2,3,6,1,8]=>[2,2,2,1,1]=>420
[7,5,3,2,4,6,1,8]=>[3,2,1,1,1]=>1120
[7,4,2,3,5,6,1,8]=>[3,2,1,1,1]=>1120
[7,2,3,4,5,6,1,8]=>[2,1,1,1,1,1,1]=>28
[6,5,4,3,2,7,1,8]=>[3,2,2,1]=>1680
[5,6,4,3,2,7,1,8]=>[5,2,1]=>4032
[5,4,6,3,2,7,1,8]=>[7,1]=>5760
[5,6,3,4,2,7,1,8]=>[5,1,1,1]=>1344
[6,3,4,5,2,7,1,8]=>[4,3,1]=>3360
[5,4,3,6,2,7,1,8]=>[6,1,1]=>3360
[4,5,3,6,2,7,1,8]=>[4,2,1,1]=>2520
[5,3,4,6,2,7,1,8]=>[7,1]=>5760
[4,3,5,6,2,7,1,8]=>[4,3,1]=>3360
[3,4,5,6,2,7,1,8]=>[7,1]=>5760
[5,4,6,2,3,7,1,8]=>[5,2,1]=>4032
[6,5,3,2,4,7,1,8]=>[3,3,1,1]=>1120
[6,4,2,3,5,7,1,8]=>[3,3,1,1]=>1120
[6,3,2,4,5,7,1,8]=>[3,2,1,1,1]=>1120
[6,2,3,4,5,7,1,8]=>[3,1,1,1,1,1]=>112
[5,4,3,2,6,7,1,8]=>[4,2,1,1]=>2520
[3,4,5,2,6,7,1,8]=>[5,2,1]=>4032
[5,4,2,3,6,7,1,8]=>[4,3,1]=>3360
[4,5,2,3,6,7,1,8]=>[7,1]=>5760
[5,2,3,4,6,7,1,8]=>[4,1,1,1,1]=>420
[4,3,2,5,6,7,1,8]=>[5,2,1]=>4032
[3,4,2,5,6,7,1,8]=>[7,1]=>5760
[4,2,3,5,6,7,1,8]=>[5,1,1,1]=>1344
[3,2,4,5,6,7,1,8]=>[6,1,1]=>3360
[2,3,4,5,6,7,1,8]=>[7,1]=>5760
[7,6,5,4,3,1,2,8]=>[4,2,1,1]=>2520
[5,4,6,7,3,1,2,8]=>[4,3,1]=>3360
[4,5,6,7,3,1,2,8]=>[7,1]=>5760
[7,6,5,3,4,1,2,8]=>[4,3,1]=>3360
[6,5,7,3,4,1,2,8]=>[5,2,1]=>4032
[6,7,3,4,5,1,2,8]=>[2,2,1,1,1,1]=>210
[6,5,4,3,7,1,2,8]=>[3,2,2,1]=>1680
[6,4,5,3,7,1,2,8]=>[5,2,1]=>4032
[4,3,5,6,7,1,2,8]=>[4,3,1]=>3360
[3,4,5,6,7,1,2,8]=>[7,1]=>5760
[7,6,5,4,2,1,3,8]=>[6,1,1]=>3360
[6,5,7,4,2,1,3,8]=>[2,2,2,1,1]=>420
[7,6,4,5,2,1,3,8]=>[7,1]=>5760
[5,4,6,7,2,1,3,8]=>[7,1]=>5760
[4,5,6,7,2,1,3,8]=>[5,2,1]=>4032
[7,6,5,4,1,2,3,8]=>[4,2,1,1]=>2520
[5,6,7,4,1,2,3,8]=>[2,2,2,1,1]=>420
[5,6,4,7,1,2,3,8]=>[3,2,2,1]=>1680
[5,4,6,7,1,2,3,8]=>[5,2,1]=>4032
[4,5,6,7,1,2,3,8]=>[7,1]=>5760
[7,6,5,3,2,1,4,8]=>[7,1]=>5760
[7,6,5,2,3,1,4,8]=>[5,2,1]=>4032
[6,7,5,2,3,1,4,8]=>[3,2,2,1]=>1680
[7,5,6,2,3,1,4,8]=>[7,1]=>5760
[6,5,7,2,3,1,4,8]=>[5,2,1]=>4032
[5,6,7,2,3,1,4,8]=>[7,1]=>5760
[5,6,7,3,1,2,4,8]=>[3,2,2,1]=>1680
[7,6,5,2,1,3,4,8]=>[7,1]=>5760
[6,7,5,2,1,3,4,8]=>[4,3,1]=>3360
[7,5,6,2,1,3,4,8]=>[5,2,1]=>4032
[5,6,7,2,1,3,4,8]=>[5,2,1]=>4032
[7,6,5,1,2,3,4,8]=>[4,3,1]=>3360
[6,5,7,1,2,3,4,8]=>[5,2,1]=>4032
[5,6,7,1,2,3,4,8]=>[7,1]=>5760
[6,7,4,3,2,1,5,8]=>[3,2,2,1]=>1680
[6,7,3,4,2,1,5,8]=>[3,2,1,1,1]=>1120
[7,6,4,2,3,1,5,8]=>[7,1]=>5760
[7,6,3,2,4,1,5,8]=>[6,1,1]=>3360
[6,7,3,2,4,1,5,8]=>[4,2,1,1]=>2520
[7,6,2,3,4,1,5,8]=>[7,1]=>5760
[6,7,2,3,4,1,5,8]=>[5,2,1]=>4032
[7,6,4,3,1,2,5,8]=>[3,2,2,1]=>1680
[6,7,3,4,1,2,5,8]=>[5,1,1,1]=>1344
[7,6,4,2,1,3,5,8]=>[4,3,1]=>3360
[7,6,3,2,1,4,5,8]=>[3,3,1,1]=>1120
[6,7,3,2,1,4,5,8]=>[6,1,1]=>3360
[7,6,2,3,1,4,5,8]=>[4,3,1]=>3360
[6,7,2,3,1,4,5,8]=>[7,1]=>5760
[6,7,3,1,2,4,5,8]=>[3,3,1,1]=>1120
[7,6,1,2,3,4,5,8]=>[4,3,1]=>3360
[6,7,1,2,3,4,5,8]=>[7,1]=>5760
[7,5,4,3,2,1,6,8]=>[3,2,2,1]=>1680
[7,5,4,2,3,1,6,8]=>[4,3,1]=>3360
[7,5,3,2,4,1,6,8]=>[3,3,1,1]=>1120
[7,5,2,3,4,1,6,8]=>[4,3,1]=>3360
[7,4,2,3,5,1,6,8]=>[3,3,1,1]=>1120
[7,2,3,4,5,1,6,8]=>[3,1,1,1,1,1]=>112
[7,5,4,3,1,2,6,8]=>[5,2,1]=>4032
[7,4,5,2,1,3,6,8]=>[5,2,1]=>4032
[7,4,5,1,2,3,6,8]=>[7,1]=>5760
[7,5,3,2,1,4,6,8]=>[6,1,1]=>3360
[7,5,2,3,1,4,6,8]=>[7,1]=>5760
[7,5,3,1,2,4,6,8]=>[4,2,1,1]=>2520
[7,5,1,2,3,4,6,8]=>[7,1]=>5760
[7,4,3,2,1,5,6,8]=>[4,2,1,1]=>2520
[7,2,3,4,1,5,6,8]=>[4,1,1,1,1]=>420
[7,4,3,1,2,5,6,8]=>[6,1,1]=>3360
[7,3,4,1,2,5,6,8]=>[7,1]=>5760
[7,4,1,2,3,5,6,8]=>[5,2,1]=>4032
[7,3,2,1,4,5,6,8]=>[5,2,1]=>4032
[7,2,3,1,4,5,6,8]=>[5,1,1,1]=>1344
[7,3,1,2,4,5,6,8]=>[7,1]=>5760
[7,2,1,3,4,5,6,8]=>[6,1,1]=>3360
[7,1,2,3,4,5,6,8]=>[7,1]=>5760
[6,5,4,3,2,1,7,8]=>[2,2,2,1,1]=>420
[5,6,4,3,2,1,7,8]=>[4,2,1,1]=>2520
[5,4,6,3,2,1,7,8]=>[6,1,1]=>3360
[4,5,6,3,2,1,7,8]=>[4,2,1,1]=>2520
[6,5,3,4,2,1,7,8]=>[2,2,1,1,1,1]=>210
[5,6,3,4,2,1,7,8]=>[4,1,1,1,1]=>420
[5,4,3,6,2,1,7,8]=>[5,1,1,1]=>1344
[3,4,5,6,2,1,7,8]=>[6,1,1]=>3360
[5,4,6,2,3,1,7,8]=>[4,2,1,1]=>2520
[5,6,3,2,4,1,7,8]=>[5,1,1,1]=>1344
[6,5,2,3,4,1,7,8]=>[4,2,1,1]=>2520
[5,6,2,3,4,1,7,8]=>[6,1,1]=>3360
[6,4,3,2,5,1,7,8]=>[2,2,1,1,1,1]=>210
[6,2,3,4,5,1,7,8]=>[2,1,1,1,1,1,1]=>28
[5,4,3,2,6,1,7,8]=>[3,2,1,1,1]=>1120
[4,5,3,2,6,1,7,8]=>[5,1,1,1]=>1344
[4,3,5,2,6,1,7,8]=>[6,1,1]=>3360
[3,4,5,2,6,1,7,8]=>[4,2,1,1]=>2520
[5,3,2,4,6,1,7,8]=>[3,2,1,1,1]=>1120
[5,2,3,4,6,1,7,8]=>[3,1,1,1,1,1]=>112
[4,3,2,5,6,1,7,8]=>[4,2,1,1]=>2520
[3,4,2,5,6,1,7,8]=>[6,1,1]=>3360
[4,2,3,5,6,1,7,8]=>[4,1,1,1,1]=>420
[3,2,4,5,6,1,7,8]=>[5,1,1,1]=>1344
[2,3,4,5,6,1,7,8]=>[6,1,1]=>3360
[6,5,4,3,1,2,7,8]=>[4,2,1,1]=>2520
[5,6,4,3,1,2,7,8]=>[2,2,2,1,1]=>420
[6,4,5,3,1,2,7,8]=>[6,1,1]=>3360
[5,4,6,3,1,2,7,8]=>[4,2,1,1]=>2520
[5,6,3,4,1,2,7,8]=>[2,2,1,1,1,1]=>210
[6,4,3,5,1,2,7,8]=>[5,1,1,1]=>1344
[5,4,3,6,1,2,7,8]=>[3,2,1,1,1]=>1120
[4,3,5,6,1,2,7,8]=>[6,1,1]=>3360
[3,4,5,6,1,2,7,8]=>[3,3,1,1]=>1120
[5,6,4,2,1,3,7,8]=>[4,2,1,1]=>2520
[6,4,5,2,1,3,7,8]=>[4,2,1,1]=>2520
[5,4,6,2,1,3,7,8]=>[2,2,2,1,1]=>420
[6,5,4,1,2,3,7,8]=>[4,2,1,1]=>2520
[4,5,6,1,2,3,7,8]=>[2,2,2,1,1]=>420
[6,5,3,2,1,4,7,8]=>[5,1,1,1]=>1344
[5,6,3,2,1,4,7,8]=>[3,2,1,1,1]=>1120
[5,6,2,1,3,4,7,8]=>[6,1,1]=>3360
[6,4,3,2,1,5,7,8]=>[3,2,1,1,1]=>1120
[6,4,3,1,2,5,7,8]=>[5,1,1,1]=>1344
[6,4,1,2,3,5,7,8]=>[4,2,1,1]=>2520
[6,2,3,1,4,5,7,8]=>[4,1,1,1,1]=>420
[6,3,1,2,4,5,7,8]=>[6,1,1]=>3360
[6,1,2,3,4,5,7,8]=>[6,1,1]=>3360
[5,4,3,2,1,6,7,8]=>[2,2,1,1,1,1]=>210
[4,5,3,2,1,6,7,8]=>[4,1,1,1,1]=>420
[5,3,4,2,1,6,7,8]=>[3,2,1,1,1]=>1120
[4,3,5,2,1,6,7,8]=>[5,1,1,1]=>1344
[3,4,5,2,1,6,7,8]=>[3,2,1,1,1]=>1120
[5,4,2,3,1,6,7,8]=>[3,2,1,1,1]=>1120
[4,5,2,3,1,6,7,8]=>[5,1,1,1]=>1344
[5,3,2,4,1,6,7,8]=>[2,2,1,1,1,1]=>210
[5,2,3,4,1,6,7,8]=>[2,1,1,1,1,1,1]=>28
[4,3,2,5,1,6,7,8]=>[3,2,1,1,1]=>1120
[3,4,2,5,1,6,7,8]=>[5,1,1,1]=>1344
[4,2,3,5,1,6,7,8]=>[3,1,1,1,1,1]=>112
[3,2,4,5,1,6,7,8]=>[4,1,1,1,1]=>420
[2,3,4,5,1,6,7,8]=>[5,1,1,1]=>1344
[5,4,3,1,2,6,7,8]=>[4,1,1,1,1]=>420
[5,3,4,1,2,6,7,8]=>[5,1,1,1]=>1344
[4,3,5,1,2,6,7,8]=>[3,2,1,1,1]=>1120
[3,4,5,1,2,6,7,8]=>[5,1,1,1]=>1344
[5,4,2,1,3,6,7,8]=>[5,1,1,1]=>1344
[4,5,2,1,3,6,7,8]=>[3,2,1,1,1]=>1120
[5,4,1,2,3,6,7,8]=>[3,2,1,1,1]=>1120
[4,5,1,2,3,6,7,8]=>[5,1,1,1]=>1344
[5,3,2,1,4,6,7,8]=>[3,2,1,1,1]=>1120
[5,2,3,1,4,6,7,8]=>[3,1,1,1,1,1]=>112
[5,3,1,2,4,6,7,8]=>[5,1,1,1]=>1344
[5,2,1,3,4,6,7,8]=>[4,1,1,1,1]=>420
[5,1,2,3,4,6,7,8]=>[5,1,1,1]=>1344
[4,3,2,1,5,6,7,8]=>[2,2,1,1,1,1]=>210
[3,4,2,1,5,6,7,8]=>[4,1,1,1,1]=>420
[4,2,3,1,5,6,7,8]=>[2,1,1,1,1,1,1]=>28
[3,2,4,1,5,6,7,8]=>[3,1,1,1,1,1]=>112
[2,3,4,1,5,6,7,8]=>[4,1,1,1,1]=>420
[4,3,1,2,5,6,7,8]=>[4,1,1,1,1]=>420
[3,4,1,2,5,6,7,8]=>[2,2,1,1,1,1]=>210
[4,2,1,3,5,6,7,8]=>[3,1,1,1,1,1]=>112
[4,1,2,3,5,6,7,8]=>[4,1,1,1,1]=>420
[3,2,1,4,5,6,7,8]=>[2,1,1,1,1,1,1]=>28
[2,3,1,4,5,6,7,8]=>[3,1,1,1,1,1]=>112
[3,1,2,4,5,6,7,8]=>[3,1,1,1,1,1]=>112
[2,1,3,4,5,6,7,8]=>[2,1,1,1,1,1,1]=>28
[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1]=>1
[6,8,7,5,4,3,2,1]=>[6,2]=>3360
[5,8,7,6,4,3,2,1]=>[8]=>5040
[5,7,8,6,4,3,2,1]=>[6,2]=>3360
[6,5,8,7,4,3,2,1]=>[4,4]=>1260
[5,6,8,7,4,3,2,1]=>[8]=>5040
[5,7,6,8,4,3,2,1]=>[4,2,2]=>1260
[4,8,7,6,5,3,2,1]=>[7,1]=>5760
[4,7,8,6,5,3,2,1]=>[5,2,1]=>4032
[4,6,8,7,5,3,2,1]=>[7,1]=>5760
[5,4,7,8,6,3,2,1]=>[8]=>5040
[4,5,8,7,6,3,2,1]=>[8]=>5040
[5,6,4,8,7,3,2,1]=>[8]=>5040
[4,6,5,8,7,3,2,1]=>[5,3]=>2688
[4,5,6,8,7,3,2,1]=>[3,3,2]=>1120
[5,7,6,4,8,3,2,1]=>[3,2,2,1]=>1680
[4,7,6,5,8,3,2,1]=>[4,2,2]=>1260
[4,6,7,5,8,3,2,1]=>[4,4]=>1260
[5,4,7,6,8,3,2,1]=>[5,3]=>2688
[4,5,7,6,8,3,2,1]=>[8]=>5040
[4,6,5,7,8,3,2,1]=>[8]=>5040
[3,8,7,6,5,4,2,1]=>[5,2,1]=>4032
[3,7,8,6,5,4,2,1]=>[3,2,2,1]=>1680
[3,6,8,7,5,4,2,1]=>[4,3,1]=>3360
[3,7,6,8,5,4,2,1]=>[5,2,1]=>4032
[3,5,8,7,6,4,2,1]=>[5,3]=>2688
[3,5,7,8,6,4,2,1]=>[8]=>5040
[3,5,6,8,7,4,2,1]=>[5,3]=>2688
[3,7,6,5,8,4,2,1]=>[6,2]=>3360
[3,5,6,7,8,4,2,1]=>[8]=>5040
[4,3,8,7,6,5,2,1]=>[6,2]=>3360
[4,3,7,8,6,5,2,1]=>[3,3,2]=>1120
[4,3,6,7,8,5,2,1]=>[8]=>5040
[3,4,8,7,6,5,2,1]=>[3,3,2]=>1120
[3,4,6,7,8,5,2,1]=>[5,3]=>2688
[5,4,3,8,7,6,2,1]=>[6,1,1]=>3360
[5,4,3,7,8,6,2,1]=>[3,3,1,1]=>1120
[3,4,5,8,7,6,2,1]=>[7,1]=>5760
[6,5,4,3,8,7,2,1]=>[6,2]=>3360
[5,6,4,3,8,7,2,1]=>[3,3,2]=>1120
[4,5,6,3,8,7,2,1]=>[8]=>5040
[3,6,5,4,8,7,2,1]=>[4,3,1]=>3360
[4,3,6,5,8,7,2,1]=>[4,4]=>1260
[5,4,3,6,8,7,2,1]=>[4,3,1]=>3360
[4,5,3,6,8,7,2,1]=>[7,1]=>5760
[3,4,5,6,8,7,2,1]=>[4,4]=>1260
[5,7,6,4,3,8,2,1]=>[5,2,1]=>4032
[4,7,6,5,3,8,2,1]=>[6,2]=>3360
[5,4,7,6,3,8,2,1]=>[8]=>5040
[3,7,6,5,4,8,2,1]=>[4,2,2]=>1260
[3,5,7,6,4,8,2,1]=>[8]=>5040
[4,3,7,6,5,8,2,1]=>[4,3,1]=>3360
[3,4,7,6,5,8,2,1]=>[7,1]=>5760
[3,4,6,7,5,8,2,1]=>[4,3,1]=>3360
[4,5,3,7,6,8,2,1]=>[7,1]=>5760
[4,3,5,7,6,8,2,1]=>[8]=>5040
[3,6,5,4,7,8,2,1]=>[7,1]=>5760
[4,3,6,5,7,8,2,1]=>[8]=>5040
[3,4,6,5,7,8,2,1]=>[4,4]=>1260
[2,8,7,6,5,4,3,1]=>[3,2,2,1]=>1680
[2,7,8,6,5,4,3,1]=>[5,2,1]=>4032
[2,6,8,7,5,4,3,1]=>[7,1]=>5760
[2,7,6,8,5,4,3,1]=>[7,1]=>5760
[2,6,7,8,5,4,3,1]=>[5,2,1]=>4032
[2,5,8,7,6,4,3,1]=>[8]=>5040
[2,6,7,5,8,4,3,1]=>[6,2]=>3360
[2,5,6,7,8,4,3,1]=>[4,4]=>1260
[2,4,8,7,6,5,3,1]=>[6,2]=>3360
[2,4,7,8,6,5,3,1]=>[4,2,2]=>1260
[2,4,6,8,7,5,3,1]=>[4,4]=>1260
[2,4,6,7,8,5,3,1]=>[8]=>5040
[2,5,4,8,7,6,3,1]=>[7,1]=>5760
[2,5,4,7,8,6,3,1]=>[4,3,1]=>3360
[2,4,5,7,8,6,3,1]=>[7,1]=>5760
[2,6,5,4,8,7,3,1]=>[7,1]=>5760
[2,5,6,4,8,7,3,1]=>[4,3,1]=>3360
[2,4,6,5,8,7,3,1]=>[5,3]=>2688
[2,4,5,6,8,7,3,1]=>[8]=>5040
[2,7,6,5,4,8,3,1]=>[6,2]=>3360
[2,5,6,7,4,8,3,1]=>[8]=>5040
[2,4,7,6,5,8,3,1]=>[5,2,1]=>4032
[2,4,6,7,5,8,3,1]=>[7,1]=>5760
[2,5,4,7,6,8,3,1]=>[5,3]=>2688
[2,5,6,4,7,8,3,1]=>[7,1]=>5760
[2,4,6,5,7,8,3,1]=>[8]=>5040
[2,5,4,6,7,8,3,1]=>[8]=>5040
[2,4,5,6,7,8,3,1]=>[5,3]=>2688
[3,2,8,7,6,5,4,1]=>[3,2,2,1]=>1680
[3,2,7,8,6,5,4,1]=>[5,2,1]=>4032
[3,2,6,8,7,5,4,1]=>[7,1]=>5760
[3,2,5,7,6,8,4,1]=>[5,2,1]=>4032
[3,2,5,6,7,8,4,1]=>[7,1]=>5760
[2,3,8,7,6,5,4,1]=>[4,2,2]=>1260
[2,3,6,7,8,5,4,1]=>[6,2]=>3360
[2,3,5,8,7,6,4,1]=>[7,1]=>5760
[2,3,5,7,8,6,4,1]=>[5,2,1]=>4032
[2,3,6,5,8,7,4,1]=>[8]=>5040
[2,3,5,6,8,7,4,1]=>[5,3]=>2688
[2,3,7,6,5,8,4,1]=>[7,1]=>5760
[2,3,5,6,7,8,4,1]=>[8]=>5040
[4,3,2,8,7,6,5,1]=>[3,2,2,1]=>1680
[4,3,2,7,8,6,5,1]=>[5,2,1]=>4032
[3,4,2,7,8,6,5,1]=>[7,1]=>5760
[2,4,3,6,8,7,5,1]=>[7,1]=>5760
[2,4,3,6,7,8,5,1]=>[5,2,1]=>4032
[3,2,4,8,7,6,5,1]=>[4,2,1,1]=>2520
[2,3,4,8,7,6,5,1]=>[5,2,1]=>4032
[2,3,4,7,8,6,5,1]=>[7,1]=>5760
[2,3,4,6,8,7,5,1]=>[8]=>5040
[2,3,4,7,6,8,5,1]=>[8]=>5040
[2,3,4,6,7,8,5,1]=>[6,2]=>3360
[5,4,3,2,8,7,6,1]=>[3,2,2,1]=>1680
[5,4,3,2,7,8,6,1]=>[5,2,1]=>4032
[3,4,5,2,7,8,6,1]=>[6,2]=>3360
[2,5,4,3,8,7,6,1]=>[4,2,2]=>1260
[2,5,4,3,7,8,6,1]=>[6,2]=>3360
[2,4,5,3,8,7,6,1]=>[6,2]=>3360
[2,4,5,3,7,8,6,1]=>[8]=>5040
[2,3,5,4,8,7,6,1]=>[5,2,1]=>4032
[4,3,2,5,8,7,6,1]=>[4,2,2]=>1260
[4,3,2,5,7,8,6,1]=>[6,2]=>3360
[3,4,2,5,8,7,6,1]=>[6,2]=>3360
[3,4,2,5,7,8,6,1]=>[8]=>5040
[3,2,4,5,7,8,6,1]=>[7,1]=>5760
[2,3,4,5,8,7,6,1]=>[6,2]=>3360
[2,3,4,5,7,8,6,1]=>[8]=>5040
[6,5,4,3,2,8,7,1]=>[3,2,2,1]=>1680
[4,6,5,3,2,8,7,1]=>[7,1]=>5760
[5,4,6,3,2,8,7,1]=>[7,1]=>5760
[4,5,6,3,2,8,7,1]=>[5,2,1]=>4032
[3,6,5,4,2,8,7,1]=>[6,1,1]=>3360
[3,5,6,4,2,8,7,1]=>[4,2,1,1]=>2520
[4,3,6,5,2,8,7,1]=>[7,1]=>5760
[5,4,3,6,2,8,7,1]=>[6,1,1]=>3360
[4,5,3,6,2,8,7,1]=>[4,2,1,1]=>2520
[3,4,5,6,2,8,7,1]=>[7,1]=>5760
[2,6,5,4,3,8,7,1]=>[4,2,1,1]=>2520
[2,4,6,5,3,8,7,1]=>[7,1]=>5760
[2,4,5,6,3,8,7,1]=>[5,2,1]=>4032
[3,2,6,5,4,8,7,1]=>[4,2,1,1]=>2520
[2,3,5,6,4,8,7,1]=>[7,1]=>5760
[4,3,2,6,5,8,7,1]=>[4,2,1,1]=>2520
[3,4,2,6,5,8,7,1]=>[6,1,1]=>3360
[2,4,3,6,5,8,7,1]=>[5,1,1,1]=>1344
[3,2,4,6,5,8,7,1]=>[5,1,1,1]=>1344
[2,3,4,6,5,8,7,1]=>[6,1,1]=>3360
[5,4,3,2,6,8,7,1]=>[4,2,1,1]=>2520
[2,4,5,3,6,8,7,1]=>[7,1]=>5760
[3,2,5,4,6,8,7,1]=>[5,1,1,1]=>1344
[4,3,2,5,6,8,7,1]=>[5,2,1]=>4032
[3,4,2,5,6,8,7,1]=>[7,1]=>5760
[2,4,3,5,6,8,7,1]=>[6,1,1]=>3360
[3,2,4,5,6,8,7,1]=>[6,1,1]=>3360
[2,3,4,5,6,8,7,1]=>[7,1]=>5760
[5,7,6,4,3,2,8,1]=>[7,1]=>5760
[4,7,6,5,3,2,8,1]=>[8]=>5040
[4,6,7,5,3,2,8,1]=>[6,2]=>3360
[4,6,5,7,3,2,8,1]=>[4,2,2]=>1260
[3,5,7,6,4,2,8,1]=>[4,4]=>1260
[3,5,6,7,4,2,8,1]=>[8]=>5040
[4,3,7,6,5,2,8,1]=>[7,1]=>5760
[4,3,6,7,5,2,8,1]=>[4,3,1]=>3360
[3,4,7,6,5,2,8,1]=>[4,3,1]=>3360
[5,4,3,7,6,2,8,1]=>[7,1]=>5760
[3,5,4,7,6,2,8,1]=>[5,3]=>2688
[3,4,5,7,6,2,8,1]=>[8]=>5040
[4,6,5,3,7,2,8,1]=>[6,2]=>3360
[3,6,5,4,7,2,8,1]=>[5,2,1]=>4032
[3,5,6,4,7,2,8,1]=>[7,1]=>5760
[4,3,6,5,7,2,8,1]=>[5,3]=>2688
[3,4,6,5,7,2,8,1]=>[8]=>5040
[3,5,4,6,7,2,8,1]=>[8]=>5040
[2,7,6,5,4,3,8,1]=>[4,2,2]=>1260
[2,6,5,7,4,3,8,1]=>[8]=>5040
[2,4,6,7,5,3,8,1]=>[5,2,1]=>4032
[2,5,4,7,6,3,8,1]=>[8]=>5040
[2,4,6,5,7,3,8,1]=>[6,2]=>3360
[2,5,4,6,7,3,8,1]=>[5,3]=>2688
[2,4,5,6,7,3,8,1]=>[8]=>5040
[3,2,7,6,5,4,8,1]=>[4,2,1,1]=>2520
[3,2,6,7,5,4,8,1]=>[6,1,1]=>3360
[3,2,6,5,7,4,8,1]=>[7,1]=>5760
[2,3,7,6,5,4,8,1]=>[5,2,1]=>4032
[2,3,5,7,6,4,8,1]=>[8]=>5040
[2,3,5,6,7,4,8,1]=>[6,2]=>3360
[3,4,2,6,7,5,8,1]=>[8]=>5040
[2,4,3,6,7,5,8,1]=>[7,1]=>5760
[2,3,4,7,6,5,8,1]=>[6,2]=>3360
[2,3,4,6,7,5,8,1]=>[8]=>5040
[5,4,3,2,7,6,8,1]=>[4,2,1,1]=>2520
[4,3,5,2,7,6,8,1]=>[7,1]=>5760
[3,2,5,4,7,6,8,1]=>[5,1,1,1]=>1344
[2,3,5,4,7,6,8,1]=>[6,1,1]=>3360
[4,3,2,5,7,6,8,1]=>[5,2,1]=>4032
[2,4,3,5,7,6,8,1]=>[6,1,1]=>3360
[3,2,4,5,7,6,8,1]=>[6,1,1]=>3360
[2,3,4,5,7,6,8,1]=>[7,1]=>5760
[3,6,5,4,2,7,8,1]=>[7,1]=>5760
[3,4,6,5,2,7,8,1]=>[5,3]=>2688
[2,6,5,4,3,7,8,1]=>[5,2,1]=>4032
[2,5,6,4,3,7,8,1]=>[7,1]=>5760
[2,4,6,5,3,7,8,1]=>[8]=>5040
[2,4,5,6,3,7,8,1]=>[6,2]=>3360
[2,3,6,5,4,7,8,1]=>[6,2]=>3360
[2,3,5,6,4,7,8,1]=>[8]=>5040
[4,3,2,6,5,7,8,1]=>[5,2,1]=>4032
[3,4,2,6,5,7,8,1]=>[7,1]=>5760
[2,4,3,6,5,7,8,1]=>[6,1,1]=>3360
[2,3,4,6,5,7,8,1]=>[7,1]=>5760
[3,5,4,2,6,7,8,1]=>[8]=>5040
[2,4,5,3,6,7,8,1]=>[8]=>5040
[3,2,5,4,6,7,8,1]=>[6,1,1]=>3360
[2,3,5,4,6,7,8,1]=>[7,1]=>5760
[2,4,3,5,6,7,8,1]=>[7,1]=>5760
[1,8,7,6,5,4,3,2]=>[2,2,2,1,1]=>420
[1,7,8,6,5,4,3,2]=>[4,2,1,1]=>2520
[1,6,8,7,5,4,3,2]=>[6,1,1]=>3360
[1,7,6,8,5,4,3,2]=>[6,1,1]=>3360
[1,6,7,8,5,4,3,2]=>[4,2,1,1]=>2520
[1,5,8,7,6,4,3,2]=>[7,1]=>5760
[1,6,5,8,7,4,3,2]=>[4,3,1]=>3360
[1,7,6,5,8,4,3,2]=>[7,1]=>5760
[1,6,7,5,8,4,3,2]=>[5,2,1]=>4032
[1,5,7,6,8,4,3,2]=>[3,2,2,1]=>1680
[1,6,5,7,8,4,3,2]=>[7,1]=>5760
[1,5,6,7,8,4,3,2]=>[4,3,1]=>3360
[1,4,8,7,6,5,3,2]=>[5,2,1]=>4032
[1,4,7,8,6,5,3,2]=>[3,2,2,1]=>1680
[1,4,6,8,7,5,3,2]=>[4,3,1]=>3360
[1,4,6,7,8,5,3,2]=>[7,1]=>5760
[1,5,4,7,8,6,3,2]=>[3,3,1,1]=>1120
[1,7,6,5,4,8,3,2]=>[5,2,1]=>4032
[1,4,7,6,5,8,3,2]=>[4,2,1,1]=>2520
[1,4,6,7,5,8,3,2]=>[6,1,1]=>3360
[1,6,5,4,7,8,3,2]=>[3,3,1,1]=>1120
[1,5,6,4,7,8,3,2]=>[6,1,1]=>3360
[1,5,4,6,7,8,3,2]=>[7,1]=>5760
[1,4,5,6,7,8,3,2]=>[4,3,1]=>3360
[1,3,8,7,6,5,4,2]=>[3,2,2,1]=>1680
[1,3,7,8,6,5,4,2]=>[5,2,1]=>4032
[1,3,6,8,7,5,4,2]=>[7,1]=>5760
[1,3,6,7,8,5,4,2]=>[5,2,1]=>4032
[1,3,5,8,7,6,4,2]=>[6,1,1]=>3360
[1,3,5,7,8,6,4,2]=>[4,2,1,1]=>2520
[1,3,5,6,8,7,4,2]=>[4,3,1]=>3360
[1,3,6,7,5,8,4,2]=>[4,2,1,1]=>2520
[1,3,6,5,7,8,4,2]=>[4,3,1]=>3360
[1,3,5,6,7,8,4,2]=>[7,1]=>5760
[1,4,3,8,7,6,5,2]=>[3,2,1,1,1]=>1120
[1,4,3,7,8,6,5,2]=>[5,1,1,1]=>1344
[1,3,4,8,7,6,5,2]=>[4,2,1,1]=>2520
[1,3,4,7,6,8,5,2]=>[7,1]=>5760
[1,3,4,6,7,8,5,2]=>[5,2,1]=>4032
[1,5,4,3,8,7,6,2]=>[3,2,2,1]=>1680
[1,4,5,3,8,7,6,2]=>[5,2,1]=>4032
[1,4,5,3,7,8,6,2]=>[7,1]=>5760
[1,4,3,5,8,7,6,2]=>[4,2,1,1]=>2520
[1,4,3,5,7,8,6,2]=>[6,1,1]=>3360
[1,3,4,5,8,7,6,2]=>[5,2,1]=>4032
[1,3,4,5,7,8,6,2]=>[7,1]=>5760
[1,6,5,4,3,8,7,2]=>[3,2,1,1,1]=>1120
[1,5,6,4,3,8,7,2]=>[5,1,1,1]=>1344
[1,3,6,5,4,8,7,2]=>[4,2,1,1]=>2520
[1,4,3,6,5,8,7,2]=>[4,1,1,1,1]=>420
[1,4,5,3,6,8,7,2]=>[6,1,1]=>3360
[1,3,4,5,6,8,7,2]=>[6,1,1]=>3360
[1,7,6,5,4,3,8,2]=>[3,2,2,1]=>1680
[1,6,7,5,4,3,8,2]=>[5,2,1]=>4032
[1,6,5,7,4,3,8,2]=>[7,1]=>5760
[1,5,6,7,4,3,8,2]=>[5,2,1]=>4032
[1,4,6,7,5,3,8,2]=>[4,2,1,1]=>2520
[1,5,6,4,7,3,8,2]=>[4,2,1,1]=>2520
[1,4,6,5,7,3,8,2]=>[5,2,1]=>4032
[1,5,4,6,7,3,8,2]=>[4,3,1]=>3360
[1,4,5,6,7,3,8,2]=>[7,1]=>5760
[1,3,5,6,7,4,8,2]=>[5,2,1]=>4032
[1,3,4,7,6,5,8,2]=>[5,2,1]=>4032
[1,3,4,6,7,5,8,2]=>[7,1]=>5760
[1,3,5,4,7,6,8,2]=>[5,1,1,1]=>1344
[1,5,4,6,3,7,8,2]=>[7,1]=>5760
[1,4,3,6,5,7,8,2]=>[5,1,1,1]=>1344
[1,3,4,6,5,7,8,2]=>[6,1,1]=>3360
[1,5,4,3,6,7,8,2]=>[5,2,1]=>4032
[1,4,5,3,6,7,8,2]=>[7,1]=>5760
[1,4,3,5,6,7,8,2]=>[6,1,1]=>3360
[1,3,4,5,6,7,8,2]=>[7,1]=>5760
[2,1,8,7,6,5,4,3]=>[2,2,2,2]=>105
[2,1,7,8,6,5,4,3]=>[4,2,2]=>1260
[2,1,6,8,7,5,4,3]=>[6,2]=>3360
[2,1,7,6,8,5,4,3]=>[6,2]=>3360
[2,1,6,7,8,5,4,3]=>[4,2,2]=>1260
[2,1,5,8,7,6,4,3]=>[5,2,1]=>4032
[2,1,5,7,8,6,4,3]=>[3,2,2,1]=>1680
[2,1,6,5,8,7,4,3]=>[6,2]=>3360
[2,1,5,6,8,7,4,3]=>[3,3,2]=>1120
[2,1,7,6,5,8,4,3]=>[5,2,1]=>4032
[2,1,6,7,5,8,4,3]=>[3,2,2,1]=>1680
[2,1,5,7,6,8,4,3]=>[4,2,2]=>1260
[2,1,6,5,7,8,4,3]=>[3,3,2]=>1120
[2,1,5,6,7,8,4,3]=>[6,2]=>3360
[2,1,4,8,7,6,5,3]=>[3,2,2,1]=>1680
[2,1,4,7,8,6,5,3]=>[5,2,1]=>4032
[2,1,4,6,8,7,5,3]=>[6,2]=>3360
[2,1,5,4,8,7,6,3]=>[3,2,2,1]=>1680
[2,1,5,4,7,8,6,3]=>[5,2,1]=>4032
[2,1,4,5,8,7,6,3]=>[4,2,2]=>1260
[2,1,4,5,7,8,6,3]=>[6,2]=>3360
[2,1,5,6,4,8,7,3]=>[5,2,1]=>4032
[2,1,4,6,5,8,7,3]=>[4,2,1,1]=>2520
[2,1,4,5,6,8,7,3]=>[5,2,1]=>4032
[2,1,7,6,5,4,8,3]=>[3,2,2,1]=>1680
[2,1,6,7,5,4,8,3]=>[5,2,1]=>4032
[2,1,5,7,6,4,8,3]=>[6,2]=>3360
[2,1,6,5,7,4,8,3]=>[6,2]=>3360
[2,1,5,6,7,4,8,3]=>[4,2,2]=>1260
[2,1,4,7,6,5,8,3]=>[4,2,2]=>1260
[2,1,4,6,7,5,8,3]=>[6,2]=>3360
[2,1,5,4,7,6,8,3]=>[4,2,1,1]=>2520
[2,1,5,6,4,7,8,3]=>[6,2]=>3360
[2,1,5,4,6,7,8,3]=>[5,2,1]=>4032
[2,1,4,5,6,7,8,3]=>[6,2]=>3360
[1,2,8,7,6,5,4,3]=>[2,2,2,1,1]=>420
[1,2,7,8,6,5,4,3]=>[4,2,1,1]=>2520
[1,2,7,6,8,5,4,3]=>[6,1,1]=>3360
[1,2,6,7,8,5,4,3]=>[4,2,1,1]=>2520
[1,2,6,5,8,7,4,3]=>[6,1,1]=>3360
[1,2,5,6,8,7,4,3]=>[3,3,1,1]=>1120
[1,2,7,6,5,8,4,3]=>[5,1,1,1]=>1344
[1,2,5,7,6,8,4,3]=>[4,2,1,1]=>2520
[1,2,6,5,7,8,4,3]=>[3,3,1,1]=>1120
[1,2,5,6,7,8,4,3]=>[6,1,1]=>3360
[1,2,4,8,7,6,5,3]=>[3,2,1,1,1]=>1120
[1,2,4,6,8,7,5,3]=>[6,1,1]=>3360
[1,2,4,6,7,8,5,3]=>[4,2,1,1]=>2520
[1,2,5,4,8,7,6,3]=>[3,2,1,1,1]=>1120
[1,2,5,4,7,8,6,3]=>[5,1,1,1]=>1344
[1,2,4,5,8,7,6,3]=>[4,2,1,1]=>2520
[1,2,4,5,7,8,6,3]=>[6,1,1]=>3360
[1,2,6,5,4,8,7,3]=>[3,2,1,1,1]=>1120
[1,2,4,6,5,8,7,3]=>[4,1,1,1,1]=>420
[1,2,5,4,6,8,7,3]=>[4,1,1,1,1]=>420
[1,2,4,5,6,8,7,3]=>[5,1,1,1]=>1344
[1,2,7,6,5,4,8,3]=>[3,2,1,1,1]=>1120
[1,2,5,7,6,4,8,3]=>[6,1,1]=>3360
[1,2,5,6,7,4,8,3]=>[4,2,1,1]=>2520
[1,2,4,7,6,5,8,3]=>[4,2,1,1]=>2520
[1,2,6,5,4,7,8,3]=>[4,2,1,1]=>2520
[1,2,5,6,4,7,8,3]=>[6,1,1]=>3360
[1,2,5,4,6,7,8,3]=>[5,1,1,1]=>1344
[1,2,4,5,6,7,8,3]=>[6,1,1]=>3360
[3,2,1,8,7,6,5,4]=>[2,2,2,1,1]=>420
[3,2,1,7,8,6,5,4]=>[4,2,1,1]=>2520
[3,2,1,6,8,7,5,4]=>[5,2,1]=>4032
[3,2,1,6,7,8,5,4]=>[3,2,2,1]=>1680
[3,2,1,5,7,8,6,4]=>[5,2,1]=>4032
[3,2,1,6,5,8,7,4]=>[3,2,1,1,1]=>1120
[3,2,1,7,6,5,8,4]=>[3,2,2,1]=>1680
[3,2,1,5,6,7,8,4]=>[5,2,1]=>4032
[2,3,1,8,7,6,5,4]=>[3,2,2,1]=>1680
[2,3,1,7,8,6,5,4]=>[4,3,1]=>3360
[2,3,1,6,8,7,5,4]=>[5,3]=>2688
[2,3,1,7,6,8,5,4]=>[5,3]=>2688
[2,3,1,6,7,8,5,4]=>[3,3,2]=>1120
[2,3,1,5,7,8,6,4]=>[5,3]=>2688
[2,3,1,6,5,8,7,4]=>[3,3,1,1]=>1120
[2,3,1,7,6,5,8,4]=>[3,3,2]=>1120
[2,3,1,6,7,5,8,4]=>[5,3]=>2688
[2,3,1,5,7,6,8,4]=>[4,3,1]=>3360
[2,3,1,5,6,7,8,4]=>[5,3]=>2688
[1,3,2,8,7,6,5,4]=>[2,2,2,1,1]=>420
[1,3,2,6,8,7,5,4]=>[5,2,1]=>4032
[1,3,2,7,6,8,5,4]=>[5,2,1]=>4032
[1,3,2,5,8,7,6,4]=>[3,2,2,1]=>1680
[1,3,2,5,7,8,6,4]=>[5,2,1]=>4032
[1,3,2,7,6,5,8,4]=>[3,2,2,1]=>1680
[1,3,2,6,7,5,8,4]=>[5,2,1]=>4032
[1,3,2,6,5,7,8,4]=>[4,2,1,1]=>2520
[1,3,2,5,6,7,8,4]=>[5,2,1]=>4032
[2,1,3,8,7,6,5,4]=>[2,2,2,1,1]=>420
[2,1,3,7,8,6,5,4]=>[4,2,1,1]=>2520
[2,1,3,6,8,7,5,4]=>[5,2,1]=>4032
[2,1,3,6,7,8,5,4]=>[3,2,2,1]=>1680
[2,1,3,5,6,7,8,4]=>[5,2,1]=>4032
[1,2,3,8,7,6,5,4]=>[2,2,1,1,1,1]=>210
[1,2,3,7,8,6,5,4]=>[4,1,1,1,1]=>420
[1,2,3,6,8,7,5,4]=>[5,1,1,1]=>1344
[1,2,3,7,6,8,5,4]=>[5,1,1,1]=>1344
[1,2,3,6,7,8,5,4]=>[3,2,1,1,1]=>1120
[1,2,3,5,8,7,6,4]=>[3,2,1,1,1]=>1120
[1,2,3,5,7,8,6,4]=>[5,1,1,1]=>1344
[1,2,3,6,5,8,7,4]=>[3,1,1,1,1,1]=>112
[1,2,3,5,6,8,7,4]=>[4,1,1,1,1]=>420
[1,2,3,7,6,5,8,4]=>[3,2,1,1,1]=>1120
[1,2,3,6,7,5,8,4]=>[5,1,1,1]=>1344
[1,2,3,5,7,6,8,4]=>[4,1,1,1,1]=>420
[1,2,3,6,5,7,8,4]=>[4,1,1,1,1]=>420
[1,2,3,5,6,7,8,4]=>[5,1,1,1]=>1344
[4,3,2,1,8,7,6,5]=>[2,2,2,2]=>105
[4,3,2,1,7,8,6,5]=>[4,2,2]=>1260
[4,3,2,1,7,6,8,5]=>[3,2,2,1]=>1680
[4,3,2,1,6,7,8,5]=>[4,2,2]=>1260
[3,4,2,1,8,7,6,5]=>[4,2,2]=>1260
[3,4,2,1,7,8,6,5]=>[4,4]=>1260
[3,4,2,1,6,8,7,5]=>[4,3,1]=>3360
[3,4,2,1,7,6,8,5]=>[4,3,1]=>3360
[3,4,2,1,6,7,8,5]=>[4,4]=>1260
[2,4,3,1,8,7,6,5]=>[3,2,2,1]=>1680
[2,4,3,1,7,8,6,5]=>[4,3,1]=>3360
[2,4,3,1,6,8,7,5]=>[3,3,1,1]=>1120
[2,4,3,1,7,6,8,5]=>[3,3,1,1]=>1120
[2,4,3,1,6,7,8,5]=>[4,3,1]=>3360
[3,2,4,1,8,7,6,5]=>[3,2,2,1]=>1680
[3,2,4,1,7,8,6,5]=>[4,3,1]=>3360
[3,2,4,1,6,8,7,5]=>[3,3,1,1]=>1120
[3,2,4,1,7,6,8,5]=>[3,3,1,1]=>1120
[3,2,4,1,6,7,8,5]=>[4,3,1]=>3360
[2,3,4,1,8,7,6,5]=>[4,2,2]=>1260
[2,3,4,1,7,8,6,5]=>[4,4]=>1260
[2,3,4,1,6,8,7,5]=>[4,3,1]=>3360
[2,3,4,1,7,6,8,5]=>[4,3,1]=>3360
[2,3,4,1,6,7,8,5]=>[4,4]=>1260
[1,4,3,2,8,7,6,5]=>[2,2,2,1,1]=>420
[1,4,3,2,6,8,7,5]=>[3,2,1,1,1]=>1120
[1,4,3,2,7,6,8,5]=>[3,2,1,1,1]=>1120
[1,4,3,2,6,7,8,5]=>[4,2,1,1]=>2520
[1,3,4,2,8,7,6,5]=>[3,2,2,1]=>1680
[1,3,4,2,7,8,6,5]=>[4,3,1]=>3360
[1,3,4,2,6,8,7,5]=>[3,3,1,1]=>1120
[1,3,4,2,7,6,8,5]=>[3,3,1,1]=>1120
[1,3,4,2,6,7,8,5]=>[4,3,1]=>3360
[2,1,4,3,8,7,6,5]=>[2,2,2,2]=>105
[2,1,4,3,7,8,6,5]=>[4,2,2]=>1260
[2,1,4,3,6,8,7,5]=>[3,2,2,1]=>1680
[2,1,4,3,7,6,8,5]=>[3,2,2,1]=>1680
[2,1,4,3,6,7,8,5]=>[4,2,2]=>1260
[1,2,4,3,8,7,6,5]=>[2,2,2,1,1]=>420
[1,2,4,3,7,8,6,5]=>[4,2,1,1]=>2520
[1,2,4,3,6,8,7,5]=>[3,2,1,1,1]=>1120
[1,2,4,3,7,6,8,5]=>[3,2,1,1,1]=>1120
[1,2,4,3,6,7,8,5]=>[4,2,1,1]=>2520
[3,2,1,4,8,7,6,5]=>[2,2,2,1,1]=>420
[3,2,1,4,7,8,6,5]=>[4,2,1,1]=>2520
[3,2,1,4,6,8,7,5]=>[3,2,1,1,1]=>1120
[3,2,1,4,7,6,8,5]=>[3,2,1,1,1]=>1120
[3,2,1,4,6,7,8,5]=>[4,2,1,1]=>2520
[2,3,1,4,8,7,6,5]=>[3,2,2,1]=>1680
[2,3,1,4,7,8,6,5]=>[4,3,1]=>3360
[2,3,1,4,7,6,8,5]=>[3,3,1,1]=>1120
[2,3,1,4,6,7,8,5]=>[4,3,1]=>3360
[1,3,2,4,8,7,6,5]=>[2,2,2,1,1]=>420
[1,3,2,4,6,8,7,5]=>[3,2,1,1,1]=>1120
[1,3,2,4,7,6,8,5]=>[3,2,1,1,1]=>1120
[1,3,2,4,6,7,8,5]=>[4,2,1,1]=>2520
[2,1,3,4,8,7,6,5]=>[2,2,2,1,1]=>420
[2,1,3,4,7,8,6,5]=>[4,2,1,1]=>2520
[2,1,3,4,7,6,8,5]=>[3,2,1,1,1]=>1120
[2,1,3,4,6,7,8,5]=>[4,2,1,1]=>2520
[1,2,3,4,8,7,6,5]=>[2,2,1,1,1,1]=>210
[1,2,3,4,7,8,6,5]=>[4,1,1,1,1]=>420
[1,2,3,4,6,8,7,5]=>[3,1,1,1,1,1]=>112
[1,2,3,4,7,6,8,5]=>[3,1,1,1,1,1]=>112
[1,2,3,4,6,7,8,5]=>[4,1,1,1,1]=>420
[5,4,3,2,1,8,7,6]=>[2,2,2,1,1]=>420
[5,4,3,2,1,7,8,6]=>[3,2,2,1]=>1680
[4,5,3,2,1,8,7,6]=>[4,2,1,1]=>2520
[3,5,4,2,1,8,7,6]=>[5,2,1]=>4032
[3,5,4,2,1,7,8,6]=>[5,3]=>2688
[4,3,5,2,1,8,7,6]=>[5,2,1]=>4032
[3,4,5,2,1,8,7,6]=>[3,2,2,1]=>1680
[2,5,4,3,1,8,7,6]=>[3,2,2,1]=>1680
[2,5,4,3,1,7,8,6]=>[3,3,2]=>1120
[2,4,5,3,1,8,7,6]=>[5,2,1]=>4032
[2,4,5,3,1,7,8,6]=>[5,3]=>2688
[3,2,5,4,1,8,7,6]=>[3,2,1,1,1]=>1120
[3,2,5,4,1,7,8,6]=>[3,3,1,1]=>1120
[2,3,5,4,1,8,7,6]=>[4,2,1,1]=>2520
[4,3,2,5,1,8,7,6]=>[3,2,2,1]=>1680
[4,3,2,5,1,7,8,6]=>[3,3,2]=>1120
[3,4,2,5,1,8,7,6]=>[5,2,1]=>4032
[3,4,2,5,1,7,8,6]=>[5,3]=>2688
[2,4,3,5,1,8,7,6]=>[4,2,1,1]=>2520
[2,4,3,5,1,7,8,6]=>[4,3,1]=>3360
[3,2,4,5,1,8,7,6]=>[4,2,1,1]=>2520
[2,3,4,5,1,8,7,6]=>[5,2,1]=>4032
[2,3,4,5,1,7,8,6]=>[5,3]=>2688
[1,5,4,3,2,8,7,6]=>[2,2,2,1,1]=>420
[1,5,4,3,2,7,8,6]=>[3,2,2,1]=>1680
[1,4,5,3,2,8,7,6]=>[4,2,1,1]=>2520
[1,4,5,3,2,7,8,6]=>[4,3,1]=>3360
[1,3,5,4,2,7,8,6]=>[3,3,1,1]=>1120
[1,3,4,5,2,8,7,6]=>[4,2,1,1]=>2520
[1,3,4,5,2,7,8,6]=>[4,3,1]=>3360
[2,1,4,5,3,8,7,6]=>[3,2,2,1]=>1680
[1,2,5,4,3,8,7,6]=>[2,2,1,1,1,1]=>210
[1,2,5,4,3,7,8,6]=>[3,2,1,1,1]=>1120
[1,2,4,5,3,8,7,6]=>[3,2,1,1,1]=>1120
[1,2,4,5,3,7,8,6]=>[3,3,1,1]=>1120
[1,3,2,5,4,8,7,6]=>[2,2,2,1,1]=>420
[1,3,2,5,4,7,8,6]=>[3,2,2,1]=>1680
[2,1,3,5,4,8,7,6]=>[2,2,2,1,1]=>420
[2,1,3,5,4,7,8,6]=>[3,2,2,1]=>1680
[1,2,3,5,4,8,7,6]=>[2,2,1,1,1,1]=>210
[1,2,3,5,4,7,8,6]=>[3,2,1,1,1]=>1120
[4,3,2,1,5,7,8,6]=>[3,2,2,1]=>1680
[3,2,4,1,5,8,7,6]=>[3,2,1,1,1]=>1120
[3,2,4,1,5,7,8,6]=>[3,3,1,1]=>1120
[2,3,4,1,5,8,7,6]=>[4,2,1,1]=>2520
[2,3,4,1,5,7,8,6]=>[4,3,1]=>3360
[1,4,3,2,5,8,7,6]=>[2,2,1,1,1,1]=>210
[1,4,3,2,5,7,8,6]=>[3,2,1,1,1]=>1120
[1,3,4,2,5,7,8,6]=>[3,3,1,1]=>1120
[2,1,4,3,5,7,8,6]=>[3,2,2,1]=>1680
[1,2,4,3,5,8,7,6]=>[2,2,1,1,1,1]=>210
[1,2,4,3,5,7,8,6]=>[3,2,1,1,1]=>1120
[3,2,1,4,5,8,7,6]=>[2,2,1,1,1,1]=>210
[3,2,1,4,5,7,8,6]=>[3,2,1,1,1]=>1120
[2,3,1,4,5,7,8,6]=>[3,3,1,1]=>1120
[1,3,2,4,5,8,7,6]=>[2,2,1,1,1,1]=>210
[1,3,2,4,5,7,8,6]=>[3,2,1,1,1]=>1120
[2,1,3,4,5,8,7,6]=>[2,2,1,1,1,1]=>210
[2,1,3,4,5,7,8,6]=>[3,2,1,1,1]=>1120
[1,2,3,4,5,8,7,6]=>[2,1,1,1,1,1,1]=>28
[1,2,3,4,5,7,8,6]=>[3,1,1,1,1,1]=>112
[6,5,4,3,2,1,8,7]=>[2,2,2,2]=>105
[5,6,4,3,2,1,8,7]=>[4,2,2]=>1260
[4,6,5,3,2,1,8,7]=>[6,2]=>3360
[5,4,6,3,2,1,8,7]=>[6,2]=>3360
[4,5,6,3,2,1,8,7]=>[4,2,2]=>1260
[3,6,5,4,2,1,8,7]=>[5,2,1]=>4032
[3,5,6,4,2,1,8,7]=>[3,2,2,1]=>1680
[4,3,6,5,2,1,8,7]=>[6,2]=>3360
[3,4,6,5,2,1,8,7]=>[3,3,2]=>1120
[5,4,3,6,2,1,8,7]=>[5,2,1]=>4032
[4,5,3,6,2,1,8,7]=>[3,2,2,1]=>1680
[4,3,5,6,2,1,8,7]=>[3,3,2]=>1120
[3,4,5,6,2,1,8,7]=>[6,2]=>3360
[2,6,5,4,3,1,8,7]=>[3,2,2,1]=>1680
[2,5,6,4,3,1,8,7]=>[5,2,1]=>4032
[2,4,6,5,3,1,8,7]=>[6,2]=>3360
[3,2,5,6,4,1,8,7]=>[5,2,1]=>4032
[2,3,6,5,4,1,8,7]=>[4,2,2]=>1260
[2,3,5,6,4,1,8,7]=>[6,2]=>3360
[4,3,2,6,5,1,8,7]=>[3,2,2,1]=>1680
[3,4,2,6,5,1,8,7]=>[5,2,1]=>4032
[2,4,3,6,5,1,8,7]=>[4,2,1,1]=>2520
[5,4,3,2,6,1,8,7]=>[3,2,2,1]=>1680
[3,5,4,2,6,1,8,7]=>[6,2]=>3360
[4,3,5,2,6,1,8,7]=>[6,2]=>3360
[3,4,5,2,6,1,8,7]=>[4,2,2]=>1260
[2,5,4,3,6,1,8,7]=>[4,2,2]=>1260
[2,4,5,3,6,1,8,7]=>[6,2]=>3360
[3,2,5,4,6,1,8,7]=>[4,2,1,1]=>2520
[4,3,2,5,6,1,8,7]=>[4,2,2]=>1260
[3,4,2,5,6,1,8,7]=>[6,2]=>3360
[2,4,3,5,6,1,8,7]=>[5,2,1]=>4032
[2,3,4,5,6,1,8,7]=>[6,2]=>3360
[1,6,5,4,3,2,8,7]=>[2,2,2,1,1]=>420
[1,5,6,4,3,2,8,7]=>[4,2,1,1]=>2520
[1,5,4,6,3,2,8,7]=>[5,2,1]=>4032
[1,3,6,5,4,2,8,7]=>[3,2,2,1]=>1680
[1,3,4,5,6,2,8,7]=>[5,2,1]=>4032
[2,1,6,5,4,3,8,7]=>[2,2,2,2]=>105
[2,1,5,6,4,3,8,7]=>[4,2,2]=>1260
[2,1,4,6,5,3,8,7]=>[3,2,2,1]=>1680
[2,1,5,4,6,3,8,7]=>[3,2,2,1]=>1680
[2,1,4,5,6,3,8,7]=>[4,2,2]=>1260
[1,2,4,5,6,3,8,7]=>[4,2,1,1]=>2520
[3,2,1,6,5,4,8,7]=>[2,2,2,1,1]=>420
[2,3,1,6,5,4,8,7]=>[3,2,2,1]=>1680
[1,3,2,6,5,4,8,7]=>[2,2,2,1,1]=>420
[1,3,2,5,6,4,8,7]=>[3,2,2,1]=>1680
[2,1,3,5,6,4,8,7]=>[3,2,2,1]=>1680
[1,2,3,6,5,4,8,7]=>[2,2,1,1,1,1]=>210
[1,2,3,5,6,4,8,7]=>[3,2,1,1,1]=>1120
[4,3,2,1,6,5,8,7]=>[2,2,2,2]=>105
[3,4,2,1,6,5,8,7]=>[4,2,2]=>1260
[2,4,3,1,6,5,8,7]=>[3,2,2,1]=>1680
[3,2,4,1,6,5,8,7]=>[3,2,2,1]=>1680
[2,3,4,1,6,5,8,7]=>[4,2,2]=>1260
[1,3,4,2,6,5,8,7]=>[3,2,2,1]=>1680
[2,1,4,3,6,5,8,7]=>[2,2,2,2]=>105
[1,2,4,3,6,5,8,7]=>[2,2,2,1,1]=>420
[2,3,1,4,6,5,8,7]=>[3,2,2,1]=>1680
[1,3,2,4,6,5,8,7]=>[2,2,2,1,1]=>420
[2,1,3,4,6,5,8,7]=>[2,2,2,1,1]=>420
[1,2,3,4,6,5,8,7]=>[2,2,1,1,1,1]=>210
[5,4,3,2,1,6,8,7]=>[2,2,2,1,1]=>420
[4,5,3,2,1,6,8,7]=>[4,2,1,1]=>2520
[3,5,4,2,1,6,8,7]=>[5,2,1]=>4032
[4,3,5,2,1,6,8,7]=>[5,2,1]=>4032
[3,4,5,2,1,6,8,7]=>[3,2,2,1]=>1680
[2,5,4,3,1,6,8,7]=>[3,2,2,1]=>1680
[2,4,5,3,1,6,8,7]=>[5,2,1]=>4032
[3,2,5,4,1,6,8,7]=>[3,2,1,1,1]=>1120
[2,3,5,4,1,6,8,7]=>[4,2,1,1]=>2520
[2,4,3,5,1,6,8,7]=>[4,2,1,1]=>2520
[2,3,4,5,1,6,8,7]=>[5,2,1]=>4032
[1,4,5,3,2,6,8,7]=>[4,2,1,1]=>2520
[1,3,5,4,2,6,8,7]=>[3,2,1,1,1]=>1120
[2,1,5,4,3,6,8,7]=>[2,2,2,1,1]=>420
[2,1,4,5,3,6,8,7]=>[3,2,2,1]=>1680
[1,2,5,4,3,6,8,7]=>[2,2,1,1,1,1]=>210
[2,1,3,5,4,6,8,7]=>[2,2,2,1,1]=>420
[1,2,3,5,4,6,8,7]=>[2,2,1,1,1,1]=>210
[4,3,2,1,5,6,8,7]=>[2,2,2,1,1]=>420
[3,2,4,1,5,6,8,7]=>[3,2,1,1,1]=>1120
[2,3,4,1,5,6,8,7]=>[4,2,1,1]=>2520
[1,4,3,2,5,6,8,7]=>[2,2,1,1,1,1]=>210
[1,3,4,2,5,6,8,7]=>[3,2,1,1,1]=>1120
[2,1,4,3,5,6,8,7]=>[2,2,2,1,1]=>420
[1,2,4,3,5,6,8,7]=>[2,2,1,1,1,1]=>210
[3,2,1,4,5,6,8,7]=>[2,2,1,1,1,1]=>210
[2,3,1,4,5,6,8,7]=>[3,2,1,1,1]=>1120
[1,3,2,4,5,6,8,7]=>[2,2,1,1,1,1]=>210
[2,1,3,4,5,6,8,7]=>[2,2,1,1,1,1]=>210
[1,2,3,4,5,6,8,7]=>[2,1,1,1,1,1,1]=>28
[5,7,6,4,3,2,1,8]=>[6,1,1]=>3360
[4,7,6,5,3,2,1,8]=>[7,1]=>5760
[4,6,7,5,3,2,1,8]=>[5,2,1]=>4032
[5,4,7,6,3,2,1,8]=>[4,3,1]=>3360
[4,5,7,6,3,2,1,8]=>[7,1]=>5760
[4,6,5,7,3,2,1,8]=>[3,2,2,1]=>1680
[3,5,7,6,4,2,1,8]=>[4,3,1]=>3360
[3,5,6,7,4,2,1,8]=>[7,1]=>5760
[4,3,7,6,5,2,1,8]=>[6,1,1]=>3360
[3,4,7,6,5,2,1,8]=>[3,3,1,1]=>1120
[5,4,3,7,6,2,1,8]=>[6,1,1]=>3360
[3,5,4,7,6,2,1,8]=>[4,3,1]=>3360
[3,5,6,4,7,2,1,8]=>[6,1,1]=>3360
[4,3,6,5,7,2,1,8]=>[4,3,1]=>3360
[2,7,6,5,4,3,1,8]=>[3,2,2,1]=>1680
[2,6,7,5,4,3,1,8]=>[5,2,1]=>4032
[2,5,6,7,4,3,1,8]=>[5,2,1]=>4032
[2,4,6,7,5,3,1,8]=>[4,2,1,1]=>2520
[2,5,4,7,6,3,1,8]=>[7,1]=>5760
[2,5,6,4,7,3,1,8]=>[4,2,1,1]=>2520
[2,5,4,6,7,3,1,8]=>[4,3,1]=>3360
[2,4,5,6,7,3,1,8]=>[7,1]=>5760
[3,2,7,6,5,4,1,8]=>[3,2,1,1,1]=>1120
[3,2,6,7,5,4,1,8]=>[5,1,1,1]=>1344
[3,2,5,7,6,4,1,8]=>[6,1,1]=>3360
[3,2,6,5,7,4,1,8]=>[6,1,1]=>3360
[3,2,5,6,7,4,1,8]=>[4,2,1,1]=>2520
[2,3,7,6,5,4,1,8]=>[4,2,1,1]=>2520
[2,3,6,7,5,4,1,8]=>[6,1,1]=>3360
[2,3,5,7,6,4,1,8]=>[7,1]=>5760
[2,3,6,5,7,4,1,8]=>[7,1]=>5760
[2,3,5,6,7,4,1,8]=>[5,2,1]=>4032
[4,3,2,6,7,5,1,8]=>[5,2,1]=>4032
[3,4,2,7,6,5,1,8]=>[5,2,1]=>4032
[3,4,2,6,7,5,1,8]=>[7,1]=>5760
[3,2,4,6,7,5,1,8]=>[6,1,1]=>3360
[2,3,4,7,6,5,1,8]=>[5,2,1]=>4032
[2,3,4,6,7,5,1,8]=>[7,1]=>5760
[5,4,3,2,7,6,1,8]=>[3,2,1,1,1]=>1120
[4,5,3,2,7,6,1,8]=>[5,1,1,1]=>1344
[3,5,4,2,7,6,1,8]=>[6,1,1]=>3360
[4,3,5,2,7,6,1,8]=>[6,1,1]=>3360
[3,4,5,2,7,6,1,8]=>[4,2,1,1]=>2520
[3,2,5,4,7,6,1,8]=>[4,1,1,1,1]=>420
[4,3,2,5,7,6,1,8]=>[4,2,1,1]=>2520
[3,4,2,5,7,6,1,8]=>[6,1,1]=>3360
[2,3,4,5,7,6,1,8]=>[6,1,1]=>3360
[3,6,5,4,2,7,1,8]=>[6,1,1]=>3360
[3,5,6,4,2,7,1,8]=>[4,2,1,1]=>2520
[3,5,4,6,2,7,1,8]=>[5,2,1]=>4032
[2,5,4,6,3,7,1,8]=>[7,1]=>5760
[3,2,6,5,4,7,1,8]=>[4,2,1,1]=>2520
[4,3,2,6,5,7,1,8]=>[4,2,1,1]=>2520
[3,4,2,6,5,7,1,8]=>[6,1,1]=>3360
[2,4,3,6,5,7,1,8]=>[5,1,1,1]=>1344
[2,3,4,6,5,7,1,8]=>[6,1,1]=>3360
[2,5,4,3,6,7,1,8]=>[5,2,1]=>4032
[1,7,6,5,4,3,2,8]=>[2,2,2,1,1]=>420
[1,6,7,5,4,3,2,8]=>[4,2,1,1]=>2520
[1,6,5,7,4,3,2,8]=>[6,1,1]=>3360
[1,5,6,7,4,3,2,8]=>[4,2,1,1]=>2520
[1,4,7,6,5,3,2,8]=>[5,1,1,1]=>1344
[1,4,6,7,5,3,2,8]=>[3,2,1,1,1]=>1120
[1,5,6,4,7,3,2,8]=>[3,2,1,1,1]=>1120
[1,4,6,5,7,3,2,8]=>[4,2,1,1]=>2520
[1,5,4,6,7,3,2,8]=>[3,3,1,1]=>1120
[1,4,5,6,7,3,2,8]=>[6,1,1]=>3360
[1,3,6,7,5,4,2,8]=>[5,1,1,1]=>1344
[1,3,5,7,6,4,2,8]=>[6,1,1]=>3360
[1,3,6,5,7,4,2,8]=>[6,1,1]=>3360
[1,3,5,6,7,4,2,8]=>[4,2,1,1]=>2520
[1,3,4,6,7,5,2,8]=>[6,1,1]=>3360
[1,3,5,4,7,6,2,8]=>[4,1,1,1,1]=>420
[1,4,3,5,7,6,2,8]=>[4,1,1,1,1]=>420
[1,3,4,5,7,6,2,8]=>[5,1,1,1]=>1344
[1,5,4,6,3,7,2,8]=>[6,1,1]=>3360
[1,3,6,5,4,7,2,8]=>[4,2,1,1]=>2520
[1,3,5,6,4,7,2,8]=>[6,1,1]=>3360
[1,4,3,6,5,7,2,8]=>[4,1,1,1,1]=>420
[1,5,4,3,6,7,2,8]=>[4,2,1,1]=>2520
[1,4,5,3,6,7,2,8]=>[6,1,1]=>3360
[1,3,4,5,6,7,2,8]=>[6,1,1]=>3360
[2,1,7,6,5,4,3,8]=>[2,2,2,1,1]=>420
[2,1,5,6,7,4,3,8]=>[3,2,2,1]=>1680
[2,1,5,4,6,7,3,8]=>[4,2,1,1]=>2520
[2,1,4,5,6,7,3,8]=>[5,2,1]=>4032
[1,2,7,6,5,4,3,8]=>[2,2,1,1,1,1]=>210
[1,2,6,7,5,4,3,8]=>[4,1,1,1,1]=>420
[1,2,5,7,6,4,3,8]=>[5,1,1,1]=>1344
[1,2,5,6,7,4,3,8]=>[3,2,1,1,1]=>1120
[1,2,4,6,7,5,3,8]=>[5,1,1,1]=>1344
[1,2,5,6,4,7,3,8]=>[5,1,1,1]=>1344
[1,2,5,4,6,7,3,8]=>[4,1,1,1,1]=>420
[1,2,4,5,6,7,3,8]=>[5,1,1,1]=>1344
[3,2,1,7,6,5,4,8]=>[2,2,2,1,1]=>420
[3,2,1,5,7,6,4,8]=>[3,2,1,1,1]=>1120
[3,2,1,6,5,7,4,8]=>[3,2,1,1,1]=>1120
[2,3,1,6,7,5,4,8]=>[4,3,1]=>3360
[2,3,1,6,5,7,4,8]=>[3,3,1,1]=>1120
[2,3,1,5,6,7,4,8]=>[4,3,1]=>3360
[1,3,2,7,6,5,4,8]=>[2,2,2,1,1]=>420
[1,3,2,6,7,5,4,8]=>[4,2,1,1]=>2520
[1,3,2,5,7,6,4,8]=>[3,2,1,1,1]=>1120
[1,3,2,6,5,7,4,8]=>[3,2,1,1,1]=>1120
[1,3,2,5,6,7,4,8]=>[4,2,1,1]=>2520
[2,1,3,6,7,5,4,8]=>[4,2,1,1]=>2520
[1,2,3,7,6,5,4,8]=>[2,2,1,1,1,1]=>210
[1,2,3,6,7,5,4,8]=>[4,1,1,1,1]=>420
[1,2,3,5,7,6,4,8]=>[3,1,1,1,1,1]=>112
[1,2,3,6,5,7,4,8]=>[3,1,1,1,1,1]=>112
[1,2,3,5,6,7,4,8]=>[4,1,1,1,1]=>420
[4,3,2,1,7,6,5,8]=>[2,2,2,1,1]=>420
[3,2,4,1,7,6,5,8]=>[3,2,1,1,1]=>1120
[3,2,4,1,6,7,5,8]=>[3,3,1,1]=>1120
[2,3,4,1,7,6,5,8]=>[4,2,1,1]=>2520
[2,3,4,1,6,7,5,8]=>[4,3,1]=>3360
[1,4,3,2,7,6,5,8]=>[2,2,1,1,1,1]=>210
[1,4,3,2,6,7,5,8]=>[3,2,1,1,1]=>1120
[1,3,4,2,6,7,5,8]=>[3,3,1,1]=>1120
[2,1,4,3,6,7,5,8]=>[3,2,2,1]=>1680
[1,2,4,3,6,7,5,8]=>[3,2,1,1,1]=>1120
[3,2,1,4,7,6,5,8]=>[2,2,1,1,1,1]=>210
[2,3,1,4,6,7,5,8]=>[3,3,1,1]=>1120
[1,3,2,4,7,6,5,8]=>[2,2,1,1,1,1]=>210
[1,2,3,4,7,6,5,8]=>[2,1,1,1,1,1,1]=>28
[1,2,3,4,6,7,5,8]=>[3,1,1,1,1,1]=>112
[5,4,3,2,1,7,6,8]=>[2,2,2,1,1]=>420
[4,5,3,2,1,7,6,8]=>[4,2,1,1]=>2520
[3,5,4,2,1,7,6,8]=>[5,2,1]=>4032
[3,4,5,2,1,7,6,8]=>[3,2,2,1]=>1680
[2,5,4,3,1,7,6,8]=>[3,2,2,1]=>1680
[2,4,5,3,1,7,6,8]=>[5,2,1]=>4032
[3,2,5,4,1,7,6,8]=>[3,2,1,1,1]=>1120
[2,3,5,4,1,7,6,8]=>[4,2,1,1]=>2520
[3,4,2,5,1,7,6,8]=>[5,2,1]=>4032
[2,4,3,5,1,7,6,8]=>[4,2,1,1]=>2520
[2,3,4,5,1,7,6,8]=>[5,2,1]=>4032
[1,5,4,3,2,7,6,8]=>[2,2,2,1,1]=>420
[1,4,5,3,2,7,6,8]=>[4,2,1,1]=>2520
[1,3,5,4,2,7,6,8]=>[3,2,1,1,1]=>1120
[1,4,3,5,2,7,6,8]=>[3,2,1,1,1]=>1120
[1,3,4,5,2,7,6,8]=>[4,2,1,1]=>2520
[1,2,4,5,3,7,6,8]=>[3,2,1,1,1]=>1120
[3,2,1,5,4,7,6,8]=>[2,2,2,1,1]=>420
[2,3,1,5,4,7,6,8]=>[3,2,2,1]=>1680
[1,3,2,5,4,7,6,8]=>[2,2,2,1,1]=>420
[1,2,3,5,4,7,6,8]=>[2,2,1,1,1,1]=>210
[3,2,4,1,5,7,6,8]=>[3,2,1,1,1]=>1120
[2,3,4,1,5,7,6,8]=>[4,2,1,1]=>2520
[1,4,3,2,5,7,6,8]=>[2,2,1,1,1,1]=>210
[1,3,4,2,5,7,6,8]=>[3,2,1,1,1]=>1120
[1,2,4,3,5,7,6,8]=>[2,2,1,1,1,1]=>210
[3,2,1,4,5,7,6,8]=>[2,2,1,1,1,1]=>210
[2,3,1,4,5,7,6,8]=>[3,2,1,1,1]=>1120
[1,3,2,4,5,7,6,8]=>[2,2,1,1,1,1]=>210
[2,1,3,4,5,7,6,8]=>[2,2,1,1,1,1]=>210
[1,2,3,4,5,7,6,8]=>[2,1,1,1,1,1,1]=>28
[3,6,5,4,2,1,7,8]=>[5,1,1,1]=>1344
[4,3,6,5,2,1,7,8]=>[6,1,1]=>3360
[2,4,6,5,3,1,7,8]=>[6,1,1]=>3360
[2,4,5,6,3,1,7,8]=>[4,2,1,1]=>2520
[2,3,5,6,4,1,7,8]=>[6,1,1]=>3360
[4,3,2,6,5,1,7,8]=>[3,2,1,1,1]=>1120
[2,3,4,6,5,1,7,8]=>[5,1,1,1]=>1344
[3,5,4,2,6,1,7,8]=>[6,1,1]=>3360
[2,3,5,4,6,1,7,8]=>[5,1,1,1]=>1344
[1,6,5,4,3,2,7,8]=>[2,2,1,1,1,1]=>210
[1,5,6,4,3,2,7,8]=>[4,1,1,1,1]=>420
[1,4,6,5,3,2,7,8]=>[5,1,1,1]=>1344
[1,5,4,6,3,2,7,8]=>[5,1,1,1]=>1344
[1,4,5,6,3,2,7,8]=>[3,2,1,1,1]=>1120
[1,3,5,6,4,2,7,8]=>[5,1,1,1]=>1344
[1,4,3,6,5,2,7,8]=>[3,1,1,1,1,1]=>112
[1,5,4,3,6,2,7,8]=>[3,2,1,1,1]=>1120
[1,4,5,3,6,2,7,8]=>[5,1,1,1]=>1344
[1,4,3,5,6,2,7,8]=>[4,1,1,1,1]=>420
[1,3,4,5,6,2,7,8]=>[5,1,1,1]=>1344
[2,1,5,6,4,3,7,8]=>[4,2,1,1]=>2520
[2,1,4,6,5,3,7,8]=>[3,2,1,1,1]=>1120
[1,2,6,5,4,3,7,8]=>[2,2,1,1,1,1]=>210
[1,2,5,6,4,3,7,8]=>[4,1,1,1,1]=>420
[1,2,4,6,5,3,7,8]=>[3,1,1,1,1,1]=>112
[1,2,4,5,6,3,7,8]=>[4,1,1,1,1]=>420
[3,2,1,6,5,4,7,8]=>[2,2,1,1,1,1]=>210
[2,3,1,6,5,4,7,8]=>[3,2,1,1,1]=>1120
[2,3,1,5,6,4,7,8]=>[3,3,1,1]=>1120
[1,3,2,6,5,4,7,8]=>[2,2,1,1,1,1]=>210
[1,3,2,5,6,4,7,8]=>[3,2,1,1,1]=>1120
[1,2,3,6,5,4,7,8]=>[2,1,1,1,1,1,1]=>28
[1,2,3,5,6,4,7,8]=>[3,1,1,1,1,1]=>112
[4,3,2,1,6,5,7,8]=>[2,2,2,1,1]=>420
[3,2,4,1,6,5,7,8]=>[3,2,1,1,1]=>1120
[2,3,4,1,6,5,7,8]=>[4,2,1,1]=>2520
[2,1,4,3,6,5,7,8]=>[2,2,2,1,1]=>420
[1,2,4,3,6,5,7,8]=>[2,2,1,1,1,1]=>210
[1,3,2,4,6,5,7,8]=>[2,2,1,1,1,1]=>210
[2,1,3,4,6,5,7,8]=>[2,2,1,1,1,1]=>210
[1,2,3,4,6,5,7,8]=>[2,1,1,1,1,1,1]=>28
[3,5,4,2,1,6,7,8]=>[5,1,1,1]=>1344
[2,5,4,3,1,6,7,8]=>[3,2,1,1,1]=>1120
[2,4,5,3,1,6,7,8]=>[5,1,1,1]=>1344
[3,2,5,4,1,6,7,8]=>[3,1,1,1,1,1]=>112
[2,3,5,4,1,6,7,8]=>[4,1,1,1,1]=>420
[2,4,3,5,1,6,7,8]=>[4,1,1,1,1]=>420
[1,5,4,3,2,6,7,8]=>[2,2,1,1,1,1]=>210
[1,4,5,3,2,6,7,8]=>[4,1,1,1,1]=>420
[1,3,4,5,2,6,7,8]=>[4,1,1,1,1]=>420
[2,1,5,4,3,6,7,8]=>[2,2,1,1,1,1]=>210
[2,1,4,5,3,6,7,8]=>[3,2,1,1,1]=>1120
[1,2,5,4,3,6,7,8]=>[2,1,1,1,1,1,1]=>28
[3,2,1,5,4,6,7,8]=>[2,2,1,1,1,1]=>210
[2,3,1,5,4,6,7,8]=>[3,2,1,1,1]=>1120
[1,3,2,5,4,6,7,8]=>[2,2,1,1,1,1]=>210
[2,1,3,5,4,6,7,8]=>[2,2,1,1,1,1]=>210
[1,2,3,5,4,6,7,8]=>[2,1,1,1,1,1,1]=>28
[2,4,3,1,5,6,7,8]=>[3,1,1,1,1,1]=>112
[1,4,3,2,5,6,7,8]=>[2,1,1,1,1,1,1]=>28
[1,3,4,2,5,6,7,8]=>[3,1,1,1,1,1]=>112
[2,1,4,3,5,6,7,8]=>[2,2,1,1,1,1]=>210
[1,2,4,3,5,6,7,8]=>[2,1,1,1,1,1,1]=>28
[1,3,2,4,5,6,7,8]=>[2,1,1,1,1,1,1]=>28
[1,2,3,4,8,6,7,5]=>[2,1,1,1,1,1,1]=>28
[1,2,3,5,8,6,7,4]=>[3,1,1,1,1,1]=>112
[1,2,3,7,5,6,4,8]=>[2,1,1,1,1,1,1]=>28
[1,2,3,7,5,6,8,4]=>[3,1,1,1,1,1]=>112
[1,2,3,8,5,6,7,4]=>[2,1,1,1,1,1,1]=>28
[1,2,3,8,5,7,6,4]=>[2,2,1,1,1,1]=>210
[1,2,3,8,6,5,7,4]=>[2,2,1,1,1,1]=>210
[1,2,3,8,6,7,5,4]=>[3,2,1,1,1]=>1120
[1,2,4,3,8,6,7,5]=>[2,2,1,1,1,1]=>210
[1,2,4,5,8,6,7,3]=>[4,1,1,1,1]=>420
[1,2,4,7,5,6,8,3]=>[4,1,1,1,1]=>420
[1,2,4,8,5,6,7,3]=>[3,1,1,1,1,1]=>112
[1,2,4,8,6,5,7,3]=>[3,2,1,1,1]=>1120
[1,2,5,4,8,6,7,3]=>[3,1,1,1,1,1]=>112
[1,2,6,4,5,3,7,8]=>[2,1,1,1,1,1,1]=>28
[1,2,6,4,5,7,8,3]=>[4,1,1,1,1]=>420
[1,2,7,4,5,6,8,3]=>[3,1,1,1,1,1]=>112
[1,2,8,4,5,6,7,3]=>[2,1,1,1,1,1,1]=>28
[1,2,8,4,6,7,5,3]=>[3,2,1,1,1]=>1120
[1,2,8,4,7,6,5,3]=>[2,2,1,1,1,1]=>210
[1,2,8,5,4,6,7,3]=>[2,2,1,1,1,1]=>210
[1,2,8,5,4,7,6,3]=>[2,2,2,1,1]=>420
[1,2,8,5,6,4,7,3]=>[3,2,1,1,1]=>1120
[1,2,8,5,6,7,4,3]=>[4,2,1,1]=>2520
[1,2,8,6,5,4,7,3]=>[2,2,1,1,1,1]=>210
[1,2,8,6,5,7,4,3]=>[3,2,1,1,1]=>1120
[1,2,8,7,5,6,4,3]=>[2,2,1,1,1,1]=>210
[1,3,2,4,8,6,7,5]=>[2,2,1,1,1,1]=>210
[1,3,2,7,5,6,8,4]=>[3,2,1,1,1]=>1120
[1,3,2,8,5,7,6,4]=>[2,2,2,1,1]=>420
[1,3,2,8,6,5,7,4]=>[2,2,2,1,1]=>420
[1,3,2,8,6,7,5,4]=>[3,2,2,1]=>1680
[1,3,4,2,8,6,7,5]=>[3,2,1,1,1]=>1120
[1,3,4,5,8,6,7,2]=>[5,1,1,1]=>1344
[1,3,4,8,5,6,7,2]=>[4,1,1,1,1]=>420
[1,3,6,4,5,2,8,7]=>[3,2,1,1,1]=>1120
[1,3,6,4,5,7,2,8]=>[4,1,1,1,1]=>420
[1,3,6,4,5,7,8,2]=>[5,1,1,1]=>1344
[1,3,6,4,5,8,7,2]=>[4,1,1,1,1]=>420
[1,3,7,4,5,6,2,8]=>[3,1,1,1,1,1]=>112
[1,3,7,4,5,6,8,2]=>[4,1,1,1,1]=>420
[1,3,8,4,5,6,7,2]=>[3,1,1,1,1,1]=>112
[1,3,8,4,6,5,7,2]=>[3,2,1,1,1]=>1120
[1,3,8,4,6,7,5,2]=>[3,3,1,1]=>1120
[1,3,8,5,4,6,7,2]=>[3,2,1,1,1]=>1120
[1,3,8,5,4,7,6,2]=>[3,2,2,1]=>1680
[1,3,8,5,6,7,4,2]=>[4,3,1]=>3360
[1,3,8,5,7,6,4,2]=>[3,3,1,1]=>1120
[1,3,8,6,5,7,4,2]=>[3,3,1,1]=>1120
[1,3,8,7,5,6,4,2]=>[3,2,1,1,1]=>1120
[1,4,3,2,8,6,7,5]=>[2,2,1,1,1,1]=>210
[1,4,3,5,8,6,7,2]=>[4,1,1,1,1]=>420
[1,4,3,8,5,6,7,2]=>[3,1,1,1,1,1]=>112
[1,4,3,8,5,7,6,2]=>[3,2,1,1,1]=>1120
[1,5,3,4,2,6,7,8]=>[2,1,1,1,1,1,1]=>28
[1,5,3,4,2,7,8,6]=>[3,2,1,1,1]=>1120
[1,5,3,4,2,8,7,6]=>[2,2,1,1,1,1]=>210
[1,5,3,4,6,2,8,7]=>[3,2,1,1,1]=>1120
[1,5,3,4,6,7,2,8]=>[4,1,1,1,1]=>420
[1,5,3,4,6,7,8,2]=>[5,1,1,1]=>1344
[1,5,3,4,8,6,7,2]=>[3,1,1,1,1,1]=>112
[1,6,3,4,5,2,7,8]=>[2,1,1,1,1,1,1]=>28
[1,7,3,4,5,6,2,8]=>[2,1,1,1,1,1,1]=>28
[1,7,3,4,5,6,8,2]=>[3,1,1,1,1,1]=>112
[1,8,3,4,5,6,7,2]=>[2,1,1,1,1,1,1]=>28
[1,8,3,4,6,7,5,2]=>[3,2,1,1,1]=>1120
[1,8,3,4,7,6,5,2]=>[2,2,1,1,1,1]=>210
[1,6,3,5,4,2,7,8]=>[2,2,1,1,1,1]=>210
[1,6,3,5,4,8,7,2]=>[3,2,1,1,1]=>1120
[1,7,3,5,4,6,2,8]=>[2,2,1,1,1,1]=>210
[1,8,3,5,4,6,7,2]=>[2,2,1,1,1,1]=>210
[1,8,3,5,4,7,6,2]=>[2,2,2,1,1]=>420
[1,8,3,5,6,4,7,2]=>[3,2,1,1,1]=>1120
[1,8,3,5,6,7,4,2]=>[4,2,1,1]=>2520
[1,8,3,5,7,6,4,2]=>[3,2,1,1,1]=>1120
[1,7,3,6,5,4,8,2]=>[3,2,1,1,1]=>1120
[1,8,3,6,5,4,7,2]=>[2,2,1,1,1,1]=>210
[1,8,3,7,5,6,4,2]=>[2,2,1,1,1,1]=>210
[1,8,3,7,6,5,4,2]=>[2,2,2,1,1]=>420
[1,6,4,3,5,2,7,8]=>[2,2,1,1,1,1]=>210
[1,6,4,3,5,8,7,2]=>[3,2,1,1,1]=>1120
[1,8,4,3,5,6,7,2]=>[2,2,1,1,1,1]=>210
[1,8,4,3,5,7,6,2]=>[2,2,2,1,1]=>420
[1,7,4,3,6,5,8,2]=>[3,2,2,1]=>1680
[1,8,4,3,6,5,7,2]=>[2,2,2,1,1]=>420
[1,6,4,5,3,2,7,8]=>[3,2,1,1,1]=>1120
[1,6,4,5,3,2,8,7]=>[3,2,2,1]=>1680
[1,7,4,5,3,6,8,2]=>[3,3,1,1]=>1120
[1,8,4,5,3,6,7,2]=>[3,2,1,1,1]=>1120
[1,7,4,5,6,3,8,2]=>[4,3,1]=>3360
[1,8,4,5,6,7,3,2]=>[5,2,1]=>4032
[1,7,4,6,5,3,2,8]=>[3,2,1,1,1]=>1120
[1,8,4,6,5,7,3,2]=>[4,2,1,1]=>2520
[1,8,4,7,6,5,3,2]=>[3,2,2,1]=>1680
[1,7,5,4,3,6,2,8]=>[2,2,1,1,1,1]=>210
[1,8,5,4,3,6,7,2]=>[2,2,1,1,1,1]=>210
[1,8,5,4,3,7,6,2]=>[2,2,2,1,1]=>420
[1,8,5,4,6,3,7,2]=>[3,2,1,1,1]=>1120
[1,8,5,4,6,7,3,2]=>[4,2,1,1]=>2520
[1,8,5,4,7,6,3,2]=>[3,2,1,1,1]=>1120
[1,7,6,4,5,3,2,8]=>[2,2,1,1,1,1]=>210
[1,8,6,4,5,3,7,2]=>[2,2,1,1,1,1]=>210
[1,8,6,4,5,7,3,2]=>[3,2,1,1,1]=>1120
[1,8,7,4,5,6,3,2]=>[2,2,1,1,1,1]=>210
[1,8,7,4,6,5,3,2]=>[2,2,2,1,1]=>420
[1,8,6,5,4,3,7,2]=>[2,2,2,1,1]=>420
[1,8,6,5,4,7,3,2]=>[3,2,2,1]=>1680
[1,8,7,5,4,6,3,2]=>[2,2,2,1,1]=>420
[1,8,7,5,6,4,3,2]=>[3,2,2,1]=>1680
[2,1,3,4,8,6,7,5]=>[2,2,1,1,1,1]=>210
[2,1,3,5,8,6,7,4]=>[3,2,1,1,1]=>1120
[2,1,3,8,5,6,7,4]=>[2,2,1,1,1,1]=>210
[2,1,3,8,5,7,6,4]=>[2,2,2,1,1]=>420
[2,1,3,8,6,7,5,4]=>[3,2,2,1]=>1680
[2,1,4,3,8,6,7,5]=>[2,2,2,1,1]=>420
[2,1,4,5,8,6,7,3]=>[4,2,1,1]=>2520
[2,1,4,8,5,6,7,3]=>[3,2,1,1,1]=>1120
[2,1,4,8,5,7,6,3]=>[3,2,2,1]=>1680
[2,1,4,8,6,5,7,3]=>[3,2,2,1]=>1680
[2,1,4,8,6,7,5,3]=>[3,3,2]=>1120
[2,1,5,4,8,6,7,3]=>[3,2,1,1,1]=>1120
[2,1,6,4,5,3,8,7]=>[2,2,2,1,1]=>420
[2,1,6,4,5,7,8,3]=>[4,2,1,1]=>2520
[2,1,6,4,5,8,7,3]=>[3,2,1,1,1]=>1120
[2,1,8,4,5,6,7,3]=>[2,2,1,1,1,1]=>210
[2,1,8,4,5,7,6,3]=>[2,2,2,1,1]=>420
[2,1,7,4,6,5,8,3]=>[3,2,2,1]=>1680
[2,1,8,4,6,5,7,3]=>[2,2,2,1,1]=>420
[2,1,8,4,6,7,5,3]=>[3,2,2,1]=>1680
[2,1,8,4,7,6,5,3]=>[2,2,2,1,1]=>420
[2,1,8,5,4,7,6,3]=>[2,2,2,2]=>105
[2,1,7,5,6,4,8,3]=>[3,3,2]=>1120
[2,1,8,5,6,4,7,3]=>[3,2,2,1]=>1680
[2,1,8,5,6,7,4,3]=>[4,2,2]=>1260
[2,1,8,5,7,6,4,3]=>[3,2,2,1]=>1680
[2,1,8,6,5,4,7,3]=>[2,2,2,1,1]=>420
[2,1,8,6,5,7,4,3]=>[3,2,2,1]=>1680
[2,1,8,7,5,6,4,3]=>[2,2,2,1,1]=>420
[2,3,1,7,5,6,4,8]=>[3,2,1,1,1]=>1120
[2,3,1,8,5,6,7,4]=>[3,2,1,1,1]=>1120
[2,3,1,8,6,7,5,4]=>[3,3,2]=>1120
[2,3,4,1,8,6,7,5]=>[4,2,1,1]=>2520
[2,3,4,5,8,6,7,1]=>[6,1,1]=>3360
[2,3,4,7,5,6,1,8]=>[5,1,1,1]=>1344
[2,3,4,7,5,6,8,1]=>[6,1,1]=>3360
[2,3,4,8,5,6,7,1]=>[5,1,1,1]=>1344
[2,3,4,8,5,7,6,1]=>[5,2,1]=>4032
[2,3,4,8,6,5,7,1]=>[5,2,1]=>4032
[2,3,4,8,6,7,5,1]=>[5,3]=>2688
[2,3,5,4,8,6,7,1]=>[5,1,1,1]=>1344
[2,3,6,4,5,1,7,8]=>[4,1,1,1,1]=>420
[2,3,6,4,5,1,8,7]=>[4,2,1,1]=>2520
[2,3,6,4,5,7,8,1]=>[6,1,1]=>3360
[2,3,6,4,5,8,7,1]=>[5,1,1,1]=>1344
[2,3,7,4,5,6,8,1]=>[5,1,1,1]=>1344
[2,3,8,4,5,6,7,1]=>[4,1,1,1,1]=>420
[2,3,7,4,6,5,8,1]=>[5,2,1]=>4032
[2,3,8,4,6,7,5,1]=>[4,3,1]=>3360
[2,3,7,5,4,6,1,8]=>[4,2,1,1]=>2520
[2,3,7,5,4,6,8,1]=>[5,2,1]=>4032
[2,3,7,5,6,4,1,8]=>[4,3,1]=>3360
[2,3,7,5,6,4,8,1]=>[5,3]=>2688
[2,3,8,5,6,7,4,1]=>[4,4]=>1260
[2,3,8,5,7,6,4,1]=>[4,3,1]=>3360
[2,4,3,5,8,6,7,1]=>[5,1,1,1]=>1344
[2,4,3,7,5,6,8,1]=>[5,1,1,1]=>1344
[2,4,3,8,5,6,7,1]=>[4,1,1,1,1]=>420
[2,4,3,8,6,5,7,1]=>[4,2,1,1]=>2520
[2,5,3,4,1,6,7,8]=>[3,1,1,1,1,1]=>112
[2,5,3,4,1,8,7,6]=>[3,2,1,1,1]=>1120
[2,5,3,4,6,7,1,8]=>[5,1,1,1]=>1344
[2,5,3,4,6,7,8,1]=>[6,1,1]=>3360
[2,5,3,4,6,8,7,1]=>[5,1,1,1]=>1344
[2,5,3,4,7,6,8,1]=>[5,1,1,1]=>1344
[2,5,3,4,8,6,7,1]=>[4,1,1,1,1]=>420
[2,5,3,4,8,7,6,1]=>[4,2,1,1]=>2520
[2,6,3,4,5,1,7,8]=>[3,1,1,1,1,1]=>112
[2,6,3,4,5,7,8,1]=>[5,1,1,1]=>1344
[2,6,3,4,5,8,7,1]=>[4,1,1,1,1]=>420
[2,7,3,4,5,6,1,8]=>[3,1,1,1,1,1]=>112
[2,8,3,4,5,6,7,1]=>[3,1,1,1,1,1]=>112
[2,8,3,4,5,7,6,1]=>[3,2,1,1,1]=>1120
[2,6,3,5,4,1,8,7]=>[3,2,2,1]=>1680
[2,6,3,5,4,7,8,1]=>[5,2,1]=>4032
[2,7,3,5,4,6,8,1]=>[4,2,1,1]=>2520
[2,8,3,5,4,7,6,1]=>[3,2,2,1]=>1680
[2,7,3,5,6,4,8,1]=>[4,3,1]=>3360
[2,8,3,5,6,7,4,1]=>[4,3,1]=>3360
[2,8,3,5,7,6,4,1]=>[3,3,1,1]=>1120
[2,7,3,6,5,4,1,8]=>[3,2,1,1,1]=>1120
[2,8,3,7,5,6,4,1]=>[3,2,1,1,1]=>1120
[2,8,3,7,6,5,4,1]=>[3,2,2,1]=>1680
[2,5,4,3,8,6,7,1]=>[4,2,1,1]=>2520
[2,6,4,3,5,1,8,7]=>[3,2,2,1]=>1680
[2,6,4,3,5,7,8,1]=>[5,2,1]=>4032
[2,6,4,3,5,8,7,1]=>[4,2,1,1]=>2520
[2,7,4,3,5,6,8,1]=>[4,2,1,1]=>2520
[2,8,4,3,5,6,7,1]=>[3,2,1,1,1]=>1120
[2,8,4,3,5,7,6,1]=>[3,2,2,1]=>1680
[2,7,4,3,6,5,8,1]=>[4,2,2]=>1260
[2,8,4,3,6,5,7,1]=>[3,2,2,1]=>1680
[2,8,4,3,6,7,5,1]=>[3,3,2]=>1120
[2,8,4,3,7,6,5,1]=>[3,2,2,1]=>1680
[2,6,4,5,3,7,8,1]=>[5,3]=>2688
[2,7,4,5,6,3,1,8]=>[4,3,1]=>3360
[2,7,4,5,6,3,8,1]=>[4,4]=>1260
[2,8,4,5,6,3,7,1]=>[4,3,1]=>3360
[2,8,4,5,6,7,3,1]=>[5,3]=>2688
[2,7,4,6,5,3,8,1]=>[4,3,1]=>3360
[2,8,4,6,5,3,7,1]=>[3,3,1,1]=>1120
[2,8,4,7,6,5,3,1]=>[3,3,2]=>1120
[2,7,5,4,3,6,8,1]=>[4,2,1,1]=>2520
[2,8,5,4,3,6,7,1]=>[3,2,1,1,1]=>1120
[2,8,5,4,3,7,6,1]=>[3,2,2,1]=>1680
[2,7,5,4,6,3,8,1]=>[4,3,1]=>3360
[2,8,5,4,6,7,3,1]=>[4,3,1]=>3360
[2,8,5,4,7,6,3,1]=>[3,3,1,1]=>1120
[2,7,6,4,5,3,8,1]=>[4,2,1,1]=>2520
[2,8,7,4,5,6,3,1]=>[3,2,1,1,1]=>1120
[2,8,7,4,6,5,3,1]=>[3,2,2,1]=>1680
[2,8,7,5,4,6,3,1]=>[3,2,2,1]=>1680
[2,8,7,5,6,4,3,1]=>[3,3,2]=>1120
[3,2,1,4,8,6,7,5]=>[2,2,1,1,1,1]=>210
[3,2,1,5,8,6,7,4]=>[3,2,1,1,1]=>1120
[3,2,1,7,5,6,4,8]=>[2,2,1,1,1,1]=>210
[3,2,1,8,5,6,7,4]=>[2,2,1,1,1,1]=>210
[3,2,1,8,5,7,6,4]=>[2,2,2,1,1]=>420
[3,2,1,8,6,5,7,4]=>[2,2,2,1,1]=>420
[3,2,1,8,6,7,5,4]=>[3,2,2,1]=>1680
[3,2,4,1,8,6,7,5]=>[3,2,1,1,1]=>1120
[3,2,4,5,8,6,7,1]=>[5,1,1,1]=>1344
[3,2,4,7,5,6,8,1]=>[5,1,1,1]=>1344
[3,2,4,8,5,6,7,1]=>[4,1,1,1,1]=>420
[3,2,4,8,6,7,5,1]=>[4,3,1]=>3360
[3,2,5,4,8,6,7,1]=>[4,1,1,1,1]=>420
[3,2,6,4,5,1,8,7]=>[3,2,1,1,1]=>1120
[3,2,7,4,5,6,1,8]=>[3,1,1,1,1,1]=>112
[3,2,8,4,5,6,7,1]=>[3,1,1,1,1,1]=>112
[3,2,7,4,6,5,1,8]=>[3,2,1,1,1]=>1120
[3,2,7,4,6,5,8,1]=>[4,2,1,1]=>2520
[3,2,8,4,6,5,7,1]=>[3,2,1,1,1]=>1120
[3,2,7,5,4,6,1,8]=>[3,2,1,1,1]=>1120
[3,2,8,5,4,6,7,1]=>[3,2,1,1,1]=>1120
[3,2,8,5,4,7,6,1]=>[3,2,2,1]=>1680
[3,2,7,5,6,4,1,8]=>[3,3,1,1]=>1120
[3,2,7,5,6,4,8,1]=>[4,3,1]=>3360
[3,2,8,5,6,4,7,1]=>[3,3,1,1]=>1120
[3,2,8,5,7,6,4,1]=>[3,3,1,1]=>1120
[3,2,8,7,5,6,4,1]=>[3,2,1,1,1]=>1120
[4,2,3,1,5,7,8,6]=>[3,2,1,1,1]=>1120
[4,2,3,1,5,8,7,6]=>[2,2,1,1,1,1]=>210
[4,2,3,1,6,5,7,8]=>[2,2,1,1,1,1]=>210
[4,2,3,1,6,5,8,7]=>[2,2,2,1,1]=>420
[4,2,3,1,6,7,8,5]=>[4,2,1,1]=>2520
[4,2,3,1,6,8,7,5]=>[3,2,1,1,1]=>1120
[4,2,3,1,7,6,5,8]=>[2,2,1,1,1,1]=>210
[4,2,3,1,7,6,8,5]=>[3,2,1,1,1]=>1120
[4,2,3,1,8,6,7,5]=>[2,2,1,1,1,1]=>210
[4,2,3,1,8,7,6,5]=>[2,2,2,1,1]=>420
[4,2,3,5,1,6,8,7]=>[3,2,1,1,1]=>1120
[4,2,3,5,1,7,8,6]=>[3,3,1,1]=>1120
[4,2,3,5,1,8,7,6]=>[3,2,1,1,1]=>1120
[4,2,3,5,6,1,8,7]=>[4,2,1,1]=>2520
[4,2,3,5,6,8,7,1]=>[5,1,1,1]=>1344
[4,2,3,6,5,8,7,1]=>[4,1,1,1,1]=>420
[4,2,3,7,5,6,1,8]=>[3,1,1,1,1,1]=>112
[4,2,3,7,5,6,8,1]=>[4,1,1,1,1]=>420
[4,2,3,8,5,6,7,1]=>[3,1,1,1,1,1]=>112
[4,2,3,8,5,7,6,1]=>[3,2,1,1,1]=>1120
[5,2,3,4,1,6,8,7]=>[2,2,1,1,1,1]=>210
[5,2,3,4,1,7,8,6]=>[3,2,1,1,1]=>1120
[5,2,3,4,1,8,7,6]=>[2,2,1,1,1,1]=>210
[5,2,3,4,6,1,8,7]=>[3,2,1,1,1]=>1120
[5,2,3,4,7,6,1,8]=>[3,1,1,1,1,1]=>112
[5,2,3,4,8,6,7,1]=>[3,1,1,1,1,1]=>112
[5,2,3,4,8,7,6,1]=>[3,2,1,1,1]=>1120
[6,2,3,4,5,1,8,7]=>[2,2,1,1,1,1]=>210
[6,2,3,4,5,8,7,1]=>[3,1,1,1,1,1]=>112
[8,2,3,4,5,7,6,1]=>[2,2,1,1,1,1]=>210
[7,2,3,4,6,5,1,8]=>[2,2,1,1,1,1]=>210
[8,2,3,4,7,6,5,1]=>[2,2,1,1,1,1]=>210
[6,2,3,5,4,1,7,8]=>[2,2,1,1,1,1]=>210
[6,2,3,5,4,1,8,7]=>[2,2,2,1,1]=>420
[6,2,3,5,4,7,1,8]=>[3,2,1,1,1]=>1120
[7,2,3,5,4,6,1,8]=>[2,2,1,1,1,1]=>210
[8,2,3,5,4,6,7,1]=>[2,2,1,1,1,1]=>210
[8,2,3,5,4,7,6,1]=>[2,2,2,1,1]=>420
[7,2,3,5,6,4,1,8]=>[3,2,1,1,1]=>1120
[8,2,3,5,6,7,4,1]=>[4,2,1,1]=>2520
[8,2,3,5,7,6,4,1]=>[3,2,1,1,1]=>1120
[7,2,3,6,5,4,1,8]=>[2,2,1,1,1,1]=>210
[8,2,3,7,5,6,4,1]=>[2,2,1,1,1,1]=>210
[8,2,3,7,6,5,4,1]=>[2,2,2,1,1]=>420
[5,2,4,3,1,6,7,8]=>[2,2,1,1,1,1]=>210
[5,2,4,3,1,6,8,7]=>[2,2,2,1,1]=>420
[5,2,4,3,1,7,6,8]=>[2,2,2,1,1]=>420
[5,2,4,3,1,8,7,6]=>[2,2,2,1,1]=>420
[5,2,4,3,6,1,7,8]=>[3,2,1,1,1]=>1120
[5,2,4,3,6,1,8,7]=>[3,2,2,1]=>1680
[5,2,4,3,7,6,1,8]=>[3,2,1,1,1]=>1120
[5,2,4,3,7,6,8,1]=>[4,2,1,1]=>2520
[6,2,4,3,5,1,8,7]=>[2,2,2,1,1]=>420
[7,2,4,3,6,5,1,8]=>[2,2,2,1,1]=>420
[7,2,4,3,6,5,8,1]=>[3,2,2,1]=>1680
[8,2,4,3,6,5,7,1]=>[2,2,2,1,1]=>420
[8,2,4,3,6,7,5,1]=>[3,2,2,1]=>1680
[8,2,4,3,7,6,5,1]=>[2,2,2,1,1]=>420
[7,2,4,5,3,6,1,8]=>[3,2,1,1,1]=>1120
[7,2,4,5,3,6,8,1]=>[3,3,1,1]=>1120
[8,2,4,5,3,7,6,1]=>[3,2,2,1]=>1680
[8,2,4,5,6,7,3,1]=>[5,2,1]=>4032
[8,2,4,5,7,6,3,1]=>[4,2,1,1]=>2520
[7,2,4,6,5,3,8,1]=>[3,3,1,1]=>1120
[8,2,4,7,5,6,3,1]=>[3,2,1,1,1]=>1120
[8,2,4,7,6,5,3,1]=>[3,2,2,1]=>1680
[6,2,5,4,3,1,7,8]=>[2,2,1,1,1,1]=>210
[6,2,5,4,3,1,8,7]=>[2,2,2,1,1]=>420
[6,2,5,4,3,7,1,8]=>[3,2,1,1,1]=>1120
[7,2,5,4,3,6,1,8]=>[2,2,1,1,1,1]=>210
[8,2,5,4,3,6,7,1]=>[2,2,1,1,1,1]=>210
[8,2,5,4,3,7,6,1]=>[2,2,2,1,1]=>420
[7,2,6,4,5,3,1,8]=>[2,2,1,1,1,1]=>210
[7,2,6,4,5,3,8,1]=>[3,2,1,1,1]=>1120
[8,2,6,4,5,3,7,1]=>[2,2,1,1,1,1]=>210
[8,2,6,4,5,7,3,1]=>[3,2,1,1,1]=>1120
[8,2,7,4,5,6,3,1]=>[2,2,1,1,1,1]=>210
[8,2,7,4,6,5,3,1]=>[2,2,2,1,1]=>420
[7,2,6,5,4,3,1,8]=>[2,2,2,1,1]=>420
[8,2,6,5,4,3,7,1]=>[2,2,2,1,1]=>420
[8,2,6,5,4,7,3,1]=>[3,2,2,1]=>1680
[8,2,7,5,4,6,3,1]=>[2,2,2,1,1]=>420
[8,2,7,5,6,4,3,1]=>[3,2,2,1]=>1680
[8,2,7,6,5,4,3,1]=>[2,2,2,1,1]=>420
[4,3,2,1,8,6,7,5]=>[2,2,2,1,1]=>420
[4,3,2,7,5,6,8,1]=>[4,2,1,1]=>2520
[4,3,2,8,5,6,7,1]=>[3,2,1,1,1]=>1120
[4,3,2,8,5,7,6,1]=>[3,2,2,1]=>1680
[4,3,2,8,6,7,5,1]=>[3,3,2]=>1120
[5,3,2,4,1,6,8,7]=>[2,2,2,1,1]=>420
[5,3,2,4,1,7,6,8]=>[2,2,2,1,1]=>420
[5,3,2,4,1,8,7,6]=>[2,2,2,1,1]=>420
[5,3,2,4,6,1,8,7]=>[3,2,2,1]=>1680
[5,3,2,4,7,6,1,8]=>[3,2,1,1,1]=>1120
[8,3,2,4,6,5,7,1]=>[2,2,2,1,1]=>420
[8,3,2,4,7,6,5,1]=>[2,2,2,1,1]=>420
[6,3,2,5,4,1,8,7]=>[2,2,2,2]=>105
[6,3,2,5,4,7,1,8]=>[3,2,2,1]=>1680
[6,3,2,5,4,7,8,1]=>[4,2,2]=>1260
[7,3,2,5,4,6,1,8]=>[2,2,2,1,1]=>420
[8,3,2,5,4,7,6,1]=>[2,2,2,2]=>105
[7,3,2,5,6,4,8,1]=>[3,3,2]=>1120
[8,3,2,5,6,7,4,1]=>[4,2,2]=>1260
[8,3,2,5,7,6,4,1]=>[3,2,2,1]=>1680
[8,3,2,6,5,7,4,1]=>[3,2,2,1]=>1680
[8,3,2,7,5,6,4,1]=>[2,2,2,1,1]=>420
[8,3,2,7,6,5,4,1]=>[2,2,2,2]=>105
[5,3,4,2,1,6,8,7]=>[3,2,2,1]=>1680
[5,3,4,2,1,7,8,6]=>[3,3,2]=>1120
[5,3,4,2,1,8,7,6]=>[3,2,2,1]=>1680
[5,3,4,2,6,1,8,7]=>[3,3,2]=>1120
[5,3,4,2,7,6,1,8]=>[3,3,1,1]=>1120
[5,3,4,2,7,6,8,1]=>[4,3,1]=>3360
[5,3,4,2,8,6,7,1]=>[3,3,1,1]=>1120
[6,3,4,2,5,1,8,7]=>[3,2,2,1]=>1680
[7,3,4,2,6,5,8,1]=>[3,3,2]=>1120
[6,3,4,5,2,1,8,7]=>[4,2,2]=>1260
[6,3,4,5,2,8,7,1]=>[4,3,1]=>3360
[8,3,4,5,2,7,6,1]=>[4,2,2]=>1260
[8,3,4,5,7,6,2,1]=>[5,2,1]=>4032
[8,3,4,7,6,5,2,1]=>[4,2,2]=>1260
[6,3,5,4,2,1,8,7]=>[3,2,2,1]=>1680
[6,3,5,4,2,7,1,8]=>[3,3,1,1]=>1120
[6,3,5,4,2,7,8,1]=>[4,3,1]=>3360
[7,3,5,4,2,6,1,8]=>[3,2,1,1,1]=>1120
[8,3,5,4,2,6,7,1]=>[3,2,1,1,1]=>1120
[7,3,5,4,6,2,8,1]=>[4,3,1]=>3360
[8,3,5,4,6,7,2,1]=>[5,2,1]=>4032
[8,3,5,4,7,6,2,1]=>[4,2,1,1]=>2520
[7,3,6,4,5,2,1,8]=>[3,2,1,1,1]=>1120
[7,3,6,4,5,2,8,1]=>[3,3,1,1]=>1120
[8,3,6,4,5,2,7,1]=>[3,2,1,1,1]=>1120
[8,3,7,4,5,6,2,1]=>[3,2,1,1,1]=>1120
[8,3,7,4,6,5,2,1]=>[3,2,2,1]=>1680
[7,3,6,5,4,2,1,8]=>[3,2,2,1]=>1680
[7,3,6,5,4,2,8,1]=>[3,3,2]=>1120
[8,3,6,5,4,2,7,1]=>[3,2,2,1]=>1680
[8,3,6,5,4,7,2,1]=>[4,2,2]=>1260
[8,3,7,5,6,4,2,1]=>[3,3,2]=>1120
[8,3,7,6,5,4,2,1]=>[3,2,2,1]=>1680
[5,4,3,2,8,6,7,1]=>[3,2,1,1,1]=>1120
[6,4,3,2,5,1,8,7]=>[2,2,2,1,1]=>420
[6,4,3,2,5,8,7,1]=>[3,2,1,1,1]=>1120
[8,4,3,2,5,7,6,1]=>[2,2,2,1,1]=>420
[7,4,3,2,6,5,1,8]=>[2,2,2,1,1]=>420
[7,4,3,2,6,5,8,1]=>[3,2,2,1]=>1680
[8,4,3,2,6,5,7,1]=>[2,2,2,1,1]=>420
[8,4,3,2,6,7,5,1]=>[3,2,2,1]=>1680
[8,4,3,2,7,6,5,1]=>[2,2,2,1,1]=>420
[6,4,3,5,2,1,8,7]=>[3,2,2,1]=>1680
[8,4,3,5,7,6,2,1]=>[4,2,1,1]=>2520
[7,4,3,6,5,2,1,8]=>[3,2,1,1,1]=>1120
[7,4,3,6,5,2,8,1]=>[3,3,1,1]=>1120
[8,4,3,7,5,6,2,1]=>[3,2,1,1,1]=>1120
[6,5,3,4,2,1,8,7]=>[2,2,2,1,1]=>420
[8,5,3,4,2,7,6,1]=>[2,2,2,1,1]=>420
[8,5,3,4,7,6,2,1]=>[3,2,1,1,1]=>1120
[8,7,3,4,6,5,2,1]=>[2,2,2,1,1]=>420
[7,6,3,5,4,2,1,8]=>[2,2,2,1,1]=>420
[7,6,3,5,4,2,8,1]=>[3,2,2,1]=>1680
[8,6,3,5,4,2,7,1]=>[2,2,2,1,1]=>420
[8,7,3,5,4,6,2,1]=>[2,2,2,1,1]=>420
[8,7,3,5,6,4,2,1]=>[3,2,2,1]=>1680
[8,7,3,6,5,4,2,1]=>[2,2,2,1,1]=>420
[8,5,4,3,2,7,6,1]=>[2,2,2,2]=>105
[8,5,4,3,7,6,2,1]=>[3,2,2,1]=>1680
[8,7,4,3,6,5,2,1]=>[2,2,2,2]=>105
[8,7,4,6,5,3,2,1]=>[3,2,2,1]=>1680
[2,4,1,3,6,5,8,7]=>[4,2,2]=>1260
[2,1,4,6,3,5,8,7]=>[4,2,2]=>1260
[2,4,1,6,3,5,8,7]=>[6,2]=>3360
[2,4,6,1,3,5,8,7]=>[3,3,2]=>1120
[2,1,4,3,6,8,5,7]=>[4,2,2]=>1260
[2,4,1,3,6,8,5,7]=>[4,4]=>1260
[2,1,4,6,3,8,5,7]=>[6,2]=>3360
[2,4,1,6,3,8,5,7]=>[8]=>5040
[2,4,6,1,3,8,5,7]=>[5,3]=>2688
[2,1,4,6,8,3,5,7]=>[3,3,2]=>1120
[2,4,1,6,8,3,5,7]=>[5,3]=>2688
[2,4,6,1,8,3,5,7]=>[3,3,2]=>1120
[2,4,6,8,1,3,5,7]=>[6,2]=>3360
[2,4,1,3,6,5,7,8]=>[4,2,1,1]=>2520
[2,4,6,1,3,5,7,8]=>[3,3,1,1]=>1120
[2,1,4,6,3,7,5,8]=>[5,2,1]=>4032
[2,4,1,6,3,7,5,8]=>[7,1]=>5760
[2,4,6,1,3,7,5,8]=>[4,3,1]=>3360
[2,4,6,7,1,3,5,8]=>[5,2,1]=>4032
[2,4,1,3,6,7,8,5]=>[4,4]=>1260
[2,1,4,6,3,7,8,5]=>[6,2]=>3360
[2,4,1,6,3,7,8,5]=>[8]=>5040
[2,1,4,6,7,3,8,5]=>[3,3,2]=>1120
[2,4,1,6,7,3,8,5]=>[5,3]=>2688
[2,4,6,1,7,3,8,5]=>[3,3,2]=>1120
[2,4,6,7,1,3,8,5]=>[6,2]=>3360
[2,1,4,6,7,8,3,5]=>[6,2]=>3360
[2,4,1,6,7,8,3,5]=>[8]=>5040
[2,4,6,7,8,1,3,5]=>[6,2]=>3360
[2,1,4,3,7,5,8,6]=>[4,2,2]=>1260
[2,4,1,3,7,5,8,6]=>[4,4]=>1260
[2,1,4,7,3,5,8,6]=>[6,2]=>3360
[2,4,1,7,3,5,8,6]=>[8]=>5040
[2,1,4,3,7,8,5,6]=>[2,2,2,2]=>105
[2,4,1,3,7,8,5,6]=>[4,2,2]=>1260
[2,4,1,7,3,8,5,6]=>[6,2]=>3360
[2,1,4,7,8,3,5,6]=>[6,2]=>3360
[2,4,1,7,8,3,5,6]=>[8]=>5040
[2,4,7,1,8,3,5,6]=>[5,3]=>2688
[2,4,7,8,1,3,5,6]=>[8]=>5040
[2,4,1,5,3,7,6,8]=>[5,2,1]=>4032
[2,4,5,1,3,7,6,8]=>[3,2,2,1]=>1680
[2,4,5,1,7,3,6,8]=>[4,3,1]=>3360
[2,4,1,5,3,7,8,6]=>[5,3]=>2688
[2,4,5,1,3,7,8,6]=>[3,3,2]=>1120
[2,1,4,5,7,3,8,6]=>[6,2]=>3360
[2,4,1,5,7,3,8,6]=>[8]=>5040
[2,4,5,1,7,3,8,6]=>[5,3]=>2688
[2,1,4,5,7,8,3,6]=>[4,2,2]=>1260
[2,4,5,1,7,8,3,6]=>[3,3,2]=>1120
[2,4,5,7,1,8,3,6]=>[6,2]=>3360
[2,4,5,7,8,1,3,6]=>[8]=>5040
[2,1,4,3,8,5,6,7]=>[4,2,2]=>1260
[2,4,1,3,8,5,6,7]=>[4,4]=>1260
[2,1,4,8,3,5,6,7]=>[6,2]=>3360
[2,4,1,8,3,5,6,7]=>[8]=>5040
[2,4,8,1,3,5,6,7]=>[5,3]=>2688
[2,1,4,3,5,8,6,7]=>[3,2,2,1]=>1680
[2,4,1,5,3,8,6,7]=>[5,3]=>2688
[2,1,4,5,8,3,6,7]=>[6,2]=>3360
[2,4,1,5,8,3,6,7]=>[8]=>5040
[2,4,5,1,8,3,6,7]=>[5,3]=>2688
[2,4,1,5,3,6,8,7]=>[5,2,1]=>4032
[2,4,1,5,6,3,8,7]=>[6,2]=>3360
[2,4,5,1,6,3,8,7]=>[3,3,2]=>1120
[2,4,5,6,1,3,8,7]=>[6,2]=>3360
[2,1,4,5,6,8,3,7]=>[6,2]=>3360
[2,4,1,5,6,8,3,7]=>[8]=>5040
[2,4,5,1,6,8,3,7]=>[5,3]=>2688
[2,4,5,6,1,8,3,7]=>[8]=>5040
[2,4,5,6,8,1,3,7]=>[4,4]=>1260
[2,4,1,3,5,6,7,8]=>[4,1,1,1,1]=>420
[2,4,1,5,3,6,7,8]=>[5,1,1,1]=>1344
[2,4,5,1,3,6,7,8]=>[3,2,1,1,1]=>1120
[2,4,1,5,6,3,7,8]=>[6,1,1]=>3360
[2,4,5,1,6,3,7,8]=>[3,3,1,1]=>1120
[2,4,5,6,1,3,7,8]=>[6,1,1]=>3360
[2,4,1,5,6,7,3,8]=>[7,1]=>5760
[2,4,5,6,1,7,3,8]=>[7,1]=>5760
[2,4,5,6,7,1,3,8]=>[4,3,1]=>3360
[2,4,1,5,6,7,8,3]=>[8]=>5040
[2,4,5,1,6,7,8,3]=>[5,3]=>2688
[2,4,5,6,1,7,8,3]=>[8]=>5040
[2,4,5,6,7,1,8,3]=>[4,4]=>1260
[2,4,5,6,7,8,1,3]=>[8]=>5040
[2,1,5,3,6,4,8,7]=>[4,2,2]=>1260
[2,5,1,3,6,4,8,7]=>[6,2]=>3360
[2,1,5,6,3,4,8,7]=>[2,2,2,2]=>105
[2,5,1,6,3,4,8,7]=>[4,2,2]=>1260
[2,5,6,1,3,4,8,7]=>[6,2]=>3360
[2,1,5,3,6,8,4,7]=>[6,2]=>3360
[2,5,1,3,6,8,4,7]=>[8]=>5040
[2,5,6,1,3,8,4,7]=>[8]=>5040
[2,1,5,6,8,3,4,7]=>[6,2]=>3360
[2,5,1,6,8,3,4,7]=>[8]=>5040
[2,5,6,8,1,3,4,7]=>[3,3,2]=>1120
[2,5,1,3,6,4,7,8]=>[6,1,1]=>3360
[2,1,5,6,3,4,7,8]=>[2,2,2,1,1]=>420
[2,5,1,6,3,4,7,8]=>[4,2,1,1]=>2520
[2,1,5,3,6,7,4,8]=>[5,2,1]=>4032
[2,1,5,6,3,7,4,8]=>[3,2,2,1]=>1680
[2,5,1,6,3,7,4,8]=>[4,3,1]=>3360
[2,5,6,1,3,7,4,8]=>[7,1]=>5760
[2,1,5,6,7,3,4,8]=>[5,2,1]=>4032
[2,5,6,1,7,3,4,8]=>[5,2,1]=>4032
[2,1,5,3,6,7,8,4]=>[6,2]=>3360
[2,5,1,3,6,7,8,4]=>[8]=>5040
[2,1,5,6,3,7,8,4]=>[4,2,2]=>1260
[2,5,1,6,3,7,8,4]=>[4,4]=>1260
[2,5,6,1,3,7,8,4]=>[8]=>5040
[2,1,5,6,7,3,8,4]=>[6,2]=>3360
[2,5,1,6,7,3,8,4]=>[8]=>5040
[2,5,6,7,1,3,8,4]=>[3,3,2]=>1120
[2,1,5,6,7,8,3,4]=>[3,3,2]=>1120
[2,5,1,6,7,8,3,4]=>[5,3]=>2688
[2,5,6,1,7,8,3,4]=>[8]=>5040
[2,5,6,7,1,8,3,4]=>[5,3]=>2688
[2,5,6,7,8,1,3,4]=>[8]=>5040
[2,1,5,3,7,4,8,6]=>[6,2]=>3360
[2,5,1,3,7,4,8,6]=>[8]=>5040
[2,1,5,7,3,4,8,6]=>[4,2,2]=>1260
[2,5,1,7,3,4,8,6]=>[4,4]=>1260
[2,5,7,1,3,4,8,6]=>[8]=>5040
[2,1,5,3,7,8,4,6]=>[4,2,2]=>1260
[2,5,1,3,7,8,4,6]=>[6,2]=>3360
[2,1,5,7,3,8,4,6]=>[2,2,2,2]=>105
[2,1,5,7,8,3,4,6]=>[4,2,2]=>1260
[2,5,1,7,8,3,4,6]=>[6,2]=>3360
[2,5,7,1,8,3,4,6]=>[8]=>5040
[2,5,7,8,1,3,4,6]=>[5,3]=>2688
[2,1,5,7,3,4,6,8]=>[3,2,2,1]=>1680
[2,3,5,1,4,7,6,8]=>[5,2,1]=>4032
[2,3,5,7,1,4,6,8]=>[4,3,1]=>3360
[2,3,5,1,7,4,8,6]=>[8]=>5040
[2,3,5,7,1,4,8,6]=>[4,4]=>1260
[2,3,1,5,7,8,4,6]=>[3,3,2]=>1120
[2,3,5,7,1,8,4,6]=>[4,2,2]=>1260
[2,3,5,7,8,1,4,6]=>[6,2]=>3360
[2,1,5,3,8,4,6,7]=>[6,2]=>3360
[2,5,1,3,8,4,6,7]=>[8]=>5040
[2,1,5,8,3,4,6,7]=>[4,2,2]=>1260
[2,5,1,8,3,4,6,7]=>[4,4]=>1260
[2,5,8,1,3,4,6,7]=>[8]=>5040
[2,3,5,1,4,8,6,7]=>[5,3]=>2688
[2,1,3,5,8,4,6,7]=>[5,2,1]=>4032
[2,3,5,1,8,4,6,7]=>[8]=>5040
[2,3,5,8,1,4,6,7]=>[4,4]=>1260
[2,1,5,3,4,6,8,7]=>[3,2,2,1]=>1680
[2,3,5,1,6,4,8,7]=>[6,2]=>3360
[2,3,5,6,1,4,8,7]=>[4,2,2]=>1260
[2,1,3,5,6,8,4,7]=>[5,2,1]=>4032
[2,3,1,5,6,8,4,7]=>[5,3]=>2688
[2,3,5,1,6,8,4,7]=>[8]=>5040
[2,3,5,6,1,8,4,7]=>[4,4]=>1260
[2,3,5,6,8,1,4,7]=>[8]=>5040
[2,1,5,3,4,6,7,8]=>[3,2,1,1,1]=>1120
[2,5,1,3,4,6,7,8]=>[5,1,1,1]=>1344
[2,3,5,1,4,6,7,8]=>[5,1,1,1]=>1344
[2,3,5,6,1,4,7,8]=>[4,2,1,1]=>2520
[2,3,5,6,7,1,4,8]=>[7,1]=>5760
[2,3,5,1,6,7,8,4]=>[8]=>5040
[2,3,5,6,1,7,8,4]=>[4,4]=>1260
[2,3,5,6,7,1,8,4]=>[8]=>5040
[2,3,5,6,7,8,1,4]=>[5,3]=>2688
[2,1,6,3,7,4,8,5]=>[3,3,2]=>1120
[2,6,1,3,7,4,8,5]=>[5,3]=>2688
[2,1,6,7,3,4,8,5]=>[6,2]=>3360
[2,6,1,7,3,4,8,5]=>[8]=>5040
[2,6,7,1,3,4,8,5]=>[4,4]=>1260
[2,1,6,3,7,8,4,5]=>[6,2]=>3360
[2,6,1,3,7,8,4,5]=>[8]=>5040
[2,6,7,1,3,8,4,5]=>[8]=>5040
[2,1,6,7,8,3,4,5]=>[2,2,2,2]=>105
[2,6,1,7,8,3,4,5]=>[4,2,2]=>1260
[2,6,7,1,8,3,4,5]=>[6,2]=>3360
[2,6,7,8,1,3,4,5]=>[8]=>5040
[2,1,6,3,7,4,5,8]=>[3,2,2,1]=>1680
[2,6,7,1,3,4,5,8]=>[4,3,1]=>3360
[2,6,1,3,4,7,5,8]=>[7,1]=>5760
[2,3,1,6,4,7,5,8]=>[4,3,1]=>3360
[2,3,6,1,4,7,5,8]=>[7,1]=>5760
[2,1,6,3,4,7,8,5]=>[6,2]=>3360
[2,6,1,3,4,7,8,5]=>[8]=>5040
[2,3,6,1,4,7,8,5]=>[8]=>5040
[2,1,3,6,7,4,8,5]=>[3,2,2,1]=>1680
[2,1,3,6,7,8,4,5]=>[5,2,1]=>4032
[2,3,1,6,7,8,4,5]=>[5,3]=>2688
[2,3,6,1,7,8,4,5]=>[8]=>5040
[2,3,6,7,1,8,4,5]=>[6,2]=>3360
[2,3,6,7,8,1,4,5]=>[4,2,2]=>1260
[2,1,6,3,8,4,5,7]=>[3,3,2]=>1120
[2,6,1,3,8,4,5,7]=>[5,3]=>2688
[2,1,6,8,3,4,5,7]=>[6,2]=>3360
[2,6,8,1,3,4,5,7]=>[4,4]=>1260
[2,1,6,3,4,8,5,7]=>[6,2]=>3360
[2,6,1,3,4,8,5,7]=>[8]=>5040
[2,3,1,6,4,8,5,7]=>[5,3]=>2688
[2,3,6,1,4,8,5,7]=>[8]=>5040
[2,3,1,6,8,4,5,7]=>[3,3,2]=>1120
[2,3,6,1,8,4,5,7]=>[5,3]=>2688
[2,1,6,3,4,5,8,7]=>[4,2,2]=>1260
[2,6,1,3,4,5,8,7]=>[6,2]=>3360
[2,1,3,6,4,5,8,7]=>[3,2,2,1]=>1680
[2,3,6,1,4,5,8,7]=>[6,2]=>3360
[2,3,4,1,6,8,5,7]=>[4,4]=>1260
[2,3,4,6,1,8,5,7]=>[8]=>5040
[2,3,4,6,8,1,5,7]=>[5,3]=>2688
[2,6,1,3,4,5,7,8]=>[6,1,1]=>3360
[2,1,3,6,4,5,7,8]=>[3,2,1,1,1]=>1120
[2,3,1,6,4,5,7,8]=>[3,3,1,1]=>1120
[2,3,6,1,4,5,7,8]=>[6,1,1]=>3360
[2,3,4,6,1,5,7,8]=>[6,1,1]=>3360
[2,3,4,6,7,1,5,8]=>[5,2,1]=>4032
[2,3,4,6,1,7,8,5]=>[8]=>5040
[2,3,4,6,7,8,1,5]=>[8]=>5040
[2,1,7,3,8,4,5,6]=>[6,2]=>3360
[2,7,1,3,8,4,5,6]=>[8]=>5040
[2,1,7,8,3,4,5,6]=>[3,3,2]=>1120
[2,7,1,8,3,4,5,6]=>[5,3]=>2688
[2,7,8,1,3,4,5,6]=>[8]=>5040
[2,1,7,3,4,8,5,6]=>[4,2,2]=>1260
[2,1,3,7,4,8,5,6]=>[3,2,2,1]=>1680
[2,3,1,7,4,8,5,6]=>[3,3,2]=>1120
[2,3,7,1,4,8,5,6]=>[6,2]=>3360
[2,1,3,7,8,4,5,6]=>[5,2,1]=>4032
[2,3,1,7,8,4,5,6]=>[5,3]=>2688
[2,3,7,8,1,4,5,6]=>[5,3]=>2688
[2,1,7,3,4,5,8,6]=>[6,2]=>3360
[2,7,1,3,4,5,8,6]=>[8]=>5040
[2,3,1,7,4,5,8,6]=>[5,3]=>2688
[2,3,7,1,4,5,8,6]=>[8]=>5040
[2,1,3,4,7,5,8,6]=>[4,2,1,1]=>2520
[2,3,4,1,7,5,8,6]=>[4,4]=>1260
[2,3,4,7,1,5,8,6]=>[8]=>5040
[2,1,3,4,7,8,5,6]=>[2,2,2,1,1]=>420
[2,3,1,4,7,8,5,6]=>[3,2,2,1]=>1680
[2,3,4,1,7,8,5,6]=>[4,2,2]=>1260
[2,3,4,7,1,8,5,6]=>[6,2]=>3360
[2,3,4,7,8,1,5,6]=>[8]=>5040
[2,1,7,3,4,5,6,8]=>[5,2,1]=>4032
[2,7,1,3,4,5,6,8]=>[7,1]=>5760
[2,3,7,1,4,5,6,8]=>[7,1]=>5760
[2,1,3,4,7,5,6,8]=>[3,2,1,1,1]=>1120
[2,3,1,4,7,5,6,8]=>[3,3,1,1]=>1120
[2,3,4,1,7,5,6,8]=>[4,3,1]=>3360
[2,3,4,7,1,5,6,8]=>[7,1]=>5760
[2,3,4,5,7,1,6,8]=>[7,1]=>5760
[2,3,4,5,7,1,8,6]=>[8]=>5040
[2,3,4,5,7,8,1,6]=>[6,2]=>3360
[2,1,8,3,4,5,6,7]=>[6,2]=>3360
[2,8,1,3,4,5,6,7]=>[8]=>5040
[2,1,3,8,4,5,6,7]=>[5,2,1]=>4032
[2,3,1,8,4,5,6,7]=>[5,3]=>2688
[2,3,8,1,4,5,6,7]=>[8]=>5040
[2,1,3,4,8,5,6,7]=>[4,2,1,1]=>2520
[2,3,1,4,8,5,6,7]=>[4,3,1]=>3360
[2,3,4,1,8,5,6,7]=>[4,4]=>1260
[2,3,4,8,1,5,6,7]=>[8]=>5040
[2,1,3,4,5,8,6,7]=>[3,2,1,1,1]=>1120
[2,3,1,4,5,8,6,7]=>[3,3,1,1]=>1120
[2,3,4,1,5,8,6,7]=>[4,3,1]=>3360
[2,3,4,5,1,8,6,7]=>[5,3]=>2688
[2,3,4,5,8,1,6,7]=>[8]=>5040
[2,3,4,5,6,8,1,7]=>[8]=>5040
[3,1,4,2,6,5,8,7]=>[4,2,2]=>1260
[3,4,1,2,6,5,8,7]=>[2,2,2,2]=>105
[3,1,4,6,2,5,8,7]=>[6,2]=>3360
[3,4,1,6,2,5,8,7]=>[4,2,2]=>1260
[3,4,6,1,2,5,8,7]=>[6,2]=>3360
[3,1,4,2,6,8,5,7]=>[4,4]=>1260
[3,4,1,2,6,8,5,7]=>[4,2,2]=>1260
[3,1,4,6,2,8,5,7]=>[8]=>5040
[3,4,1,6,2,8,5,7]=>[6,2]=>3360
[3,1,4,6,8,2,5,7]=>[5,3]=>2688
[3,4,1,6,8,2,5,7]=>[3,3,2]=>1120
[3,4,6,8,1,2,5,7]=>[8]=>5040
[3,1,4,2,6,5,7,8]=>[4,2,1,1]=>2520
[3,4,1,2,6,5,7,8]=>[2,2,2,1,1]=>420
[3,1,4,2,6,7,5,8]=>[4,3,1]=>3360
[3,4,1,2,6,7,5,8]=>[3,2,2,1]=>1680
[3,4,1,6,2,7,5,8]=>[5,2,1]=>4032
[3,4,6,7,1,2,5,8]=>[7,1]=>5760
[3,1,4,2,6,7,8,5]=>[4,4]=>1260
[3,4,1,2,6,7,8,5]=>[4,2,2]=>1260
[3,1,4,6,2,7,8,5]=>[8]=>5040
[3,4,1,6,2,7,8,5]=>[6,2]=>3360
[3,4,6,1,2,7,8,5]=>[8]=>5040
[3,1,4,6,7,2,8,5]=>[5,3]=>2688
[3,4,1,6,7,2,8,5]=>[3,3,2]=>1120
[3,4,6,1,7,2,8,5]=>[5,3]=>2688
[3,1,4,6,7,8,2,5]=>[8]=>5040
[3,4,1,6,7,8,2,5]=>[6,2]=>3360
[3,4,6,1,7,8,2,5]=>[8]=>5040
[3,4,6,7,1,8,2,5]=>[5,3]=>2688
[3,4,6,7,8,1,2,5]=>[3,3,2]=>1120
[3,1,4,2,7,5,8,6]=>[4,4]=>1260
[3,4,1,2,7,5,8,6]=>[4,2,2]=>1260
[3,1,4,7,2,5,8,6]=>[8]=>5040
[3,4,7,1,2,5,8,6]=>[8]=>5040
[3,1,4,2,7,8,5,6]=>[4,2,2]=>1260
[3,4,1,2,7,8,5,6]=>[2,2,2,2]=>105
[3,4,7,1,8,2,5,6]=>[8]=>5040
[3,4,7,8,1,2,5,6]=>[4,4]=>1260
[3,1,4,2,7,5,6,8]=>[4,3,1]=>3360
[3,4,1,2,7,5,6,8]=>[3,2,2,1]=>1680
[3,4,1,2,5,7,6,8]=>[2,2,2,1,1]=>420
[3,1,4,5,2,7,6,8]=>[5,2,1]=>4032
[3,4,1,5,2,7,6,8]=>[3,2,2,1]=>1680
[3,4,1,5,7,2,6,8]=>[5,2,1]=>4032
[3,4,5,7,1,2,6,8]=>[4,3,1]=>3360
[3,1,4,2,5,7,8,6]=>[4,3,1]=>3360
[3,4,1,2,5,7,8,6]=>[3,2,2,1]=>1680
[3,1,4,5,2,7,8,6]=>[5,3]=>2688
[3,4,5,1,2,7,8,6]=>[5,3]=>2688
[3,1,4,5,7,2,8,6]=>[8]=>5040
[3,4,1,5,7,2,8,6]=>[6,2]=>3360
[3,1,4,5,7,8,2,6]=>[6,2]=>3360
[3,4,1,5,7,8,2,6]=>[4,2,2]=>1260
[3,4,5,1,7,8,2,6]=>[6,2]=>3360
[3,4,5,7,1,8,2,6]=>[3,3,2]=>1120
[3,4,5,7,8,1,2,6]=>[5,3]=>2688
[3,1,4,2,8,5,6,7]=>[4,4]=>1260
[3,4,1,2,8,5,6,7]=>[4,2,2]=>1260
[3,1,4,8,2,5,6,7]=>[8]=>5040
[3,4,1,8,2,5,6,7]=>[6,2]=>3360
[3,4,8,1,2,5,6,7]=>[8]=>5040
[3,1,4,2,5,8,6,7]=>[4,3,1]=>3360
[3,4,1,2,5,8,6,7]=>[3,2,2,1]=>1680
[3,4,1,5,2,8,6,7]=>[3,3,2]=>1120
[3,1,4,5,8,2,6,7]=>[8]=>5040
[3,4,1,5,8,2,6,7]=>[6,2]=>3360
[3,4,5,8,1,2,6,7]=>[5,3]=>2688
[3,4,1,2,5,6,8,7]=>[2,2,2,1,1]=>420
[3,4,5,1,2,6,8,7]=>[5,2,1]=>4032
[3,1,4,5,6,2,8,7]=>[6,2]=>3360
[3,4,1,5,6,2,8,7]=>[4,2,2]=>1260
[3,4,5,1,6,2,8,7]=>[6,2]=>3360
[3,4,5,6,1,2,8,7]=>[3,3,2]=>1120
[3,1,4,5,6,8,2,7]=>[8]=>5040
[3,4,1,5,6,8,2,7]=>[6,2]=>3360
[3,4,5,6,1,8,2,7]=>[5,3]=>2688
[3,4,5,6,8,1,2,7]=>[8]=>5040
[3,1,4,2,5,6,7,8]=>[4,1,1,1,1]=>420
[3,1,4,5,2,6,7,8]=>[5,1,1,1]=>1344
[3,4,1,5,2,6,7,8]=>[3,2,1,1,1]=>1120
[3,4,1,5,6,2,7,8]=>[4,2,1,1]=>2520
[3,4,5,1,6,2,7,8]=>[6,1,1]=>3360
[3,1,4,5,6,7,2,8]=>[7,1]=>5760
[3,4,1,5,6,7,2,8]=>[5,2,1]=>4032
[3,4,5,1,6,7,2,8]=>[7,1]=>5760
[3,4,5,6,1,7,2,8]=>[4,3,1]=>3360
[3,1,4,5,6,7,8,2]=>[8]=>5040
[3,4,1,5,6,7,8,2]=>[6,2]=>3360
[3,4,5,1,6,7,8,2]=>[8]=>5040
[3,4,5,6,1,7,8,2]=>[5,3]=>2688
[3,4,5,6,7,1,8,2]=>[8]=>5040
[3,1,5,2,6,4,8,7]=>[6,2]=>3360
[3,5,1,2,6,4,8,7]=>[4,2,2]=>1260
[3,1,5,6,2,4,8,7]=>[4,2,2]=>1260
[3,5,1,6,2,4,8,7]=>[2,2,2,2]=>105
[3,5,6,1,2,4,8,7]=>[4,2,2]=>1260
[3,1,5,2,6,8,4,7]=>[8]=>5040
[3,5,1,2,6,8,4,7]=>[6,2]=>3360
[3,1,5,6,2,8,4,7]=>[4,4]=>1260
[3,1,5,6,8,2,4,7]=>[8]=>5040
[3,5,1,6,8,2,4,7]=>[6,2]=>3360
[3,5,6,1,8,2,4,7]=>[8]=>5040
[3,5,6,8,1,2,4,7]=>[5,3]=>2688
[3,1,5,6,2,4,7,8]=>[4,2,1,1]=>2520
[3,5,1,6,2,4,7,8]=>[2,2,2,1,1]=>420
[3,5,6,1,2,4,7,8]=>[4,2,1,1]=>2520
[3,5,1,2,6,7,4,8]=>[5,2,1]=>4032
[3,5,1,6,2,7,4,8]=>[3,2,2,1]=>1680
[3,5,6,1,2,7,4,8]=>[5,2,1]=>4032
[3,5,1,6,7,2,4,8]=>[5,2,1]=>4032
[3,5,6,7,1,2,4,8]=>[5,2,1]=>4032
[3,1,5,2,6,7,8,4]=>[8]=>5040
[3,5,1,2,6,7,8,4]=>[6,2]=>3360
[3,1,5,6,2,7,8,4]=>[4,4]=>1260
[3,5,1,6,2,7,8,4]=>[4,2,2]=>1260
[3,5,6,1,2,7,8,4]=>[6,2]=>3360
[3,1,5,6,7,2,8,4]=>[8]=>5040
[3,5,1,6,7,2,8,4]=>[6,2]=>3360
[3,5,6,1,7,2,8,4]=>[8]=>5040
[3,5,6,7,1,2,8,4]=>[5,3]=>2688
[3,1,5,6,7,8,2,4]=>[5,3]=>2688
[3,5,1,6,7,8,2,4]=>[3,3,2]=>1120
[3,5,6,1,7,8,2,4]=>[5,3]=>2688
[3,5,6,7,1,8,2,4]=>[8]=>5040
[3,5,6,7,8,1,2,4]=>[5,3]=>2688
[3,1,5,2,7,4,8,6]=>[8]=>5040
[3,5,1,2,7,4,8,6]=>[6,2]=>3360
[3,1,5,7,2,4,8,6]=>[4,4]=>1260
[3,5,7,1,2,4,8,6]=>[6,2]=>3360
[3,1,5,2,7,8,4,6]=>[6,2]=>3360
[3,5,1,2,7,8,4,6]=>[4,2,2]=>1260
[3,1,5,7,2,8,4,6]=>[4,2,2]=>1260
[3,5,1,7,2,8,4,6]=>[2,2,2,2]=>105
[3,1,5,7,8,2,4,6]=>[6,2]=>3360
[3,5,1,7,8,2,4,6]=>[4,2,2]=>1260
[3,5,7,8,1,2,4,6]=>[8]=>5040
[3,1,5,2,7,4,6,8]=>[7,1]=>5760
[3,5,1,2,7,4,6,8]=>[5,2,1]=>4032
[3,1,5,7,2,4,6,8]=>[4,3,1]=>3360
[3,5,1,7,2,4,6,8]=>[3,2,2,1]=>1680
[3,5,7,1,2,4,6,8]=>[5,2,1]=>4032
[3,1,5,2,4,7,6,8]=>[5,2,1]=>4032
[3,5,1,2,4,7,6,8]=>[3,2,2,1]=>1680
[3,1,2,5,4,7,6,8]=>[3,2,2,1]=>1680
[1,3,5,2,4,7,6,8]=>[4,2,1,1]=>2520
[3,1,2,5,7,4,6,8]=>[4,3,1]=>3360
[1,3,2,5,7,4,6,8]=>[4,2,1,1]=>2520
[1,3,5,2,7,4,6,8]=>[6,1,1]=>3360
[1,3,5,7,2,4,6,8]=>[3,3,1,1]=>1120
[3,5,1,2,4,7,8,6]=>[3,3,2]=>1120
[3,1,2,5,7,4,8,6]=>[5,3]=>2688
[1,3,5,2,7,4,8,6]=>[7,1]=>5760
[1,3,5,7,2,4,8,6]=>[4,3,1]=>3360
[1,3,2,5,7,8,4,6]=>[3,2,2,1]=>1680
[1,3,5,2,7,8,4,6]=>[5,2,1]=>4032
[1,3,5,7,2,8,4,6]=>[3,2,2,1]=>1680
[1,3,5,7,8,2,4,6]=>[5,2,1]=>4032
[3,1,5,2,8,4,6,7]=>[8]=>5040
[3,5,1,2,8,4,6,7]=>[6,2]=>3360
[3,1,5,8,2,4,6,7]=>[4,4]=>1260
[3,5,1,8,2,4,6,7]=>[4,2,2]=>1260
[3,1,5,2,4,8,6,7]=>[5,3]=>2688
[1,3,2,5,4,8,6,7]=>[3,2,2,1]=>1680
[1,3,5,2,4,8,6,7]=>[4,3,1]=>3360
[3,1,2,5,8,4,6,7]=>[5,3]=>2688
[1,3,2,5,8,4,6,7]=>[5,2,1]=>4032
[1,3,5,2,8,4,6,7]=>[7,1]=>5760
[1,3,5,8,2,4,6,7]=>[4,3,1]=>3360
[3,5,1,2,4,6,8,7]=>[3,2,2,1]=>1680
[3,1,2,5,4,6,8,7]=>[3,2,2,1]=>1680
[1,3,5,2,4,6,8,7]=>[4,2,1,1]=>2520
[1,3,5,2,6,4,8,7]=>[5,2,1]=>4032
[1,3,5,6,2,4,8,7]=>[3,2,2,1]=>1680
[3,1,2,5,6,8,4,7]=>[5,3]=>2688
[1,3,5,2,6,8,4,7]=>[7,1]=>5760
[1,3,5,6,2,8,4,7]=>[4,3,1]=>3360
[1,3,5,6,8,2,4,7]=>[7,1]=>5760
[3,5,1,2,4,6,7,8]=>[3,2,1,1,1]=>1120
[1,3,5,2,4,6,7,8]=>[4,1,1,1,1]=>420
[1,3,5,6,2,4,7,8]=>[3,2,1,1,1]=>1120
[1,3,5,2,6,7,4,8]=>[6,1,1]=>3360
[1,3,5,6,2,7,4,8]=>[3,3,1,1]=>1120
[1,3,5,6,7,2,4,8]=>[6,1,1]=>3360
[3,1,2,5,6,7,8,4]=>[5,3]=>2688
[1,3,5,6,2,7,8,4]=>[4,3,1]=>3360
[1,3,5,6,7,8,2,4]=>[4,3,1]=>3360
[3,1,6,2,7,4,8,5]=>[5,3]=>2688
[3,6,1,2,7,4,8,5]=>[3,3,2]=>1120
[3,6,1,7,2,4,8,5]=>[6,2]=>3360
[3,6,1,2,7,8,4,5]=>[6,2]=>3360
[3,1,6,7,2,8,4,5]=>[6,2]=>3360
[3,6,1,7,2,8,4,5]=>[4,2,2]=>1260
[3,6,7,1,2,8,4,5]=>[4,4]=>1260
[3,6,1,7,8,2,4,5]=>[2,2,2,2]=>105
[3,6,7,8,1,2,4,5]=>[6,2]=>3360
[3,1,6,2,7,4,5,8]=>[5,2,1]=>4032
[3,6,7,1,2,4,5,8]=>[7,1]=>5760
[3,6,1,2,4,7,5,8]=>[5,2,1]=>4032
[3,1,2,6,4,7,5,8]=>[4,3,1]=>3360
[1,3,2,6,4,7,5,8]=>[4,2,1,1]=>2520
[1,3,6,2,4,7,5,8]=>[6,1,1]=>3360
[1,3,2,6,7,4,5,8]=>[2,2,2,1,1]=>420
[1,3,6,2,7,4,5,8]=>[4,2,1,1]=>2520
[3,1,6,2,4,7,8,5]=>[8]=>5040
[3,6,1,2,4,7,8,5]=>[6,2]=>3360
[3,1,2,6,4,7,8,5]=>[5,3]=>2688
[1,3,6,2,4,7,8,5]=>[7,1]=>5760
[3,1,2,6,7,4,8,5]=>[3,3,2]=>1120
[1,3,2,6,7,4,8,5]=>[3,2,2,1]=>1680
[1,3,6,2,7,4,8,5]=>[4,3,1]=>3360
[1,3,6,7,2,4,8,5]=>[7,1]=>5760
[3,1,2,6,7,8,4,5]=>[5,3]=>2688
[1,3,2,6,7,8,4,5]=>[5,2,1]=>4032
[1,3,6,2,7,8,4,5]=>[7,1]=>5760
[1,3,6,7,8,2,4,5]=>[3,2,2,1]=>1680
[3,1,6,2,8,4,5,7]=>[5,3]=>2688
[3,6,1,2,8,4,5,7]=>[3,3,2]=>1120
[3,1,6,8,2,4,5,7]=>[8]=>5040
[3,6,1,8,2,4,5,7]=>[6,2]=>3360
[3,6,8,1,2,4,5,7]=>[8]=>5040
[3,1,6,2,4,8,5,7]=>[8]=>5040
[3,6,1,2,4,8,5,7]=>[6,2]=>3360
[1,3,2,6,4,8,5,7]=>[5,2,1]=>4032
[1,3,6,2,4,8,5,7]=>[7,1]=>5760
[3,1,2,6,8,4,5,7]=>[3,3,2]=>1120
[1,3,2,6,8,4,5,7]=>[3,2,2,1]=>1680
[3,1,6,2,4,5,8,7]=>[6,2]=>3360
[3,6,1,2,4,5,8,7]=>[4,2,2]=>1260
[3,1,2,6,4,5,8,7]=>[3,3,2]=>1120
[1,3,6,2,4,5,8,7]=>[5,2,1]=>4032
[3,1,2,4,6,5,8,7]=>[3,2,2,1]=>1680
[1,3,4,6,2,5,8,7]=>[5,2,1]=>4032
[3,1,2,4,6,8,5,7]=>[4,3,1]=>3360
[1,3,2,4,6,8,5,7]=>[4,2,1,1]=>2520
[1,3,4,6,8,2,5,7]=>[4,3,1]=>3360
[3,1,6,2,4,5,7,8]=>[6,1,1]=>3360
[3,6,1,2,4,5,7,8]=>[4,2,1,1]=>2520
[1,3,2,6,4,5,7,8]=>[3,2,1,1,1]=>1120
[1,3,6,2,4,5,7,8]=>[5,1,1,1]=>1344
[1,3,4,6,2,5,7,8]=>[5,1,1,1]=>1344
[3,1,2,4,6,7,5,8]=>[3,3,1,1]=>1120
[1,3,4,6,2,7,5,8]=>[6,1,1]=>3360
[1,3,4,6,7,2,5,8]=>[4,2,1,1]=>2520
[3,1,2,4,6,7,8,5]=>[4,3,1]=>3360
[1,3,4,6,7,2,8,5]=>[4,3,1]=>3360
[3,1,7,2,8,4,5,6]=>[8]=>5040
[3,7,1,2,8,4,5,6]=>[6,2]=>3360
[3,1,7,8,2,4,5,6]=>[5,3]=>2688
[3,7,1,8,2,4,5,6]=>[3,3,2]=>1120
[3,7,8,1,2,4,5,6]=>[5,3]=>2688
[3,7,1,2,4,8,5,6]=>[4,2,2]=>1260
[3,1,2,7,4,8,5,6]=>[3,3,2]=>1120
[1,3,2,7,4,8,5,6]=>[3,2,2,1]=>1680
[1,3,7,2,4,8,5,6]=>[5,2,1]=>4032
[3,1,2,7,8,4,5,6]=>[5,3]=>2688
[1,3,7,2,8,4,5,6]=>[7,1]=>5760
[1,3,7,8,2,4,5,6]=>[4,3,1]=>3360
[3,1,7,2,4,5,8,6]=>[8]=>5040
[3,7,1,2,4,5,8,6]=>[6,2]=>3360
[1,3,7,2,4,5,8,6]=>[7,1]=>5760
[3,1,2,4,7,5,8,6]=>[4,3,1]=>3360
[1,3,2,4,7,5,8,6]=>[4,2,1,1]=>2520
[1,3,4,2,7,5,8,6]=>[4,3,1]=>3360
[1,3,4,7,2,5,8,6]=>[7,1]=>5760
[3,1,2,4,7,8,5,6]=>[3,2,2,1]=>1680
[1,3,2,4,7,8,5,6]=>[2,2,2,1,1]=>420
[1,3,4,2,7,8,5,6]=>[3,2,2,1]=>1680
[1,3,4,7,8,2,5,6]=>[7,1]=>5760
[3,1,7,2,4,5,6,8]=>[7,1]=>5760
[3,7,1,2,4,5,6,8]=>[5,2,1]=>4032
[3,1,2,7,4,5,6,8]=>[4,3,1]=>3360
[1,3,2,7,4,5,6,8]=>[4,2,1,1]=>2520
[1,3,7,2,4,5,6,8]=>[6,1,1]=>3360
[3,1,2,4,7,5,6,8]=>[3,3,1,1]=>1120
[1,3,4,7,2,5,6,8]=>[6,1,1]=>3360
[3,1,2,4,5,7,6,8]=>[3,2,1,1,1]=>1120
[3,1,2,4,5,7,8,6]=>[3,3,1,1]=>1120
[1,3,4,5,7,8,2,6]=>[5,2,1]=>4032
[3,1,8,2,4,5,6,7]=>[8]=>5040
[3,8,1,2,4,5,6,7]=>[6,2]=>3360
[3,1,2,8,4,5,6,7]=>[5,3]=>2688
[1,3,2,8,4,5,6,7]=>[5,2,1]=>4032
[1,3,8,2,4,5,6,7]=>[7,1]=>5760
[3,1,2,4,8,5,6,7]=>[4,3,1]=>3360
[1,3,2,4,8,5,6,7]=>[4,2,1,1]=>2520
[1,3,4,2,8,5,6,7]=>[4,3,1]=>3360
[1,3,4,8,2,5,6,7]=>[7,1]=>5760
[3,1,2,4,5,8,6,7]=>[3,3,1,1]=>1120
[1,3,2,4,5,8,6,7]=>[3,2,1,1,1]=>1120
[1,3,4,2,5,8,6,7]=>[3,3,1,1]=>1120
[1,3,4,5,2,8,6,7]=>[4,3,1]=>3360
[1,3,4,5,8,2,6,7]=>[7,1]=>5760
[3,1,2,4,5,6,8,7]=>[3,2,1,1,1]=>1120
[1,3,4,5,6,8,2,7]=>[7,1]=>5760
[4,1,5,2,6,3,8,7]=>[3,3,2]=>1120
[4,5,1,2,6,3,8,7]=>[6,2]=>3360
[4,1,5,6,2,3,8,7]=>[6,2]=>3360
[4,5,1,6,2,3,8,7]=>[4,2,2]=>1260
[4,5,6,1,2,3,8,7]=>[2,2,2,2]=>105
[4,1,5,2,6,8,3,7]=>[5,3]=>2688
[4,5,1,2,6,8,3,7]=>[8]=>5040
[4,1,5,6,2,8,3,7]=>[8]=>5040
[4,5,1,6,2,8,3,7]=>[6,2]=>3360
[4,5,6,1,2,8,3,7]=>[4,2,2]=>1260
[4,1,5,6,8,2,3,7]=>[4,4]=>1260
[4,5,1,6,8,2,3,7]=>[8]=>5040
[4,5,6,1,8,2,3,7]=>[6,2]=>3360
[4,5,6,8,1,2,3,7]=>[8]=>5040
[4,1,5,2,6,3,7,8]=>[3,3,1,1]=>1120
[4,1,5,6,2,3,7,8]=>[6,1,1]=>3360
[4,5,1,6,2,3,7,8]=>[4,2,1,1]=>2520
[4,5,1,2,6,7,3,8]=>[7,1]=>5760
[4,5,1,6,2,7,3,8]=>[5,2,1]=>4032
[4,5,6,1,2,7,3,8]=>[3,2,2,1]=>1680
[4,1,5,6,7,2,3,8]=>[4,3,1]=>3360
[4,5,1,6,7,2,3,8]=>[7,1]=>5760
[4,5,6,1,7,2,3,8]=>[5,2,1]=>4032
[4,1,5,2,6,7,8,3]=>[5,3]=>2688
[4,5,1,2,6,7,8,3]=>[8]=>5040
[4,5,1,6,2,7,8,3]=>[6,2]=>3360
[4,5,6,1,2,7,8,3]=>[4,2,2]=>1260
[4,1,5,6,7,2,8,3]=>[4,4]=>1260
[4,5,1,6,7,2,8,3]=>[8]=>5040
[4,5,6,1,7,2,8,3]=>[6,2]=>3360
[4,5,6,7,1,2,8,3]=>[8]=>5040
[4,1,5,6,7,8,2,3]=>[8]=>5040
[4,5,1,6,7,8,2,3]=>[5,3]=>2688
[4,5,6,1,7,8,2,3]=>[3,3,2]=>1120
[4,5,6,7,1,8,2,3]=>[5,3]=>2688
[4,1,5,2,7,3,8,6]=>[5,3]=>2688
[4,5,1,2,7,3,8,6]=>[8]=>5040
[4,5,1,7,2,3,8,6]=>[6,2]=>3360
[4,1,5,2,7,8,3,6]=>[3,3,2]=>1120
[4,5,1,2,7,8,3,6]=>[6,2]=>3360
[4,1,5,7,2,8,3,6]=>[6,2]=>3360
[4,5,1,7,2,8,3,6]=>[4,2,2]=>1260
[4,5,7,1,2,8,3,6]=>[2,2,2,2]=>105
[4,5,1,7,8,2,3,6]=>[4,4]=>1260
[4,5,7,8,1,2,3,6]=>[6,2]=>3360
[4,1,5,2,7,3,6,8]=>[4,3,1]=>3360
[4,1,5,2,3,7,6,8]=>[3,2,2,1]=>1680
[4,5,1,2,3,7,6,8]=>[5,2,1]=>4032
[4,1,2,5,3,7,6,8]=>[5,2,1]=>4032
[1,4,2,5,3,7,6,8]=>[4,2,1,1]=>2520
[1,4,5,2,3,7,6,8]=>[2,2,2,1,1]=>420
[4,1,2,5,7,3,6,8]=>[7,1]=>5760
[1,4,2,5,7,3,6,8]=>[6,1,1]=>3360
[1,4,5,2,7,3,6,8]=>[4,2,1,1]=>2520
[1,4,5,7,2,3,6,8]=>[6,1,1]=>3360
[4,1,5,2,3,7,8,6]=>[3,3,2]=>1120
[4,1,2,5,3,7,8,6]=>[5,3]=>2688
[1,4,5,2,3,7,8,6]=>[3,2,2,1]=>1680
[4,1,2,5,7,3,8,6]=>[8]=>5040
[1,4,2,5,7,3,8,6]=>[7,1]=>5760
[1,4,5,2,7,3,8,6]=>[5,2,1]=>4032
[1,4,5,7,2,3,8,6]=>[7,1]=>5760
[4,1,2,5,7,8,3,6]=>[6,2]=>3360
[1,4,2,5,7,8,3,6]=>[5,2,1]=>4032
[1,4,5,2,7,8,3,6]=>[3,2,2,1]=>1680
[1,4,5,7,8,2,3,6]=>[7,1]=>5760
[4,1,5,2,8,3,6,7]=>[5,3]=>2688
[4,5,1,8,2,3,6,7]=>[6,2]=>3360
[4,5,8,1,2,3,6,7]=>[4,2,2]=>1260
[4,1,5,2,3,8,6,7]=>[3,3,2]=>1120
[4,5,1,2,3,8,6,7]=>[5,3]=>2688
[4,1,2,5,3,8,6,7]=>[5,3]=>2688
[1,4,2,5,3,8,6,7]=>[4,3,1]=>3360
[1,4,5,2,3,8,6,7]=>[3,2,2,1]=>1680
[4,1,2,5,8,3,6,7]=>[8]=>5040
[1,4,5,2,8,3,6,7]=>[5,2,1]=>4032
[1,4,2,5,3,6,8,7]=>[4,2,1,1]=>2520
[4,1,2,5,6,3,8,7]=>[6,2]=>3360
[1,4,5,2,6,3,8,7]=>[3,2,2,1]=>1680
[4,1,2,5,6,8,3,7]=>[8]=>5040
[1,4,5,2,6,8,3,7]=>[5,2,1]=>4032
[1,4,5,6,8,2,3,7]=>[4,3,1]=>3360
[4,1,5,2,3,6,7,8]=>[3,2,1,1,1]=>1120
[4,1,2,5,3,6,7,8]=>[5,1,1,1]=>1344
[1,4,2,5,3,6,7,8]=>[4,1,1,1,1]=>420
[1,4,5,2,3,6,7,8]=>[2,2,1,1,1,1]=>210
[4,1,2,5,6,3,7,8]=>[6,1,1]=>3360
[1,4,5,2,6,3,7,8]=>[3,2,1,1,1]=>1120
[1,4,5,6,2,3,7,8]=>[5,1,1,1]=>1344
[4,1,2,5,6,7,3,8]=>[7,1]=>5760
[1,4,2,5,6,7,3,8]=>[6,1,1]=>3360
[1,4,5,2,6,7,3,8]=>[4,2,1,1]=>2520
[1,4,5,6,2,7,3,8]=>[6,1,1]=>3360
[1,4,5,6,7,2,3,8]=>[3,3,1,1]=>1120
[4,1,2,5,6,7,8,3]=>[8]=>5040
[1,4,2,5,6,7,8,3]=>[7,1]=>5760
[1,4,5,2,6,7,8,3]=>[5,2,1]=>4032
[1,4,5,6,7,2,8,3]=>[4,3,1]=>3360
[1,4,5,6,7,8,2,3]=>[7,1]=>5760
[4,1,6,2,7,3,8,5]=>[3,3,2]=>1120
[4,1,6,7,2,3,8,5]=>[6,2]=>3360
[4,6,1,2,7,8,3,5]=>[8]=>5040
[4,6,1,7,2,8,3,5]=>[4,4]=>1260
[4,6,7,1,2,8,3,5]=>[4,2,2]=>1260
[4,1,6,7,8,2,3,5]=>[6,2]=>3360
[4,6,1,7,8,2,3,5]=>[4,2,2]=>1260
[4,6,7,1,8,2,3,5]=>[2,2,2,2]=>105
[4,6,7,8,1,2,3,5]=>[4,2,2]=>1260
[4,1,6,2,7,3,5,8]=>[3,2,2,1]=>1680
[4,6,1,2,7,3,5,8]=>[5,2,1]=>4032
[4,1,6,7,2,3,5,8]=>[5,2,1]=>4032
[4,6,1,7,2,3,5,8]=>[7,1]=>5760
[4,6,7,1,2,3,5,8]=>[5,2,1]=>4032
[4,1,6,2,3,7,5,8]=>[4,3,1]=>3360
[4,6,1,2,3,7,5,8]=>[7,1]=>5760
[4,1,2,6,3,7,5,8]=>[7,1]=>5760
[1,4,2,6,3,7,5,8]=>[6,1,1]=>3360
[4,1,2,6,7,3,5,8]=>[5,2,1]=>4032
[1,4,2,6,7,3,5,8]=>[4,2,1,1]=>2520
[1,4,6,2,7,3,5,8]=>[2,2,2,1,1]=>420
[1,4,6,7,2,3,5,8]=>[4,2,1,1]=>2520
[4,1,6,2,3,7,8,5]=>[5,3]=>2688
[4,1,2,6,3,7,8,5]=>[8]=>5040
[1,4,6,2,3,7,8,5]=>[5,2,1]=>4032
[4,1,2,6,7,3,8,5]=>[5,3]=>2688
[1,4,6,2,7,3,8,5]=>[3,2,2,1]=>1680
[1,4,2,6,7,8,3,5]=>[7,1]=>5760
[1,4,6,2,7,8,3,5]=>[5,2,1]=>4032
[1,4,6,7,2,8,3,5]=>[7,1]=>5760
[1,4,6,7,8,2,3,5]=>[5,2,1]=>4032
[4,1,6,2,8,3,5,7]=>[3,3,2]=>1120
[4,6,1,2,8,3,5,7]=>[5,3]=>2688
[4,1,6,8,2,3,5,7]=>[6,2]=>3360
[4,6,1,8,2,3,5,7]=>[8]=>5040
[4,6,8,1,2,3,5,7]=>[6,2]=>3360
[4,1,6,2,3,8,5,7]=>[5,3]=>2688
[4,6,1,2,3,8,5,7]=>[8]=>5040
[4,1,2,6,3,8,5,7]=>[8]=>5040
[1,4,2,6,3,8,5,7]=>[7,1]=>5760
[1,4,6,2,3,8,5,7]=>[5,2,1]=>4032
[1,4,2,6,8,3,5,7]=>[4,3,1]=>3360
[1,4,6,2,8,3,5,7]=>[3,2,2,1]=>1680
[1,4,6,8,2,3,5,7]=>[5,2,1]=>4032
[4,1,6,2,3,5,8,7]=>[3,3,2]=>1120
[4,6,1,2,3,5,8,7]=>[6,2]=>3360
[4,1,2,6,3,5,8,7]=>[6,2]=>3360
[1,4,2,6,3,5,8,7]=>[5,2,1]=>4032
[1,4,6,2,3,5,8,7]=>[3,2,2,1]=>1680
[4,1,2,3,6,5,8,7]=>[4,2,2]=>1260
[1,4,2,3,6,5,8,7]=>[3,2,2,1]=>1680
[1,2,4,6,3,5,8,7]=>[4,2,1,1]=>2520
[4,1,2,3,6,8,5,7]=>[4,4]=>1260
[1,2,4,3,6,8,5,7]=>[4,2,1,1]=>2520
[1,2,4,6,3,8,5,7]=>[6,1,1]=>3360
[1,2,4,6,8,3,5,7]=>[3,3,1,1]=>1120
[4,1,6,2,3,5,7,8]=>[3,3,1,1]=>1120
[4,6,1,2,3,5,7,8]=>[6,1,1]=>3360
[1,4,2,6,3,5,7,8]=>[5,1,1,1]=>1344
[1,4,6,2,3,5,7,8]=>[3,2,1,1,1]=>1120
[4,1,2,3,6,5,7,8]=>[4,2,1,1]=>2520
[1,4,2,3,6,5,7,8]=>[3,2,1,1,1]=>1120
[1,2,4,6,3,5,7,8]=>[4,1,1,1,1]=>420
[4,1,2,3,6,7,5,8]=>[4,3,1]=>3360
[1,4,2,3,6,7,5,8]=>[3,3,1,1]=>1120
[4,1,2,3,6,7,8,5]=>[4,4]=>1260
[1,4,2,3,6,7,8,5]=>[4,3,1]=>3360
[1,2,4,6,7,8,3,5]=>[6,1,1]=>3360
[4,1,7,2,8,3,5,6]=>[5,3]=>2688
[4,7,1,2,8,3,5,6]=>[8]=>5040
[4,1,7,8,2,3,5,6]=>[8]=>5040
[4,7,1,8,2,3,5,6]=>[5,3]=>2688
[4,1,7,2,3,8,5,6]=>[3,3,2]=>1120
[4,7,1,2,3,8,5,6]=>[6,2]=>3360
[1,4,2,7,3,8,5,6]=>[5,2,1]=>4032
[1,4,7,2,3,8,5,6]=>[3,2,2,1]=>1680
[4,1,2,7,8,3,5,6]=>[8]=>5040
[1,4,2,7,8,3,5,6]=>[7,1]=>5760
[1,4,7,2,8,3,5,6]=>[5,2,1]=>4032
[1,4,7,8,2,3,5,6]=>[7,1]=>5760
[4,1,7,2,3,5,8,6]=>[5,3]=>2688
[4,7,1,2,3,5,8,6]=>[8]=>5040
[4,1,2,7,3,5,8,6]=>[8]=>5040
[1,4,2,7,3,5,8,6]=>[7,1]=>5760
[1,4,7,2,3,5,8,6]=>[5,2,1]=>4032
[4,1,2,3,7,5,8,6]=>[4,4]=>1260
[1,4,2,3,7,5,8,6]=>[4,3,1]=>3360
[1,2,4,7,3,5,8,6]=>[6,1,1]=>3360
[4,1,2,3,7,8,5,6]=>[4,2,2]=>1260
[1,4,2,3,7,8,5,6]=>[3,2,2,1]=>1680
[1,2,4,3,7,8,5,6]=>[2,2,2,1,1]=>420
[1,2,4,7,3,8,5,6]=>[4,2,1,1]=>2520
[1,2,4,7,8,3,5,6]=>[6,1,1]=>3360
[4,1,7,2,3,5,6,8]=>[4,3,1]=>3360
[4,7,1,2,3,5,6,8]=>[7,1]=>5760
[4,1,2,7,3,5,6,8]=>[7,1]=>5760
[1,4,2,7,3,5,6,8]=>[6,1,1]=>3360
[1,4,7,2,3,5,6,8]=>[4,2,1,1]=>2520
[4,1,2,3,7,5,6,8]=>[4,3,1]=>3360
[1,4,2,3,7,5,6,8]=>[3,3,1,1]=>1120
[1,2,4,3,7,5,6,8]=>[3,2,1,1,1]=>1120
[1,2,4,7,3,5,6,8]=>[5,1,1,1]=>1344
[4,1,2,3,5,7,6,8]=>[4,2,1,1]=>2520
[1,4,2,3,5,7,6,8]=>[3,2,1,1,1]=>1120
[1,2,4,5,7,3,6,8]=>[5,1,1,1]=>1344
[4,1,2,3,5,7,8,6]=>[4,3,1]=>3360
[1,4,2,3,5,7,8,6]=>[3,3,1,1]=>1120
[1,2,4,5,7,8,3,6]=>[4,2,1,1]=>2520
[4,1,8,2,3,5,6,7]=>[5,3]=>2688
[4,8,1,2,3,5,6,7]=>[8]=>5040
[4,1,2,8,3,5,6,7]=>[8]=>5040
[1,4,2,8,3,5,6,7]=>[7,1]=>5760
[1,4,8,2,3,5,6,7]=>[5,2,1]=>4032
[4,1,2,3,8,5,6,7]=>[4,4]=>1260
[1,4,2,3,8,5,6,7]=>[4,3,1]=>3360
[1,2,4,3,8,5,6,7]=>[4,2,1,1]=>2520
[1,2,4,8,3,5,6,7]=>[6,1,1]=>3360
[4,1,2,3,5,8,6,7]=>[4,3,1]=>3360
[1,4,2,3,5,8,6,7]=>[3,3,1,1]=>1120
[1,2,4,3,5,8,6,7]=>[3,2,1,1,1]=>1120
[1,2,4,5,3,8,6,7]=>[3,3,1,1]=>1120
[1,2,4,5,8,3,6,7]=>[6,1,1]=>3360
[4,1,2,3,5,6,8,7]=>[4,2,1,1]=>2520
[1,4,2,3,5,6,8,7]=>[3,2,1,1,1]=>1120
[1,2,4,5,6,8,3,7]=>[6,1,1]=>3360
[1,4,2,3,5,6,7,8]=>[3,1,1,1,1,1]=>112
[5,1,6,2,7,3,8,4]=>[6,2]=>3360
[5,6,1,2,7,3,8,4]=>[8]=>5040
[5,1,6,7,2,3,8,4]=>[3,3,2]=>1120
[5,6,1,7,2,3,8,4]=>[5,3]=>2688
[5,6,7,1,2,3,8,4]=>[8]=>5040
[5,6,1,2,7,8,3,4]=>[4,4]=>1260
[5,1,6,7,2,8,3,4]=>[5,3]=>2688
[5,6,7,1,2,8,3,4]=>[6,2]=>3360
[5,1,6,7,8,2,3,4]=>[8]=>5040
[5,6,1,7,8,2,3,4]=>[6,2]=>3360
[5,6,7,1,8,2,3,4]=>[4,2,2]=>1260
[5,1,6,2,7,3,4,8]=>[5,2,1]=>4032
[5,6,1,7,2,3,4,8]=>[5,2,1]=>4032
[5,1,6,2,3,7,4,8]=>[7,1]=>5760
[5,1,2,6,3,7,4,8]=>[4,3,1]=>3360
[1,5,2,6,3,7,4,8]=>[3,3,1,1]=>1120
[5,1,2,6,7,3,4,8]=>[7,1]=>5760
[1,5,2,6,7,3,4,8]=>[6,1,1]=>3360
[1,5,6,7,2,3,4,8]=>[2,2,2,1,1]=>420
[5,1,6,2,3,7,8,4]=>[8]=>5040
[5,6,1,2,3,7,8,4]=>[5,3]=>2688
[5,1,2,6,3,7,8,4]=>[4,4]=>1260
[1,5,2,6,3,7,8,4]=>[4,3,1]=>3360
[1,5,6,2,3,7,8,4]=>[7,1]=>5760
[5,1,2,6,7,3,8,4]=>[8]=>5040
[1,5,6,7,2,3,8,4]=>[3,2,2,1]=>1680
[5,1,2,6,7,8,3,4]=>[5,3]=>2688
[1,5,2,6,7,8,3,4]=>[4,3,1]=>3360
[1,5,6,2,7,8,3,4]=>[7,1]=>5760
[1,5,6,7,2,8,3,4]=>[5,2,1]=>4032
[1,5,6,7,8,2,3,4]=>[7,1]=>5760
[5,1,6,2,8,3,4,7]=>[6,2]=>3360
[5,6,1,2,8,3,4,7]=>[8]=>5040
[5,6,1,8,2,3,4,7]=>[5,3]=>2688
[5,6,8,1,2,3,4,7]=>[8]=>5040
[5,1,6,2,3,8,4,7]=>[8]=>5040
[5,6,1,2,3,8,4,7]=>[5,3]=>2688
[5,1,2,6,3,8,4,7]=>[4,4]=>1260
[1,5,2,6,3,8,4,7]=>[4,3,1]=>3360
[1,5,6,2,3,8,4,7]=>[7,1]=>5760
[5,1,2,6,8,3,4,7]=>[8]=>5040
[1,5,2,6,8,3,4,7]=>[7,1]=>5760
[1,5,6,2,8,3,4,7]=>[5,2,1]=>4032
[1,5,6,8,2,3,4,7]=>[3,2,2,1]=>1680
[5,1,6,2,3,4,8,7]=>[6,2]=>3360
[5,6,1,2,3,4,8,7]=>[3,3,2]=>1120
[1,5,2,6,3,4,8,7]=>[3,2,2,1]=>1680
[1,5,6,2,3,4,8,7]=>[5,2,1]=>4032
[1,5,2,3,6,4,8,7]=>[5,2,1]=>4032
[1,2,5,3,6,4,8,7]=>[4,2,1,1]=>2520
[5,1,2,3,6,8,4,7]=>[8]=>5040
[1,5,2,3,6,8,4,7]=>[7,1]=>5760
[1,2,5,6,3,8,4,7]=>[4,2,1,1]=>2520
[1,2,5,6,8,3,4,7]=>[6,1,1]=>3360
[5,1,6,2,3,4,7,8]=>[6,1,1]=>3360
[5,1,2,6,3,4,7,8]=>[4,2,1,1]=>2520
[1,5,2,6,3,4,7,8]=>[3,2,1,1,1]=>1120
[1,5,6,2,3,4,7,8]=>[5,1,1,1]=>1344
[5,1,2,3,6,4,7,8]=>[6,1,1]=>3360
[1,5,2,3,6,4,7,8]=>[5,1,1,1]=>1344
[1,2,5,3,6,4,7,8]=>[4,1,1,1,1]=>420
[1,2,5,6,3,4,7,8]=>[2,2,1,1,1,1]=>210
[5,1,2,3,6,7,4,8]=>[7,1]=>5760
[1,5,2,3,6,7,4,8]=>[6,1,1]=>3360
[1,2,5,3,6,7,4,8]=>[5,1,1,1]=>1344
[1,2,5,6,3,7,4,8]=>[3,2,1,1,1]=>1120
[5,1,2,3,6,7,8,4]=>[8]=>5040
[1,5,2,3,6,7,8,4]=>[7,1]=>5760
[1,2,5,3,6,7,8,4]=>[6,1,1]=>3360
[1,2,5,6,3,7,8,4]=>[4,2,1,1]=>2520
[1,2,5,6,7,3,8,4]=>[6,1,1]=>3360
[1,2,5,6,7,8,3,4]=>[3,3,1,1]=>1120
[5,1,7,2,8,3,4,6]=>[8]=>5040
[5,7,1,2,8,3,4,6]=>[5,3]=>2688
[5,1,7,8,2,3,4,6]=>[5,3]=>2688
[5,7,1,8,2,3,4,6]=>[8]=>5040
[5,7,8,1,2,3,4,6]=>[5,3]=>2688
[5,1,2,7,3,8,4,6]=>[4,2,2]=>1260
[1,5,2,7,3,8,4,6]=>[3,2,2,1]=>1680
[1,5,7,2,3,8,4,6]=>[5,2,1]=>4032
[5,1,2,7,8,3,4,6]=>[6,2]=>3360
[1,5,2,7,8,3,4,6]=>[5,2,1]=>4032
[1,5,7,2,8,3,4,6]=>[7,1]=>5760
[1,5,7,8,2,3,4,6]=>[5,2,1]=>4032
[5,1,7,2,3,4,8,6]=>[8]=>5040
[5,7,1,2,3,4,8,6]=>[5,3]=>2688
[5,1,2,7,3,4,8,6]=>[4,4]=>1260
[1,5,2,7,3,4,8,6]=>[4,3,1]=>3360
[1,5,7,2,3,4,8,6]=>[7,1]=>5760
[5,1,2,3,7,4,8,6]=>[8]=>5040
[1,5,2,3,7,4,8,6]=>[7,1]=>5760
[1,2,5,3,7,4,8,6]=>[6,1,1]=>3360
[1,2,5,7,3,4,8,6]=>[4,2,1,1]=>2520
[5,1,2,3,7,8,4,6]=>[6,2]=>3360
[1,5,2,3,7,8,4,6]=>[5,2,1]=>4032
[1,2,5,3,7,8,4,6]=>[4,2,1,1]=>2520
[1,2,5,7,3,8,4,6]=>[2,2,2,1,1]=>420
[1,2,5,7,8,3,4,6]=>[4,2,1,1]=>2520
[5,1,7,2,3,4,6,8]=>[7,1]=>5760
[5,7,1,2,3,4,6,8]=>[4,3,1]=>3360
[1,5,2,7,3,4,6,8]=>[3,3,1,1]=>1120
[1,5,2,3,7,4,6,8]=>[6,1,1]=>3360
[1,2,5,3,7,4,6,8]=>[5,1,1,1]=>1344
[1,2,5,7,3,4,6,8]=>[3,2,1,1,1]=>1120
[1,5,2,3,4,7,6,8]=>[4,2,1,1]=>2520
[1,2,5,3,4,7,6,8]=>[3,2,1,1,1]=>1120
[1,2,3,5,7,4,6,8]=>[4,1,1,1,1]=>420
[5,1,2,3,4,7,8,6]=>[5,3]=>2688
[1,5,2,3,4,7,8,6]=>[4,3,1]=>3360
[1,2,5,3,4,7,8,6]=>[3,3,1,1]=>1120
[1,2,3,5,7,4,8,6]=>[5,1,1,1]=>1344
[1,2,3,5,7,8,4,6]=>[3,2,1,1,1]=>1120
[5,8,1,2,3,4,6,7]=>[5,3]=>2688
[5,1,2,8,3,4,6,7]=>[4,4]=>1260
[1,5,2,8,3,4,6,7]=>[4,3,1]=>3360
[1,5,8,2,3,4,6,7]=>[7,1]=>5760
[5,1,2,3,8,4,6,7]=>[8]=>5040
[1,5,2,3,8,4,6,7]=>[7,1]=>5760
[1,2,5,3,8,4,6,7]=>[6,1,1]=>3360
[1,2,5,8,3,4,6,7]=>[4,2,1,1]=>2520
[5,1,2,3,4,8,6,7]=>[5,3]=>2688
[1,5,2,3,4,8,6,7]=>[4,3,1]=>3360
[1,2,5,3,4,8,6,7]=>[3,3,1,1]=>1120
[1,2,3,5,4,8,6,7]=>[3,2,1,1,1]=>1120
[1,2,3,5,8,4,6,7]=>[5,1,1,1]=>1344
[5,1,2,3,4,6,8,7]=>[5,2,1]=>4032
[1,5,2,3,4,6,8,7]=>[4,2,1,1]=>2520
[1,2,5,3,4,6,8,7]=>[3,2,1,1,1]=>1120
[1,2,3,5,6,8,4,7]=>[5,1,1,1]=>1344
[1,5,2,3,4,6,7,8]=>[4,1,1,1,1]=>420
[1,2,5,3,4,6,7,8]=>[3,1,1,1,1,1]=>112
[6,1,7,2,8,3,4,5]=>[6,2]=>3360
[6,1,7,8,2,3,4,5]=>[8]=>5040
[6,7,1,8,2,3,4,5]=>[5,3]=>2688
[6,1,7,2,3,8,4,5]=>[8]=>5040
[6,7,1,2,3,8,4,5]=>[5,3]=>2688
[6,1,2,7,3,8,4,5]=>[6,2]=>3360
[1,6,2,7,3,8,4,5]=>[5,2,1]=>4032
[1,6,7,2,3,8,4,5]=>[7,1]=>5760
[1,6,2,7,8,3,4,5]=>[3,2,2,1]=>1680
[1,6,7,2,8,3,4,5]=>[5,2,1]=>4032
[1,6,7,8,2,3,4,5]=>[7,1]=>5760
[6,1,7,2,3,4,8,5]=>[4,4]=>1260
[6,7,1,2,3,4,8,5]=>[8]=>5040
[6,1,2,7,3,4,8,5]=>[8]=>5040
[1,6,2,7,3,4,8,5]=>[7,1]=>5760
[6,1,2,3,7,4,8,5]=>[5,3]=>2688
[1,6,2,3,7,4,8,5]=>[4,3,1]=>3360
[1,2,6,3,7,4,8,5]=>[3,3,1,1]=>1120
[1,2,6,7,3,4,8,5]=>[6,1,1]=>3360
[6,1,2,3,7,8,4,5]=>[8]=>5040
[1,6,2,3,7,8,4,5]=>[7,1]=>5760
[1,2,6,3,7,8,4,5]=>[6,1,1]=>3360
[1,2,6,7,3,8,4,5]=>[4,2,1,1]=>2520
[1,2,6,7,8,3,4,5]=>[2,2,2,1,1]=>420
[6,1,7,2,3,4,5,8]=>[4,3,1]=>3360
[6,1,2,7,3,4,5,8]=>[7,1]=>5760
[1,6,2,7,3,4,5,8]=>[6,1,1]=>3360
[1,6,7,2,3,4,5,8]=>[3,3,1,1]=>1120
[6,1,2,3,7,4,5,8]=>[5,2,1]=>4032
[1,6,2,3,7,4,5,8]=>[4,2,1,1]=>2520
[1,2,6,3,7,4,5,8]=>[3,2,1,1,1]=>1120
[1,2,6,7,3,4,5,8]=>[5,1,1,1]=>1344
[6,1,2,3,4,7,5,8]=>[7,1]=>5760
[1,6,2,3,4,7,5,8]=>[6,1,1]=>3360
[1,2,6,3,4,7,5,8]=>[5,1,1,1]=>1344
[1,2,3,6,4,7,5,8]=>[4,1,1,1,1]=>420
[1,2,3,6,7,4,5,8]=>[2,2,1,1,1,1]=>210
[6,1,2,3,4,7,8,5]=>[8]=>5040
[1,6,2,3,4,7,8,5]=>[7,1]=>5760
[1,2,6,3,4,7,8,5]=>[6,1,1]=>3360
[1,2,3,6,4,7,8,5]=>[5,1,1,1]=>1344
[1,2,3,6,7,4,8,5]=>[3,2,1,1,1]=>1120
[1,2,3,6,7,8,4,5]=>[5,1,1,1]=>1344
[6,1,8,2,3,4,5,7]=>[4,4]=>1260
[6,8,1,2,3,4,5,7]=>[8]=>5040
[6,1,2,8,3,4,5,7]=>[8]=>5040
[1,6,2,8,3,4,5,7]=>[7,1]=>5760
[1,6,8,2,3,4,5,7]=>[4,3,1]=>3360
[6,1,2,3,8,4,5,7]=>[5,3]=>2688
[1,6,2,3,8,4,5,7]=>[4,3,1]=>3360
[1,2,6,3,8,4,5,7]=>[3,3,1,1]=>1120
[1,2,6,8,3,4,5,7]=>[6,1,1]=>3360
[6,1,2,3,4,8,5,7]=>[8]=>5040
[1,6,2,3,4,8,5,7]=>[7,1]=>5760
[1,2,6,3,4,8,5,7]=>[6,1,1]=>3360
[1,2,3,6,4,8,5,7]=>[5,1,1,1]=>1344
[1,2,3,6,8,4,5,7]=>[3,2,1,1,1]=>1120
[6,1,2,3,4,5,8,7]=>[6,2]=>3360
[1,6,2,3,4,5,8,7]=>[5,2,1]=>4032
[1,2,6,3,4,5,8,7]=>[4,2,1,1]=>2520
[1,2,3,6,4,5,8,7]=>[3,2,1,1,1]=>1120
[1,2,3,4,6,8,5,7]=>[4,1,1,1,1]=>420
[1,6,2,3,4,5,7,8]=>[5,1,1,1]=>1344
[1,2,6,3,4,5,7,8]=>[4,1,1,1,1]=>420
[1,2,3,6,4,5,7,8]=>[3,1,1,1,1,1]=>112
[7,1,8,2,3,4,5,6]=>[8]=>5040
[7,1,2,8,3,4,5,6]=>[5,3]=>2688
[1,7,2,8,3,4,5,6]=>[4,3,1]=>3360
[1,7,8,2,3,4,5,6]=>[7,1]=>5760
[7,1,2,3,8,4,5,6]=>[8]=>5040
[1,7,2,3,8,4,5,6]=>[7,1]=>5760
[1,2,7,3,8,4,5,6]=>[6,1,1]=>3360
[1,2,7,8,3,4,5,6]=>[3,3,1,1]=>1120
[7,1,2,3,4,8,5,6]=>[6,2]=>3360
[1,7,2,3,4,8,5,6]=>[5,2,1]=>4032
[1,2,7,3,4,8,5,6]=>[4,2,1,1]=>2520
[1,2,3,7,4,8,5,6]=>[3,2,1,1,1]=>1120
[1,2,3,7,8,4,5,6]=>[5,1,1,1]=>1344
[7,1,2,3,4,5,8,6]=>[8]=>5040
[1,7,2,3,4,5,8,6]=>[7,1]=>5760
[1,2,7,3,4,5,8,6]=>[6,1,1]=>3360
[1,2,3,7,4,5,8,6]=>[5,1,1,1]=>1344
[1,2,3,4,7,5,8,6]=>[4,1,1,1,1]=>420
[1,2,3,4,7,8,5,6]=>[2,2,1,1,1,1]=>210
[1,7,2,3,4,5,6,8]=>[6,1,1]=>3360
[1,2,7,3,4,5,6,8]=>[5,1,1,1]=>1344
[1,2,3,7,4,5,6,8]=>[4,1,1,1,1]=>420
[1,2,3,4,7,5,6,8]=>[3,1,1,1,1,1]=>112
[1,8,2,3,4,5,6,7]=>[7,1]=>5760
[1,2,8,3,4,5,6,7]=>[6,1,1]=>3360
[1,2,3,8,4,5,6,7]=>[5,1,1,1]=>1344
[1,2,3,4,8,5,6,7]=>[4,1,1,1,1]=>420
[1,2,3,4,5,8,6,7]=>[3,1,1,1,1,1]=>112
[5,3,2,6,1,4,8,7]=>[2,2,2,2]=>105
[7,3,2,5,4,8,1,6]=>[2,2,2,2]=>105
[8,4,5,2,3,7,6,1]=>[2,2,2,2]=>105
[7,4,5,2,3,8,1,6]=>[2,2,2,2]=>105
[6,4,5,2,3,1,8,7]=>[2,2,2,2]=>105
[5,4,6,2,1,3,8,7]=>[2,2,2,2]=>105
[3,6,1,5,4,2,8,7]=>[2,2,2,2]=>105
[4,6,5,1,3,2,8,7]=>[2,2,2,2]=>105
[5,6,4,3,1,2,8,7]=>[2,2,2,2]=>105
[7,5,4,3,2,8,1,6]=>[2,2,2,2]=>105
[8,6,4,3,7,2,5,1]=>[2,2,2,2]=>105
[7,6,4,3,8,2,1,5]=>[2,2,2,2]=>105
[6,7,4,3,8,1,2,5]=>[2,2,2,2]=>105
[5,7,4,3,1,8,2,6]=>[2,2,2,2]=>105
[4,7,5,1,3,8,2,6]=>[2,2,2,2]=>105
[3,7,1,5,4,8,2,6]=>[2,2,2,2]=>105
[2,1,7,5,4,8,3,6]=>[2,2,2,2]=>105
[3,8,1,5,4,7,6,2]=>[2,2,2,2]=>105
[4,8,5,1,3,7,6,2]=>[2,2,2,2]=>105
[5,8,4,3,1,7,6,2]=>[2,2,2,2]=>105
[6,8,4,3,7,1,5,2]=>[2,2,2,2]=>105
[7,8,4,3,6,5,1,2]=>[2,2,2,2]=>105
[6,8,5,7,3,1,4,2]=>[2,2,2,2]=>105
[5,8,6,7,1,3,4,2]=>[2,2,2,2]=>105
[4,8,6,1,7,3,5,2]=>[2,2,2,2]=>105
[3,8,1,6,7,4,5,2]=>[2,2,2,2]=>105
[2,1,8,6,7,4,5,3]=>[2,2,2,2]=>105
[2,1,7,6,8,4,3,5]=>[2,2,2,2]=>105
[3,7,1,6,8,4,2,5]=>[2,2,2,2]=>105
[4,7,6,1,8,3,2,5]=>[2,2,2,2]=>105
[5,7,6,8,1,3,2,4]=>[2,2,2,2]=>105
[5,4,7,2,1,8,3,6]=>[2,2,2,2]=>105
[6,4,7,2,8,1,3,5]=>[2,2,2,2]=>105
[7,4,6,2,8,3,1,5]=>[2,2,2,2]=>105
[8,4,6,2,7,3,5,1]=>[2,2,2,2]=>105
[8,3,2,6,7,4,5,1]=>[2,2,2,2]=>105
[7,3,2,6,8,4,1,5]=>[2,2,2,2]=>105
[6,3,2,7,8,1,4,5]=>[2,2,2,2]=>105
[5,3,2,7,1,8,4,6]=>[2,2,2,2]=>105
[4,3,2,1,7,8,5,6]=>[2,2,2,2]=>105
[3,4,1,2,8,7,6,5]=>[2,2,2,2]=>105
[5,3,2,8,1,7,6,4]=>[2,2,2,2]=>105
[6,3,2,8,7,1,5,4]=>[2,2,2,2]=>105
[7,3,2,8,6,5,1,4]=>[2,2,2,2]=>105
[8,4,7,2,6,5,3,1]=>[2,2,2,2]=>105
[7,4,8,2,6,5,1,3]=>[2,2,2,2]=>105
[6,4,8,2,7,1,5,3]=>[2,2,2,2]=>105
[5,4,8,2,1,7,6,3]=>[2,2,2,2]=>105
[4,5,8,1,2,7,6,3]=>[2,2,2,2]=>105
[3,5,1,8,2,7,6,4]=>[2,2,2,2]=>105
[2,1,5,8,3,7,6,4]=>[2,2,2,2]=>105
[2,1,6,8,7,3,5,4]=>[2,2,2,2]=>105
[3,6,1,8,7,2,5,4]=>[2,2,2,2]=>105
[4,6,8,1,7,2,5,3]=>[2,2,2,2]=>105
[5,6,8,7,1,2,4,3]=>[2,2,2,2]=>105
[6,5,8,7,2,1,4,3]=>[2,2,2,2]=>105
[7,5,8,6,2,4,1,3]=>[2,2,2,2]=>105
[8,5,7,6,2,4,3,1]=>[2,2,2,2]=>105
[5,7,8,6,1,4,2,3]=>[2,2,2,2]=>105
[4,7,8,1,6,5,2,3]=>[2,2,2,2]=>105
[3,7,1,8,6,5,2,4]=>[2,2,2,2]=>105
[2,1,7,8,6,5,3,4]=>[2,2,2,2]=>105
[3,8,1,7,6,5,4,2]=>[2,2,2,2]=>105
[4,8,7,1,6,5,3,2]=>[2,2,2,2]=>105
[5,8,7,6,1,4,3,2]=>[2,2,2,2]=>105
[6,8,7,5,4,1,3,2]=>[2,2,2,2]=>105
[2,1,4,3,6,5,8,7,10,9]=>[2,2,2,2,2]=>945
[3,4,1,2,6,5,8,7,10,9]=>[2,2,2,2,2]=>945
[4,3,2,1,6,5,8,7,10,9]=>[2,2,2,2,2]=>945
[6,5,4,3,2,1,8,7,10,9]=>[2,2,2,2,2]=>945
[8,9,5,6,3,4,10,1,2,7]=>[2,2,2,2,2]=>945
[4,3,2,1,8,7,6,5,10,9]=>[2,2,2,2,2]=>945
[8,7,6,5,4,3,2,1,10,9]=>[2,2,2,2,2]=>945
[9,7,6,5,4,3,2,10,1,8]=>[2,2,2,2,2]=>945
[10,8,9,6,7,4,5,2,3,1]=>[2,2,2,2,2]=>945
[6,7,8,9,10,1,2,3,4,5]=>[2,2,2,2,2]=>945
[7,3,2,8,9,10,1,4,5,6]=>[2,2,2,2,2]=>945
[8,5,4,3,2,9,10,1,6,7]=>[2,2,2,2,2]=>945
[6,5,4,3,2,1,10,9,8,7]=>[2,2,2,2,2]=>945
[9,7,5,10,3,8,2,6,1,4]=>[2,2,2,2,2]=>945
[4,3,2,1,10,9,8,7,6,5]=>[2,2,2,2,2]=>945
[2,1,10,9,8,7,6,5,4,3]=>[2,2,2,2,2]=>945
[9,10,8,7,6,5,4,3,1,2]=>[2,2,2,2,2]=>945
[10,9,8,7,6,5,4,3,2,1]=>[2,2,2,2,2]=>945
[3,2,5,1,4,6,7,8]=>[4,1,1,1,1]=>420
[4,2,5,1,3,6,7,8]=>[2,2,1,1,1,1]=>210
[5,2,4,1,3,6,7,8]=>[4,1,1,1,1]=>420
[3,2,6,1,4,5,7,8]=>[5,1,1,1]=>1344
[5,3,6,1,2,4,7,8]=>[6,1,1]=>3360
[6,3,5,1,2,4,7,8]=>[3,3,1,1]=>1120
[5,3,7,1,2,4,6,8]=>[7,1]=>5760
[5,4,7,1,2,3,6,8]=>[4,3,1]=>3360
[6,2,7,1,3,4,5,8]=>[3,3,1,1]=>1120
[6,3,7,1,2,4,5,8]=>[4,3,1]=>3360
[6,4,7,1,2,3,5,8]=>[7,1]=>5760
[7,3,5,1,2,4,6,8]=>[4,3,1]=>3360
[7,3,6,1,2,4,5,8]=>[7,1]=>5760
[7,4,6,1,2,3,5,8]=>[5,2,1]=>4032
[3,2,8,1,4,5,6,7]=>[7,1]=>5760
[4,2,8,1,3,5,6,7]=>[5,2,1]=>4032
[5,4,8,1,2,3,6,7]=>[4,4]=>1260
[6,2,8,1,3,4,5,7]=>[4,3,1]=>3360
[6,3,8,1,2,4,5,7]=>[5,3]=>2688
[6,4,8,1,2,3,5,7]=>[8]=>5040
[7,2,8,1,3,4,5,6]=>[7,1]=>5760
[7,3,8,1,2,4,5,6]=>[8]=>5040
[7,4,8,1,2,3,5,6]=>[5,3]=>2688
[7,5,8,1,2,3,4,6]=>[3,3,2]=>1120
[8,2,4,1,3,5,6,7]=>[7,1]=>5760
[8,3,5,1,2,4,6,7]=>[5,3]=>2688
[8,3,6,1,2,4,5,7]=>[8]=>5040
[8,3,7,1,2,4,5,6]=>[4,4]=>1260
[8,4,7,1,2,3,5,6]=>[8]=>5040
[8,5,7,1,2,3,4,6]=>[6,2]=>3360
[3,2,5,7,1,4,6,8]=>[3,3,1,1]=>1120
[4,2,5,7,1,3,6,8]=>[6,1,1]=>3360
[4,2,6,7,1,3,5,8]=>[4,2,1,1]=>2520
[5,2,6,7,1,3,4,8]=>[2,2,2,1,1]=>420
[5,3,6,7,1,2,4,8]=>[3,2,2,1]=>1680
[6,2,5,7,1,3,4,8]=>[4,2,1,1]=>2520
[6,3,5,7,1,2,4,8]=>[5,2,1]=>4032
[4,2,5,8,1,3,6,7]=>[7,1]=>5760
[5,2,4,8,1,3,6,7]=>[5,2,1]=>4032
[4,2,6,8,1,3,5,7]=>[5,2,1]=>4032
[5,2,6,8,1,3,4,7]=>[3,2,2,1]=>1680
[6,2,4,8,1,3,5,7]=>[7,1]=>5760
[6,3,4,8,1,2,5,7]=>[8]=>5040
[6,3,5,8,1,2,4,7]=>[5,3]=>2688
[6,4,5,8,1,2,3,7]=>[8]=>5040
[3,2,7,8,1,4,5,6]=>[4,3,1]=>3360
[4,3,7,8,1,2,5,6]=>[8]=>5040
[5,4,7,8,1,2,3,6]=>[4,2,2]=>1260
[6,2,7,8,1,3,4,5]=>[7,1]=>5760
[6,3,7,8,1,2,4,5]=>[8]=>5040
[6,4,7,8,1,2,3,5]=>[6,2]=>3360
[7,2,4,8,1,3,5,6]=>[4,3,1]=>3360
[7,3,4,8,1,2,5,6]=>[5,3]=>2688
[7,3,5,8,1,2,4,6]=>[8]=>5040
[7,4,5,8,1,2,3,6]=>[4,4]=>1260
[7,4,6,8,1,2,3,5]=>[8]=>5040
[8,3,4,6,1,2,5,7]=>[4,4]=>1260
[8,3,5,6,1,2,4,7]=>[8]=>5040
[8,3,5,7,1,2,4,6]=>[6,2]=>3360
[8,2,6,7,1,3,4,5]=>[3,2,2,1]=>1680
[3,6,2,5,1,4,7,8]=>[6,1,1]=>3360
[4,6,2,5,1,3,7,8]=>[3,3,1,1]=>1120
[4,6,3,5,1,2,7,8]=>[3,2,1,1,1]=>1120
[5,6,2,4,1,3,7,8]=>[3,2,1,1,1]=>1120
[3,7,2,5,1,4,6,8]=>[7,1]=>5760
[4,7,3,5,1,2,6,8]=>[3,3,1,1]=>1120
[5,7,2,4,1,3,6,8]=>[4,2,1,1]=>2520
[3,7,2,6,1,4,5,8]=>[5,2,1]=>4032
[4,7,3,6,1,2,5,8]=>[6,1,1]=>3360
[4,8,2,5,1,3,6,7]=>[5,3]=>2688
[5,8,2,4,1,3,6,7]=>[5,2,1]=>4032
[5,8,3,4,1,2,6,7]=>[4,2,1,1]=>2520
[3,8,2,6,1,4,5,7]=>[6,2]=>3360
[5,8,3,6,1,2,4,7]=>[5,2,1]=>4032
[5,8,4,6,1,2,3,7]=>[6,2]=>3360
[6,8,3,5,1,2,4,7]=>[7,1]=>5760
[3,8,2,7,1,4,5,6]=>[8]=>5040
[4,8,2,7,1,3,5,6]=>[4,4]=>1260
[4,8,3,7,1,2,5,6]=>[4,3,1]=>3360
[5,8,2,7,1,3,4,6]=>[4,2,2]=>1260
[5,8,3,7,1,2,4,6]=>[3,2,2,1]=>1680
[5,8,4,7,1,2,3,6]=>[3,3,2]=>1120
[6,8,2,7,1,3,4,5]=>[6,2]=>3360
[6,8,5,7,1,2,3,4]=>[8]=>5040
[7,8,2,4,1,3,5,6]=>[4,3,1]=>3360
[7,8,2,5,1,3,4,6]=>[4,4]=>1260
[7,8,3,5,1,2,4,6]=>[4,3,1]=>3360
[7,8,4,6,1,2,3,5]=>[8]=>5040
[4,3,2,6,1,5,7,8]=>[4,2,1,1]=>2520
[5,3,2,6,1,4,7,8]=>[2,2,2,1,1]=>420
[5,4,2,6,1,3,7,8]=>[4,2,1,1]=>2520
[6,3,2,5,1,4,7,8]=>[4,2,1,1]=>2520
[6,5,2,4,1,3,7,8]=>[5,1,1,1]=>1344
[4,3,2,7,1,5,6,8]=>[5,2,1]=>4032
[5,3,2,7,1,4,6,8]=>[3,2,2,1]=>1680
[6,3,2,7,1,4,5,8]=>[5,2,1]=>4032
[6,4,2,7,1,3,5,8]=>[7,1]=>5760
[6,4,3,7,1,2,5,8]=>[6,1,1]=>3360
[6,5,2,7,1,3,4,8]=>[5,2,1]=>4032
[6,5,3,7,1,2,4,8]=>[4,2,1,1]=>2520
[7,3,2,5,1,4,6,8]=>[5,2,1]=>4032
[7,4,2,5,1,3,6,8]=>[7,1]=>5760
[7,3,2,6,1,4,5,8]=>[3,2,2,1]=>1680
[7,4,3,6,1,2,5,8]=>[3,3,1,1]=>1120
[7,6,3,5,1,2,4,8]=>[4,2,1,1]=>2520
[4,3,2,8,1,5,6,7]=>[6,2]=>3360
[6,4,2,8,1,3,5,7]=>[8]=>5040
[6,4,3,8,1,2,5,7]=>[7,1]=>5760
[6,5,2,8,1,3,4,7]=>[5,3]=>2688
[6,5,3,8,1,2,4,7]=>[4,3,1]=>3360
[7,3,2,8,1,4,5,6]=>[3,3,2]=>1120
[7,4,2,8,1,3,5,6]=>[5,3]=>2688
[7,4,3,8,1,2,5,6]=>[4,3,1]=>3360
[7,5,3,8,1,2,4,6]=>[7,1]=>5760
[7,5,4,8,1,2,3,6]=>[8]=>5040
[7,6,2,8,1,3,4,5]=>[5,3]=>2688
[8,3,2,5,1,4,6,7]=>[6,2]=>3360
[8,4,2,5,1,3,6,7]=>[8]=>5040
[8,3,2,6,1,4,5,7]=>[4,2,2]=>1260
[8,4,2,6,1,3,5,7]=>[4,4]=>1260
[8,5,3,6,1,2,4,7]=>[7,1]=>5760
[8,6,2,4,1,3,5,7]=>[4,3,1]=>3360
[8,6,2,5,1,3,4,7]=>[5,3]=>2688
[8,3,2,7,1,4,5,6]=>[6,2]=>3360
[8,4,2,7,1,3,5,6]=>[8]=>5040
[8,4,3,7,1,2,5,6]=>[7,1]=>5760
[8,5,2,7,1,3,4,6]=>[6,2]=>3360
[8,5,3,7,1,2,4,6]=>[5,2,1]=>4032
[8,6,3,7,1,2,4,5]=>[3,2,2,1]=>1680
[8,7,2,4,1,3,5,6]=>[7,1]=>5760
[8,7,2,5,1,3,4,6]=>[8]=>5040
[8,7,3,5,1,2,4,6]=>[7,1]=>5760
[8,7,2,6,1,3,4,5]=>[5,3]=>2688
[8,7,3,6,1,2,4,5]=>[4,3,1]=>3360
[8,7,4,6,1,2,3,5]=>[5,3]=>2688
[3,6,2,5,8,1,4,7]=>[4,4]=>1260
[5,6,2,4,8,1,3,7]=>[7,1]=>5760
[4,7,2,5,8,1,3,6]=>[5,3]=>2688
[4,7,3,5,8,1,2,6]=>[5,2,1]=>4032
[5,7,2,4,8,1,3,6]=>[4,3,1]=>3360
[5,7,3,4,8,1,2,6]=>[4,2,1,1]=>2520
[4,7,3,6,8,1,2,5]=>[3,2,2,1]=>1680
[5,7,2,6,8,1,3,4]=>[5,3]=>2688
[5,7,4,6,8,1,2,3]=>[6,2]=>3360
[6,7,3,4,8,1,2,5]=>[2,2,2,1,1]=>420
[6,7,3,5,8,1,2,4]=>[3,2,2,1]=>1680
[3,8,2,5,7,1,4,6]=>[5,3]=>2688
[5,8,2,4,7,1,3,6]=>[7,1]=>5760
[3,8,2,6,7,1,4,5]=>[8]=>5040
[5,8,2,6,7,1,3,4]=>[8]=>5040
[5,8,3,6,7,1,2,4]=>[7,1]=>5760
[6,8,2,5,7,1,3,4]=>[6,2]=>3360
[6,8,4,5,7,1,2,3]=>[6,2]=>3360
[7,8,2,4,6,1,3,5]=>[7,1]=>5760
[7,8,3,4,6,1,2,5]=>[6,1,1]=>3360
[7,8,2,5,6,1,3,4]=>[8]=>5040
[7,8,3,5,6,1,2,4]=>[7,1]=>5760
[4,3,2,6,8,1,5,7]=>[3,3,2]=>1120
[5,3,2,6,8,1,4,7]=>[6,2]=>3360
[5,4,2,6,8,1,3,7]=>[8]=>5040
[5,4,3,6,8,1,2,7]=>[7,1]=>5760
[6,3,2,5,8,1,4,7]=>[4,2,2]=>1260
[6,4,3,5,8,1,2,7]=>[5,2,1]=>4032
[6,5,2,4,8,1,3,7]=>[5,2,1]=>4032
[4,3,2,7,8,1,5,6]=>[6,2]=>3360
[5,4,2,7,8,1,3,6]=>[4,4]=>1260
[5,4,3,7,8,1,2,6]=>[4,3,1]=>3360
[6,4,2,7,8,1,3,5]=>[4,2,2]=>1260
[6,4,3,7,8,1,2,5]=>[3,2,2,1]=>1680
[6,5,2,7,8,1,3,4]=>[6,2]=>3360
[7,4,2,5,8,1,3,6]=>[8]=>5040
[7,4,3,5,8,1,2,6]=>[7,1]=>5760
[7,5,2,6,8,1,3,4]=>[8]=>5040
[7,5,3,6,8,1,2,4]=>[7,1]=>5760
[7,6,2,4,8,1,3,5]=>[5,2,1]=>4032
[7,6,3,5,8,1,2,4]=>[4,3,1]=>3360
[8,3,2,5,7,1,4,6]=>[3,3,2]=>1120
[8,4,2,5,7,1,3,6]=>[5,3]=>2688
[8,5,2,4,7,1,3,6]=>[4,3,1]=>3360
[8,3,2,6,7,1,4,5]=>[6,2]=>3360
[8,5,2,6,7,1,3,4]=>[4,4]=>1260
[8,5,3,6,7,1,2,4]=>[4,3,1]=>3360
[8,6,2,4,7,1,3,5]=>[7,1]=>5760
[8,6,2,5,7,1,3,4]=>[8]=>5040
[8,6,3,5,7,1,2,4]=>[7,1]=>5760
[8,7,2,4,6,1,3,5]=>[4,3,1]=>3360
[8,7,3,4,6,1,2,5]=>[4,2,1,1]=>2520
[8,7,2,5,6,1,3,4]=>[5,3]=>2688
[4,3,7,2,6,1,5,8]=>[7,1]=>5760
[5,3,7,2,6,1,4,8]=>[4,3,1]=>3360
[5,4,7,2,6,1,3,8]=>[3,2,2,1]=>1680
[6,3,7,2,5,1,4,8]=>[4,2,1,1]=>2520
[6,4,7,2,5,1,3,8]=>[2,2,2,1,1]=>420
[7,3,6,2,5,1,4,8]=>[6,1,1]=>3360
[4,3,8,2,6,1,5,7]=>[8]=>5040
[5,3,8,2,6,1,4,7]=>[5,3]=>2688
[5,4,8,2,6,1,3,7]=>[3,3,2]=>1120
[5,4,8,3,6,1,2,7]=>[5,3]=>2688
[6,3,8,2,5,1,4,7]=>[5,2,1]=>4032
[6,4,8,2,5,1,3,7]=>[3,2,2,1]=>1680
[6,4,8,3,5,1,2,7]=>[5,2,1]=>4032
[6,5,8,2,4,1,3,7]=>[3,3,2]=>1120
[6,5,8,3,4,1,2,7]=>[6,2]=>3360
[4,3,8,2,7,1,5,6]=>[6,2]=>3360
[5,3,8,2,7,1,4,6]=>[8]=>5040
[5,4,8,2,7,1,3,6]=>[6,2]=>3360
[5,4,8,3,7,1,2,6]=>[8]=>5040
[6,3,8,2,7,1,4,5]=>[6,2]=>3360
[6,4,8,2,7,1,3,5]=>[4,2,2]=>1260
[7,3,8,2,5,1,4,6]=>[7,1]=>5760
[7,4,8,3,5,1,2,6]=>[7,1]=>5760
[7,5,8,2,4,1,3,6]=>[5,3]=>2688
[7,5,8,2,6,1,3,4]=>[8]=>5040
[7,5,8,4,6,1,2,3]=>[5,2,1]=>4032
[7,6,8,2,5,1,3,4]=>[7,1]=>5760
[7,6,8,3,5,1,2,4]=>[4,3,1]=>3360
[8,3,6,2,5,1,4,7]=>[7,1]=>5760
[8,4,6,2,5,1,3,7]=>[5,2,1]=>4032
[8,5,6,2,4,1,3,7]=>[5,3]=>2688
[8,3,7,2,5,1,4,6]=>[4,3,1]=>3360
[8,4,7,3,5,1,2,6]=>[4,3,1]=>3360
[8,5,7,2,4,1,3,6]=>[3,3,2]=>1120
[8,3,7,2,6,1,4,5]=>[4,4]=>1260
[8,4,7,2,6,1,3,5]=>[4,2,2]=>1260
[8,4,7,3,6,1,2,5]=>[4,4]=>1260
[8,5,7,2,6,1,3,4]=>[6,2]=>3360
[8,6,7,2,4,1,3,5]=>[6,2]=>3360
[8,6,7,2,5,1,3,4]=>[5,2,1]=>4032
[8,6,7,3,5,1,2,4]=>[7,1]=>5760
[5,4,3,2,7,1,6,8]=>[4,2,1,1]=>2520
[6,4,3,2,7,1,5,8]=>[2,2,2,1,1]=>420
[6,5,3,2,7,1,4,8]=>[4,2,1,1]=>2520
[6,5,4,2,7,1,3,8]=>[5,2,1]=>4032
[7,5,3,2,6,1,4,8]=>[6,1,1]=>3360
[7,5,4,2,6,1,3,8]=>[7,1]=>5760
[5,4,3,2,8,1,6,7]=>[5,2,1]=>4032
[6,5,3,2,8,1,4,7]=>[5,2,1]=>4032
[6,5,4,2,8,1,3,7]=>[6,2]=>3360
[6,5,4,3,8,1,2,7]=>[4,2,2]=>1260
[7,5,3,2,8,1,4,6]=>[7,1]=>5760
[7,5,4,2,8,1,3,6]=>[8]=>5040
[7,6,3,2,8,1,4,5]=>[5,2,1]=>4032
[7,6,4,3,8,1,2,5]=>[4,2,2]=>1260
[7,6,5,2,8,1,3,4]=>[8]=>5040
[8,5,3,2,6,1,4,7]=>[7,1]=>5760
[8,5,4,2,6,1,3,7]=>[8]=>5040
[8,6,5,2,4,1,3,7]=>[8]=>5040
[8,5,3,2,7,1,4,6]=>[4,3,1]=>3360
[8,6,3,2,7,1,4,5]=>[7,1]=>5760
[8,6,4,3,7,1,2,5]=>[6,2]=>3360
[8,7,3,2,6,1,4,5]=>[4,3,1]=>3360
[8,7,4,2,6,1,3,5]=>[4,4]=>1260
[8,7,4,3,6,1,2,5]=>[4,2,2]=>1260
[8,7,5,2,6,1,3,4]=>[8]=>5040
[8,7,5,3,6,1,2,4]=>[6,2]=>3360
[8,7,6,2,4,1,3,5]=>[8]=>5040
[8,7,6,2,5,1,3,4]=>[7,1]=>5760
[8,7,6,3,5,1,2,4]=>[5,2,1]=>4032
[4,8,3,7,2,6,1,5]=>[3,3,1,1]=>1120
[5,8,3,7,2,6,1,4]=>[6,1,1]=>3360
[5,8,4,7,2,6,1,3]=>[7,1]=>5760
[5,8,4,7,3,6,1,2]=>[5,2,1]=>4032
[6,8,3,7,2,5,1,4]=>[7,1]=>5760
[6,8,4,7,2,5,1,3]=>[8]=>5040
[6,8,4,7,3,5,1,2]=>[6,2]=>3360
[6,8,5,7,2,4,1,3]=>[4,4]=>1260
[6,8,5,7,3,4,1,2]=>[4,2,2]=>1260
[7,8,3,6,2,5,1,4]=>[5,2,1]=>4032
[7,8,4,6,2,5,1,3]=>[6,2]=>3360
[7,8,4,6,3,5,1,2]=>[4,2,2]=>1260
[7,8,5,6,2,4,1,3]=>[4,2,2]=>1260
[5,4,3,8,2,7,1,6]=>[7,1]=>5760
[6,4,3,8,2,7,1,5]=>[4,3,1]=>3360
[6,5,3,8,2,7,1,4]=>[3,2,2,1]=>1680
[6,5,4,8,3,7,1,2]=>[5,3]=>2688
[7,4,3,8,2,6,1,5]=>[4,2,1,1]=>2520
[7,5,3,8,2,6,1,4]=>[2,2,2,1,1]=>420
[7,5,4,8,2,6,1,3]=>[3,2,2,1]=>1680
[7,6,3,8,2,5,1,4]=>[3,2,2,1]=>1680
[7,6,4,8,2,5,1,3]=>[3,3,2]=>1120
[7,6,5,8,2,4,1,3]=>[6,2]=>3360
[8,4,3,7,2,6,1,5]=>[6,1,1]=>3360
[8,5,3,7,2,6,1,4]=>[4,2,1,1]=>2520
[8,5,4,7,2,6,1,3]=>[5,2,1]=>4032
[8,5,4,7,3,6,1,2]=>[7,1]=>5760
[8,6,3,7,2,5,1,4]=>[4,3,1]=>3360
[8,6,4,7,2,5,1,3]=>[5,3]=>2688
[8,6,4,7,3,5,1,2]=>[8]=>5040
[8,6,5,7,2,4,1,3]=>[8]=>5040
[8,7,3,6,2,5,1,4]=>[7,1]=>5760
[8,7,4,6,2,5,1,3]=>[8]=>5040
[8,7,4,6,3,5,1,2]=>[4,4]=>1260
[8,7,5,6,2,4,1,3]=>[6,2]=>3360
[6,5,4,3,2,8,1,7]=>[4,2,2]=>1260
[7,6,5,4,2,8,1,3]=>[5,2,1]=>4032
[8,5,4,3,2,7,1,6]=>[4,2,2]=>1260
[8,7,4,3,2,6,1,5]=>[5,2,1]=>4032
[8,7,5,3,2,6,1,4]=>[7,1]=>5760
[8,7,5,4,2,6,1,3]=>[6,1,1]=>3360
[8,7,6,3,2,5,1,4]=>[8]=>5040
[8,7,6,4,2,5,1,3]=>[7,1]=>5760
[8,7,6,5,2,4,1,3]=>[8]=>5040
[8,1,2,3,4,7,5,6]=>[8]=>5040
[8,1,2,3,6,4,5,7]=>[8]=>5040
[8,1,2,3,7,4,5,6]=>[6,2]=>3360
[7,1,2,3,6,4,8,5]=>[8]=>5040
[5,1,2,3,8,7,4,6]=>[8]=>5040
[8,1,2,3,6,7,4,5]=>[8]=>5040
[4,1,2,8,3,7,5,6]=>[8]=>5040
[8,1,2,5,3,4,6,7]=>[8]=>5040
[7,1,2,5,3,4,8,6]=>[8]=>5040
[8,1,2,6,3,4,5,7]=>[6,2]=>3360
[7,1,2,6,3,4,8,5]=>[6,2]=>3360
[6,1,2,5,3,8,4,7]=>[8]=>5040
[8,1,2,5,3,7,4,6]=>[8]=>5040
[8,1,2,6,3,7,4,5]=>[5,3]=>2688
[6,1,2,5,3,7,8,4]=>[8]=>5040
[4,1,2,8,6,3,5,7]=>[8]=>5040
[4,1,2,8,7,3,5,6]=>[6,2]=>3360
[4,1,2,7,6,3,8,5]=>[8]=>5040
[8,1,2,5,6,3,4,7]=>[8]=>5040
[8,1,2,5,7,3,4,6]=>[5,3]=>2688
[8,1,2,7,6,3,4,5]=>[6,2]=>3360
[7,1,2,5,6,3,8,4]=>[8]=>5040
[4,1,2,5,8,7,3,6]=>[8]=>5040
[4,1,2,8,6,7,3,5]=>[8]=>5040
[8,1,2,5,6,7,3,4]=>[8]=>5040
[3,1,8,2,4,7,5,6]=>[8]=>5040
[3,1,8,2,6,4,5,7]=>[8]=>5040
[3,1,8,2,7,4,5,6]=>[6,2]=>3360
[3,1,7,2,6,4,8,5]=>[8]=>5040
[3,1,5,2,8,7,4,6]=>[8]=>5040
[3,1,8,2,6,7,4,5]=>[8]=>5040
[8,1,4,2,3,5,6,7]=>[8]=>5040
[7,1,4,2,3,5,8,6]=>[8]=>5040
[6,1,4,2,3,8,5,7]=>[8]=>5040
[8,1,4,2,3,7,5,6]=>[8]=>5040
[6,1,4,2,3,7,8,5]=>[8]=>5040
[8,1,5,2,3,4,6,7]=>[6,2]=>3360
[7,1,5,2,3,4,8,6]=>[6,2]=>3360
[8,1,7,2,3,4,5,6]=>[5,3]=>2688
[6,1,5,2,3,8,4,7]=>[6,2]=>3360
[8,1,5,2,3,7,4,6]=>[6,2]=>3360
[6,1,8,2,3,7,4,5]=>[5,3]=>2688
[6,1,5,2,3,7,8,4]=>[6,2]=>3360
[5,1,4,2,8,3,6,7]=>[8]=>5040
[5,1,4,2,7,3,8,6]=>[8]=>5040
[8,1,4,2,6,3,5,7]=>[8]=>5040
[8,1,4,2,7,3,5,6]=>[6,2]=>3360
[7,1,4,2,6,3,8,5]=>[8]=>5040
[8,1,5,2,6,3,4,7]=>[5,3]=>2688
[8,1,5,2,7,3,4,6]=>[8]=>5040
[7,1,8,2,6,3,4,5]=>[4,4]=>1260
[7,1,5,2,6,3,8,4]=>[5,3]=>2688
[5,1,4,2,6,8,3,7]=>[8]=>5040
[5,1,4,2,8,7,3,6]=>[8]=>5040
[8,1,4,2,6,7,3,5]=>[8]=>5040
[8,1,5,2,6,7,3,4]=>[4,4]=>1260
[5,1,4,2,6,7,8,3]=>[8]=>5040
[3,1,4,8,2,7,5,6]=>[8]=>5040
[3,1,8,5,2,4,6,7]=>[8]=>5040
[3,1,7,5,2,4,8,6]=>[8]=>5040
[3,1,8,6,2,4,5,7]=>[6,2]=>3360
[3,1,7,6,2,4,8,5]=>[6,2]=>3360
[3,1,6,5,2,8,4,7]=>[8]=>5040
[3,1,8,5,2,7,4,6]=>[8]=>5040
[3,1,8,6,2,7,4,5]=>[5,3]=>2688
[3,1,6,5,2,7,8,4]=>[8]=>5040
[8,1,4,5,2,3,6,7]=>[8]=>5040
[7,1,4,5,2,3,8,6]=>[8]=>5040
[8,1,4,6,2,3,5,7]=>[5,3]=>2688
[7,1,4,8,2,3,5,6]=>[4,4]=>1260
[7,1,4,6,2,3,8,5]=>[5,3]=>2688
[8,1,6,5,2,3,4,7]=>[6,2]=>3360
[7,1,8,5,2,3,4,6]=>[5,3]=>2688
[7,1,8,6,2,3,4,5]=>[8]=>5040
[7,1,6,5,2,3,8,4]=>[6,2]=>3360
[6,1,4,5,2,8,3,7]=>[8]=>5040
[8,1,4,5,2,7,3,6]=>[8]=>5040
[8,1,4,6,2,7,3,5]=>[4,4]=>1260
[8,1,6,5,2,7,3,4]=>[5,3]=>2688
[6,1,4,5,2,7,8,3]=>[8]=>5040
[3,1,4,8,6,2,5,7]=>[8]=>5040
[3,1,4,8,7,2,5,6]=>[6,2]=>3360
[3,1,4,7,6,2,8,5]=>[8]=>5040
[3,1,8,5,6,2,4,7]=>[8]=>5040
[3,1,8,5,7,2,4,6]=>[5,3]=>2688
[3,1,8,7,6,2,4,5]=>[6,2]=>3360
[3,1,7,5,6,2,8,4]=>[8]=>5040
[8,1,4,5,6,2,3,7]=>[8]=>5040
[8,1,4,5,7,2,3,6]=>[4,4]=>1260
[8,1,4,7,6,2,3,5]=>[5,3]=>2688
[8,1,7,5,6,2,3,4]=>[6,2]=>3360
[7,1,4,5,6,2,8,3]=>[8]=>5040
[3,1,4,5,8,7,2,6]=>[8]=>5040
[3,1,4,8,6,7,2,5]=>[8]=>5040
[3,1,8,5,6,7,2,4]=>[8]=>5040
[8,1,4,5,6,7,2,3]=>[8]=>5040
[2,8,1,3,4,7,5,6]=>[8]=>5040
[2,8,1,3,6,4,5,7]=>[8]=>5040
[2,8,1,3,7,4,5,6]=>[6,2]=>3360
[2,7,1,3,6,4,8,5]=>[8]=>5040
[2,5,1,3,8,7,4,6]=>[8]=>5040
[2,8,1,3,6,7,4,5]=>[8]=>5040
[2,4,1,8,3,7,5,6]=>[8]=>5040
[2,8,1,5,3,4,6,7]=>[8]=>5040
[2,7,1,5,3,4,8,6]=>[8]=>5040
[2,8,1,6,3,4,5,7]=>[6,2]=>3360
[2,7,1,6,3,4,8,5]=>[6,2]=>3360
[2,6,1,5,3,8,4,7]=>[8]=>5040
[2,8,1,5,3,7,4,6]=>[8]=>5040
[2,6,1,5,3,7,8,4]=>[8]=>5040
[2,4,1,8,6,3,5,7]=>[8]=>5040
[2,4,1,8,7,3,5,6]=>[6,2]=>3360
[2,4,1,7,6,3,8,5]=>[8]=>5040
[2,8,1,5,6,3,4,7]=>[8]=>5040
[2,8,1,5,7,3,4,6]=>[5,3]=>2688
[2,8,1,7,6,3,4,5]=>[6,2]=>3360
[2,7,1,5,6,3,8,4]=>[8]=>5040
[2,4,1,5,8,7,3,6]=>[8]=>5040
[2,4,1,8,6,7,3,5]=>[8]=>5040
[2,8,1,5,6,7,3,4]=>[8]=>5040
[7,3,1,2,4,5,8,6]=>[8]=>5040
[6,3,1,2,4,8,5,7]=>[8]=>5040
[8,3,1,2,4,7,5,6]=>[8]=>5040
[6,3,1,2,4,7,8,5]=>[8]=>5040
[5,3,1,2,8,4,6,7]=>[8]=>5040
[5,3,1,2,7,4,8,6]=>[8]=>5040
[8,3,1,2,6,4,5,7]=>[8]=>5040
[8,3,1,2,7,4,5,6]=>[6,2]=>3360
[7,3,1,2,6,4,8,5]=>[8]=>5040
[5,3,1,2,6,8,4,7]=>[8]=>5040
[5,3,1,2,8,7,4,6]=>[8]=>5040
[8,3,1,2,6,7,4,5]=>[8]=>5040
[5,3,1,2,6,7,8,4]=>[8]=>5040
[7,4,1,2,3,5,8,6]=>[6,2]=>3360
[6,4,1,2,3,8,5,7]=>[6,2]=>3360
[8,4,1,2,3,7,5,6]=>[6,2]=>3360
[6,4,1,2,3,7,8,5]=>[6,2]=>3360
[7,6,1,2,3,4,8,5]=>[5,3]=>2688
[5,8,1,2,3,7,4,6]=>[5,3]=>2688
[8,6,1,2,3,7,4,5]=>[4,4]=>1260
[5,4,1,2,8,3,6,7]=>[6,2]=>3360
[5,4,1,2,7,3,8,6]=>[6,2]=>3360
[8,4,1,2,6,3,5,7]=>[6,2]=>3360
[8,4,1,2,7,3,5,6]=>[4,2,2]=>1260
[7,4,1,2,6,3,8,5]=>[6,2]=>3360
[5,8,1,2,6,3,4,7]=>[4,4]=>1260
[5,8,1,2,7,3,4,6]=>[8]=>5040
[8,7,1,2,6,3,4,5]=>[5,3]=>2688
[5,7,1,2,6,3,8,4]=>[4,4]=>1260
[5,4,1,2,6,8,3,7]=>[6,2]=>3360
[5,4,1,2,8,7,3,6]=>[6,2]=>3360
[8,4,1,2,6,7,3,5]=>[6,2]=>3360
[5,8,1,2,6,7,3,4]=>[5,3]=>2688
[5,4,1,2,6,7,8,3]=>[6,2]=>3360
[4,3,1,8,2,5,6,7]=>[8]=>5040
[4,3,1,7,2,5,8,6]=>[8]=>5040
[4,3,1,6,2,8,5,7]=>[8]=>5040
[4,3,1,8,2,7,5,6]=>[8]=>5040
[4,3,1,6,2,7,8,5]=>[8]=>5040
[8,3,1,5,2,4,6,7]=>[8]=>5040
[7,3,1,5,2,4,8,6]=>[8]=>5040
[8,3,1,6,2,4,5,7]=>[6,2]=>3360
[7,3,1,8,2,4,5,6]=>[5,3]=>2688
[7,3,1,6,2,4,8,5]=>[6,2]=>3360
[6,3,1,5,2,8,4,7]=>[8]=>5040
[8,3,1,5,2,7,4,6]=>[8]=>5040
[8,3,1,6,2,7,4,5]=>[5,3]=>2688
[6,3,1,5,2,7,8,4]=>[8]=>5040
[8,4,1,5,2,3,6,7]=>[5,3]=>2688
[7,4,1,5,2,3,8,6]=>[5,3]=>2688
[8,4,1,6,2,3,5,7]=>[8]=>5040
[7,4,1,8,2,3,5,6]=>[8]=>5040
[7,4,1,6,2,3,8,5]=>[8]=>5040
[6,8,1,5,2,3,4,7]=>[5,3]=>2688
[8,7,1,5,2,3,4,6]=>[4,4]=>1260
[8,7,1,6,2,3,4,5]=>[8]=>5040
[6,7,1,5,2,3,8,4]=>[5,3]=>2688
[6,4,1,5,2,8,3,7]=>[5,3]=>2688
[8,4,1,5,2,7,3,6]=>[5,3]=>2688
[8,4,1,6,2,7,3,5]=>[8]=>5040
[6,8,1,5,2,7,3,4]=>[4,4]=>1260
[6,4,1,5,2,7,8,3]=>[5,3]=>2688
[4,3,1,5,8,2,6,7]=>[8]=>5040
[4,3,1,5,7,2,8,6]=>[8]=>5040
[4,3,1,8,6,2,5,7]=>[8]=>5040
[4,3,1,8,7,2,5,6]=>[6,2]=>3360
[4,3,1,7,6,2,8,5]=>[8]=>5040
[8,3,1,5,6,2,4,7]=>[8]=>5040
[8,3,1,5,7,2,4,6]=>[5,3]=>2688
[8,3,1,7,6,2,4,5]=>[6,2]=>3360
[7,3,1,5,6,2,8,4]=>[8]=>5040
[8,4,1,5,6,2,3,7]=>[4,4]=>1260
[8,4,1,5,7,2,3,6]=>[8]=>5040
[8,4,1,7,6,2,3,5]=>[8]=>5040
[7,8,1,5,6,2,3,4]=>[5,3]=>2688
[7,4,1,5,6,2,8,3]=>[4,4]=>1260
[4,3,1,5,6,8,2,7]=>[8]=>5040
[4,3,1,5,8,7,2,6]=>[8]=>5040
[4,3,1,8,6,7,2,5]=>[8]=>5040
[8,3,1,5,6,7,2,4]=>[8]=>5040
[8,4,1,5,6,7,2,3]=>[5,3]=>2688
[4,3,1,5,6,7,8,2]=>[8]=>5040
[2,3,8,1,4,7,5,6]=>[8]=>5040
[2,3,8,1,6,4,5,7]=>[8]=>5040
[2,3,8,1,7,4,5,6]=>[6,2]=>3360
[2,3,7,1,6,4,8,5]=>[8]=>5040
[2,3,5,1,8,7,4,6]=>[8]=>5040
[2,3,8,1,6,7,4,5]=>[8]=>5040
[2,8,4,1,3,5,6,7]=>[8]=>5040
[2,7,4,1,3,5,8,6]=>[8]=>5040
[2,6,4,1,3,8,5,7]=>[8]=>5040
[2,8,4,1,3,7,5,6]=>[8]=>5040
[2,6,4,1,3,7,8,5]=>[8]=>5040
[2,8,5,1,3,4,6,7]=>[6,2]=>3360
[2,7,5,1,3,4,8,6]=>[6,2]=>3360
[2,8,7,1,3,4,5,6]=>[5,3]=>2688
[2,6,5,1,3,8,4,7]=>[6,2]=>3360
[2,8,5,1,3,7,4,6]=>[6,2]=>3360
[2,6,8,1,3,7,4,5]=>[5,3]=>2688
[2,6,5,1,3,7,8,4]=>[6,2]=>3360
[2,5,4,1,8,3,6,7]=>[8]=>5040
[2,5,4,1,7,3,8,6]=>[8]=>5040
[2,8,4,1,6,3,5,7]=>[8]=>5040
[2,8,4,1,7,3,5,6]=>[6,2]=>3360
[2,7,4,1,6,3,8,5]=>[8]=>5040
[2,8,5,1,6,3,4,7]=>[5,3]=>2688
[2,8,5,1,7,3,4,6]=>[8]=>5040
[2,7,8,1,6,3,4,5]=>[4,4]=>1260
[2,7,5,1,6,3,8,4]=>[5,3]=>2688
[2,5,4,1,6,8,3,7]=>[8]=>5040
[2,5,4,1,8,7,3,6]=>[8]=>5040
[2,8,4,1,6,7,3,5]=>[8]=>5040
[2,8,5,1,6,7,3,4]=>[4,4]=>1260
[2,5,4,1,6,7,8,3]=>[8]=>5040
[7,3,4,1,2,5,8,6]=>[8]=>5040
[6,3,4,1,2,8,5,7]=>[8]=>5040
[8,3,4,1,2,7,5,6]=>[8]=>5040
[6,3,4,1,2,7,8,5]=>[8]=>5040
[7,3,5,1,2,4,8,6]=>[5,3]=>2688
[6,3,7,1,2,4,8,5]=>[5,3]=>2688
[6,3,5,1,2,8,4,7]=>[5,3]=>2688
[8,3,5,1,2,7,4,6]=>[5,3]=>2688
[6,3,8,1,2,7,4,5]=>[4,4]=>1260
[6,3,5,1,2,7,8,4]=>[5,3]=>2688
[7,5,4,1,2,3,8,6]=>[6,2]=>3360
[6,8,4,1,2,3,5,7]=>[4,4]=>1260
[6,7,4,1,2,3,8,5]=>[4,4]=>1260
[6,8,5,1,2,3,4,7]=>[8]=>5040
[6,7,5,1,2,3,8,4]=>[8]=>5040
[6,5,4,1,2,8,3,7]=>[6,2]=>3360
[8,5,4,1,2,7,3,6]=>[6,2]=>3360
[6,8,4,1,2,7,3,5]=>[5,3]=>2688
[6,8,5,1,2,7,3,4]=>[8]=>5040
[6,5,4,1,2,7,8,3]=>[6,2]=>3360
[5,3,4,1,8,2,6,7]=>[8]=>5040
[5,3,4,1,7,2,8,6]=>[8]=>5040
[8,3,4,1,6,2,5,7]=>[8]=>5040
[8,3,4,1,7,2,5,6]=>[6,2]=>3360
[7,3,4,1,6,2,8,5]=>[8]=>5040
[8,3,5,1,6,2,4,7]=>[4,4]=>1260
[8,3,5,1,7,2,4,6]=>[8]=>5040
[7,3,8,1,6,2,4,5]=>[5,3]=>2688
[7,3,5,1,6,2,8,4]=>[4,4]=>1260
[8,5,4,1,6,2,3,7]=>[5,3]=>2688
[8,5,4,1,7,2,3,6]=>[8]=>5040
[7,8,4,1,6,2,3,5]=>[4,4]=>1260
[7,8,5,1,6,2,3,4]=>[8]=>5040
[7,5,4,1,6,2,8,3]=>[5,3]=>2688
[5,3,4,1,6,8,2,7]=>[8]=>5040
[5,3,4,1,8,7,2,6]=>[8]=>5040
[8,3,4,1,6,7,2,5]=>[8]=>5040
[8,3,5,1,6,7,2,4]=>[5,3]=>2688
[8,5,4,1,6,7,2,3]=>[4,4]=>1260
[5,3,4,1,6,7,8,2]=>[8]=>5040
[2,3,4,8,1,7,5,6]=>[8]=>5040
[2,3,8,5,1,4,6,7]=>[8]=>5040
[2,3,7,5,1,4,8,6]=>[8]=>5040
[2,3,8,6,1,4,5,7]=>[6,2]=>3360
[2,3,7,6,1,4,8,5]=>[6,2]=>3360
[2,3,6,5,1,8,4,7]=>[8]=>5040
[2,3,8,5,1,7,4,6]=>[8]=>5040
[2,3,8,6,1,7,4,5]=>[5,3]=>2688
[2,3,6,5,1,7,8,4]=>[8]=>5040
[2,8,4,5,1,3,6,7]=>[8]=>5040
[2,7,4,5,1,3,8,6]=>[8]=>5040
[2,8,4,6,1,3,5,7]=>[5,3]=>2688
[2,7,4,8,1,3,5,6]=>[4,4]=>1260
[2,7,4,6,1,3,8,5]=>[5,3]=>2688
[2,8,6,5,1,3,4,7]=>[6,2]=>3360
[2,7,8,5,1,3,4,6]=>[5,3]=>2688
[2,7,8,6,1,3,4,5]=>[8]=>5040
[2,7,6,5,1,3,8,4]=>[6,2]=>3360
[2,6,4,5,1,8,3,7]=>[8]=>5040
[2,8,4,5,1,7,3,6]=>[8]=>5040
[2,8,4,6,1,7,3,5]=>[4,4]=>1260
[2,8,6,5,1,7,3,4]=>[5,3]=>2688
[2,6,4,5,1,7,8,3]=>[8]=>5040
[7,3,4,5,1,2,8,6]=>[8]=>5040
[7,3,4,6,1,2,8,5]=>[4,4]=>1260
[8,3,6,5,1,2,4,7]=>[5,3]=>2688
[7,3,8,5,1,2,4,6]=>[4,4]=>1260
[7,3,8,6,1,2,4,5]=>[8]=>5040
[7,3,6,5,1,2,8,4]=>[5,3]=>2688
[7,6,4,5,1,2,8,3]=>[6,2]=>3360
[6,3,4,5,1,8,2,7]=>[8]=>5040
[8,3,4,5,1,7,2,6]=>[8]=>5040
[8,3,4,6,1,7,2,5]=>[5,3]=>2688
[8,3,6,5,1,7,2,4]=>[4,4]=>1260
[8,6,4,5,1,7,2,3]=>[5,3]=>2688
[6,3,4,5,1,7,8,2]=>[8]=>5040
[2,3,4,8,6,1,5,7]=>[8]=>5040
[2,3,4,8,7,1,5,6]=>[6,2]=>3360
[2,3,4,7,6,1,8,5]=>[8]=>5040
[2,3,8,5,6,1,4,7]=>[8]=>5040
[2,3,8,5,7,1,4,6]=>[5,3]=>2688
[2,3,8,7,6,1,4,5]=>[6,2]=>3360
[2,3,7,5,6,1,8,4]=>[8]=>5040
[2,8,4,5,6,1,3,7]=>[8]=>5040
[2,8,4,5,7,1,3,6]=>[4,4]=>1260
[2,8,4,7,6,1,3,5]=>[5,3]=>2688
[2,8,7,5,6,1,3,4]=>[6,2]=>3360
[2,7,4,5,6,1,8,3]=>[8]=>5040
[8,3,4,5,7,1,2,6]=>[5,3]=>2688
[8,3,4,7,6,1,2,5]=>[4,4]=>1260
[8,3,7,5,6,1,2,4]=>[5,3]=>2688
[7,3,4,5,6,1,8,2]=>[8]=>5040
[2,3,4,5,8,7,1,6]=>[8]=>5040
[2,3,4,8,6,7,1,5]=>[8]=>5040
[2,3,8,5,6,7,1,4]=>[8]=>5040
[2,8,4,5,6,7,1,3]=>[8]=>5040
[9,1,2,3,4,5,6,7,8]=>[9]=>40320
[8,1,2,3,4,5,6,9,7]=>[9]=>40320
[7,1,2,3,4,5,9,6,8]=>[9]=>40320
[9,1,2,3,4,5,8,6,7]=>[9]=>40320
[7,1,2,3,4,5,8,9,6]=>[9]=>40320
[6,1,2,3,4,9,5,7,8]=>[9]=>40320
[6,1,2,3,4,8,5,9,7]=>[9]=>40320
[9,1,2,3,4,7,5,6,8]=>[9]=>40320
[9,1,2,3,4,8,5,6,7]=>[7,2]=>25920
[8,1,2,3,4,7,5,9,6]=>[9]=>40320
[6,1,2,3,4,7,9,5,8]=>[9]=>40320
[6,1,2,3,4,9,8,5,7]=>[9]=>40320
[9,1,2,3,4,7,8,5,6]=>[9]=>40320
[6,1,2,3,4,7,8,9,5]=>[9]=>40320
[5,1,2,3,9,4,6,7,8]=>[9]=>40320
[5,1,2,3,8,4,6,9,7]=>[9]=>40320
[9,1,2,3,6,4,5,7,8]=>[9]=>40320
[8,1,2,3,9,4,5,6,7]=>[6,3]=>20160
[5,1,2,3,9,8,4,6,7]=>[7,2]=>25920
[9,1,2,3,6,8,4,5,7]=>[6,3]=>20160
[5,1,2,3,6,9,8,4,7]=>[9]=>40320
[5,1,2,3,6,7,8,9,4]=>[9]=>40320
[4,1,2,8,3,5,6,9,7]=>[9]=>40320
[4,1,2,9,3,5,8,6,7]=>[9]=>40320
[4,1,2,9,3,8,5,6,7]=>[7,2]=>25920
[9,1,2,8,3,4,5,6,7]=>[6,3]=>20160
[7,1,2,8,3,4,5,9,6]=>[5,4]=>18144
[4,1,2,5,9,3,6,7,8]=>[9]=>40320
[4,1,2,8,9,3,5,6,7]=>[6,3]=>20160
[8,1,2,5,9,3,4,6,7]=>[5,4]=>18144
[8,1,2,9,6,3,4,5,7]=>[6,3]=>20160
[4,1,2,5,9,8,3,6,7]=>[7,2]=>25920
[9,1,2,8,6,7,3,4,5]=>[7,2]=>25920
[4,1,2,5,6,7,9,3,8]=>[9]=>40320
[4,1,2,9,6,7,8,3,5]=>[9]=>40320
[9,1,2,5,6,7,8,3,4]=>[9]=>40320
[4,1,2,5,6,7,8,9,3]=>[9]=>40320
[3,1,9,2,4,5,6,7,8]=>[9]=>40320
[3,1,8,2,4,5,6,9,7]=>[9]=>40320
[3,1,9,2,4,5,8,6,7]=>[9]=>40320
[3,1,5,2,7,4,9,6,8]=>[9]=>40320
[8,1,4,2,3,5,6,9,7]=>[9]=>40320
[9,1,4,2,3,5,8,6,7]=>[9]=>40320
[6,1,4,2,3,7,8,9,5]=>[9]=>40320
[9,1,8,2,3,4,5,6,7]=>[9]=>40320
[8,1,7,2,3,4,5,9,6]=>[6,3]=>20160
[3,1,4,9,2,5,6,7,8]=>[9]=>40320
[3,1,4,9,2,5,8,6,7]=>[9]=>40320
[3,1,9,8,2,4,5,6,7]=>[6,3]=>20160
[9,1,4,5,2,3,6,7,8]=>[9]=>40320
[7,1,4,5,2,3,8,9,6]=>[9]=>40320
[7,1,4,9,2,3,5,6,8]=>[5,4]=>18144
[9,1,4,8,2,3,5,6,7]=>[5,4]=>18144
[9,1,6,5,2,3,4,7,8]=>[7,2]=>25920
[7,1,9,6,2,3,4,5,8]=>[9]=>40320
[9,1,8,6,2,3,4,5,7]=>[9]=>40320
[7,1,8,9,2,3,4,5,6]=>[9]=>40320
[3,1,4,8,9,2,5,6,7]=>[6,3]=>20160
[3,1,8,9,7,2,4,5,6]=>[9]=>40320
[8,1,4,5,6,2,3,9,7]=>[9]=>40320
[8,1,4,9,7,2,3,5,6]=>[9]=>40320
[8,1,9,5,6,2,3,4,7]=>[6,3]=>20160
[8,1,9,7,6,2,3,4,5]=>[9]=>40320
[7,1,4,5,6,2,8,9,3]=>[9]=>40320
[3,1,4,5,6,9,2,7,8]=>[9]=>40320
[3,1,4,5,6,8,2,9,7]=>[9]=>40320
[3,1,4,9,8,7,2,5,6]=>[7,2]=>25920
[3,1,9,8,6,7,2,4,5]=>[7,2]=>25920
[9,1,4,5,6,7,2,3,8]=>[9]=>40320
[9,1,4,8,6,7,2,3,5]=>[6,3]=>20160
[9,1,8,5,6,7,2,3,4]=>[7,2]=>25920
[8,1,4,5,6,7,2,9,3]=>[9]=>40320
[3,1,4,5,6,7,9,2,8]=>[9]=>40320
[3,1,4,9,6,7,8,2,5]=>[9]=>40320
[3,1,9,5,6,7,8,2,4]=>[9]=>40320
[9,1,4,5,6,7,8,2,3]=>[9]=>40320
[3,1,4,5,6,7,8,9,2]=>[9]=>40320
[2,9,1,3,4,5,6,7,8]=>[9]=>40320
[2,8,1,3,4,5,6,9,7]=>[9]=>40320
[2,7,1,3,4,5,9,6,8]=>[9]=>40320
[2,9,1,3,4,5,8,6,7]=>[9]=>40320
[2,7,1,3,4,5,8,9,6]=>[9]=>40320
[2,6,1,3,4,9,5,7,8]=>[9]=>40320
[2,9,1,3,4,8,5,6,7]=>[7,2]=>25920
[2,8,1,3,9,4,5,6,7]=>[6,3]=>20160
[2,9,1,3,8,7,4,5,6]=>[7,2]=>25920
[2,9,1,3,6,7,8,4,5]=>[9]=>40320
[2,5,1,3,6,7,8,9,4]=>[9]=>40320
[2,4,1,6,3,8,5,9,7]=>[9]=>40320
[2,9,1,8,3,4,5,6,7]=>[6,3]=>20160
[2,7,1,6,3,4,8,9,5]=>[7,2]=>25920
[2,6,1,5,3,7,8,9,4]=>[9]=>40320
[2,4,1,5,9,3,6,7,8]=>[9]=>40320
[2,4,1,8,9,3,5,6,7]=>[6,3]=>20160
[2,8,1,9,7,3,4,5,6]=>[9]=>40320
[2,9,1,8,6,7,3,4,5]=>[7,2]=>25920
[2,4,1,5,6,7,9,3,8]=>[9]=>40320
[2,4,1,5,6,9,8,3,7]=>[9]=>40320
[2,9,1,5,6,7,8,3,4]=>[9]=>40320
[2,4,1,5,6,7,8,9,3]=>[9]=>40320
[9,3,1,2,4,5,6,7,8]=>[9]=>40320
[8,3,1,2,4,5,6,9,7]=>[9]=>40320
[9,3,1,2,4,5,8,6,7]=>[9]=>40320
[6,3,1,2,4,7,8,9,5]=>[9]=>40320
[9,3,1,2,6,7,8,4,5]=>[9]=>40320
[5,3,1,2,6,7,8,9,4]=>[9]=>40320
[9,4,1,2,3,5,6,7,8]=>[7,2]=>25920
[7,4,1,2,3,5,8,9,6]=>[7,2]=>25920
[6,4,1,2,3,7,8,9,5]=>[7,2]=>25920
[5,9,1,2,3,4,6,7,8]=>[6,3]=>20160
[5,8,1,2,3,4,6,9,7]=>[6,3]=>20160
[5,7,1,2,3,4,8,9,6]=>[6,3]=>20160
[9,6,1,2,3,4,5,7,8]=>[6,3]=>20160
[8,6,1,2,3,4,5,9,7]=>[6,3]=>20160
[9,7,1,2,3,4,5,6,8]=>[9]=>40320
[8,9,1,2,3,4,5,6,7]=>[9]=>40320
[8,7,1,2,3,4,5,9,6]=>[9]=>40320
[9,6,1,2,3,4,8,5,7]=>[6,3]=>20160
[9,7,1,2,3,4,8,5,6]=>[9]=>40320
[7,6,1,2,3,4,8,9,5]=>[6,3]=>20160
[5,9,1,2,3,8,4,6,7]=>[4,3,2]=>15120
[9,8,1,2,3,7,4,5,6]=>[9]=>40320
[8,6,1,2,3,7,4,9,5]=>[5,4]=>18144
[9,6,1,2,3,7,8,4,5]=>[5,4]=>18144
[5,6,1,2,3,7,8,9,4]=>[6,3]=>20160
[5,4,1,2,9,3,6,7,8]=>[7,2]=>25920
[8,4,1,2,9,3,5,6,7]=>[4,3,2]=>15120
[5,8,1,2,9,3,4,6,7]=>[9]=>40320
[9,7,1,2,6,3,8,4,5]=>[5,4]=>18144
[9,8,1,2,6,7,3,4,5]=>[6,3]=>20160
[5,4,1,2,6,7,9,3,8]=>[7,2]=>25920
[5,4,1,2,6,7,8,9,3]=>[7,2]=>25920
[4,3,1,9,2,5,6,7,8]=>[9]=>40320
[9,3,1,8,2,4,5,6,7]=>[6,3]=>20160
[9,4,1,8,2,3,5,6,7]=>[9]=>40320
[6,9,1,5,2,3,4,7,8]=>[6,3]=>20160
[9,7,1,6,2,3,4,5,8]=>[9]=>40320
[8,7,1,9,2,3,4,5,6]=>[9]=>40320
[8,7,1,6,2,3,4,9,5]=>[9]=>40320
[9,4,1,6,2,8,3,5,7]=>[5,4]=>18144
[9,8,1,6,2,7,3,4,5]=>[9]=>40320
[9,8,1,7,6,2,3,4,5]=>[9]=>40320
[4,3,1,5,6,8,2,9,7]=>[9]=>40320
[4,3,1,5,9,8,2,6,7]=>[7,2]=>25920
[4,3,1,5,8,7,2,9,6]=>[9]=>40320
[8,9,1,5,6,7,2,3,4]=>[6,3]=>20160
[4,3,1,5,6,7,9,2,8]=>[9]=>40320
[4,3,1,5,6,9,8,2,7]=>[9]=>40320
[9,3,1,5,6,7,8,2,4]=>[9]=>40320
[9,4,1,5,6,7,8,2,3]=>[6,3]=>20160
[4,3,1,5,6,7,8,9,2]=>[9]=>40320
[2,3,9,1,4,5,6,7,8]=>[9]=>40320
[2,3,8,1,4,5,6,9,7]=>[9]=>40320
[2,3,9,1,4,5,8,6,7]=>[9]=>40320
[2,3,9,1,4,7,8,5,6]=>[9]=>40320
[2,3,9,1,8,7,4,5,6]=>[7,2]=>25920
[2,3,8,1,6,7,4,9,5]=>[9]=>40320
[2,3,5,1,6,7,9,4,8]=>[9]=>40320
[2,3,9,1,6,7,8,4,5]=>[9]=>40320
[2,3,5,1,6,7,8,9,4]=>[9]=>40320
[2,9,4,1,3,5,6,7,8]=>[9]=>40320
[2,6,4,1,3,7,8,9,5]=>[9]=>40320
[2,9,5,1,3,4,6,7,8]=>[7,2]=>25920
[2,6,9,1,3,4,5,7,8]=>[5,4]=>18144
[2,9,7,1,3,4,5,6,8]=>[6,3]=>20160
[2,9,8,1,3,4,5,6,7]=>[9]=>40320
[2,9,4,1,6,3,5,7,8]=>[9]=>40320
[2,8,4,1,9,3,5,6,7]=>[6,3]=>20160
[2,9,4,1,6,3,8,5,7]=>[9]=>40320
[2,9,8,1,7,3,4,5,6]=>[9]=>40320
[2,9,5,1,6,7,8,3,4]=>[5,4]=>18144
[9,3,4,1,2,5,6,7,8]=>[9]=>40320
[6,3,4,1,2,7,8,9,5]=>[9]=>40320
[9,3,7,1,2,4,5,6,8]=>[5,4]=>18144
[9,3,8,1,2,4,5,6,7]=>[9]=>40320
[9,5,4,1,2,3,6,7,8]=>[7,2]=>25920
[8,5,4,1,2,3,6,9,7]=>[7,2]=>25920
[6,9,4,1,2,3,5,7,8]=>[5,4]=>18144
[6,8,4,1,2,3,5,9,7]=>[5,4]=>18144
[9,7,4,1,2,3,5,6,8]=>[6,3]=>20160
[9,8,4,1,2,3,5,6,7]=>[9]=>40320
[6,9,5,1,2,3,4,7,8]=>[9]=>40320
[6,8,5,1,2,3,4,9,7]=>[9]=>40320
[8,7,5,1,2,3,4,9,6]=>[9]=>40320
[6,7,9,1,2,3,4,5,8]=>[9]=>40320
[6,9,8,1,2,3,4,5,7]=>[9]=>40320
[9,7,8,1,2,3,4,5,6]=>[9]=>40320
[6,7,8,1,2,3,4,9,5]=>[9]=>40320
[6,5,4,1,2,8,3,9,7]=>[7,2]=>25920
[9,8,5,1,7,2,3,4,6]=>[6,3]=>20160
[7,8,9,1,6,2,3,4,5]=>[9]=>40320
[7,8,5,1,6,2,3,9,4]=>[9]=>40320
[5,3,4,1,6,8,2,9,7]=>[9]=>40320
[9,3,4,1,8,7,2,5,6]=>[7,2]=>25920
[8,3,4,1,6,7,2,9,5]=>[9]=>40320
[9,5,4,1,8,7,2,3,6]=>[9]=>40320
[8,5,4,1,6,7,2,9,3]=>[5,4]=>18144
[5,3,4,1,9,7,8,2,6]=>[9]=>40320
[9,3,5,1,6,7,8,2,4]=>[6,3]=>20160
[9,5,4,1,6,7,8,2,3]=>[5,4]=>18144
[5,3,4,1,6,7,8,9,2]=>[9]=>40320
[2,3,4,9,1,5,6,7,8]=>[9]=>40320
[2,3,4,9,1,5,8,6,7]=>[9]=>40320
[2,3,4,9,1,7,8,5,6]=>[9]=>40320
[2,3,4,6,1,7,8,9,5]=>[9]=>40320
[2,3,9,5,1,4,6,7,8]=>[9]=>40320
[2,3,9,6,1,4,5,7,8]=>[7,2]=>25920
[2,3,7,9,1,4,5,6,8]=>[5,4]=>18144
[2,3,9,8,1,4,5,6,7]=>[6,3]=>20160
[2,3,9,5,1,7,4,6,8]=>[9]=>40320
[2,3,9,6,1,7,8,4,5]=>[5,4]=>18144
[2,9,4,5,1,3,6,7,8]=>[9]=>40320
[2,7,4,5,1,3,8,9,6]=>[9]=>40320
[2,9,8,6,1,3,4,5,7]=>[9]=>40320
[2,7,8,9,1,3,4,5,6]=>[9]=>40320
[2,8,9,6,1,7,3,4,5]=>[9]=>40320
[2,9,6,5,1,7,8,3,4]=>[5,4]=>18144
[7,3,4,5,1,2,8,9,6]=>[9]=>40320
[9,3,4,8,1,2,5,6,7]=>[5,4]=>18144
[7,3,8,9,1,2,4,5,6]=>[9]=>40320
[9,8,4,5,1,2,3,6,7]=>[6,3]=>20160
[7,8,4,6,1,2,3,9,5]=>[9]=>40320
[9,8,6,5,1,2,3,4,7]=>[9]=>40320
[7,8,9,6,1,2,3,4,5]=>[5,4]=>18144
[7,8,6,5,1,2,3,9,4]=>[9]=>40320
[8,3,9,6,1,7,2,4,5]=>[9]=>40320
[8,3,6,5,1,7,2,9,4]=>[5,4]=>18144
[8,6,4,5,1,7,2,9,3]=>[6,3]=>20160
[6,3,4,5,1,7,9,2,8]=>[9]=>40320
[6,3,4,5,1,9,8,2,7]=>[9]=>40320
[9,3,4,6,1,7,8,2,5]=>[6,3]=>20160
[6,3,4,5,1,7,8,9,2]=>[9]=>40320
[2,3,4,5,9,1,6,7,8]=>[9]=>40320
[2,3,4,5,8,1,6,9,7]=>[9]=>40320
[2,3,4,5,9,1,8,6,7]=>[9]=>40320
[2,3,4,5,7,1,8,9,6]=>[9]=>40320
[2,3,4,9,6,1,5,7,8]=>[9]=>40320
[2,3,4,9,7,1,5,6,8]=>[7,2]=>25920
[2,3,4,9,6,1,8,5,7]=>[9]=>40320
[2,3,4,9,7,1,8,5,6]=>[6,3]=>20160
[2,3,9,5,6,1,4,7,8]=>[9]=>40320
[2,3,8,5,6,1,4,9,7]=>[9]=>40320
[2,3,9,5,6,1,8,4,7]=>[9]=>40320
[2,8,4,5,6,1,3,9,7]=>[9]=>40320
[2,8,9,5,7,1,3,4,6]=>[9]=>40320
[2,8,9,7,6,1,3,4,5]=>[9]=>40320
[2,9,7,5,6,1,8,3,4]=>[6,3]=>20160
[8,3,4,5,6,1,2,9,7]=>[9]=>40320
[8,3,4,7,6,1,2,9,5]=>[5,4]=>18144
[8,3,9,7,6,1,2,4,5]=>[9]=>40320
[8,3,7,5,6,1,2,9,4]=>[6,3]=>20160
[9,7,4,5,6,1,2,3,8]=>[7,2]=>25920
[8,9,4,5,6,1,2,3,7]=>[6,3]=>20160
[8,9,7,5,6,1,2,3,4]=>[9]=>40320
[8,7,4,5,6,1,2,9,3]=>[7,2]=>25920
[7,3,4,5,6,1,9,2,8]=>[9]=>40320
[9,3,4,5,6,1,8,2,7]=>[9]=>40320
[9,3,7,5,6,1,8,2,4]=>[5,4]=>18144
[7,3,4,5,6,1,8,9,2]=>[9]=>40320
[2,3,4,5,6,9,1,7,8]=>[9]=>40320
[2,3,4,5,6,8,1,9,7]=>[9]=>40320
[2,3,4,5,9,7,1,6,8]=>[9]=>40320
[2,3,4,5,9,8,1,6,7]=>[7,2]=>25920
[2,3,4,9,6,7,1,5,8]=>[9]=>40320
[2,3,9,5,6,7,1,4,8]=>[9]=>40320
[2,3,9,5,6,8,1,4,7]=>[5,4]=>18144
[2,9,4,5,6,7,1,3,8]=>[9]=>40320
[2,9,4,5,6,8,1,3,7]=>[5,4]=>18144
[2,9,4,5,8,7,1,3,6]=>[5,4]=>18144
[2,9,4,8,6,7,1,3,5]=>[6,3]=>20160
[2,9,8,5,6,7,1,3,4]=>[7,2]=>25920
[2,8,4,5,6,7,1,9,3]=>[9]=>40320
[9,3,4,5,6,7,1,2,8]=>[9]=>40320
[9,3,4,5,6,8,1,2,7]=>[6,3]=>20160
[9,8,4,5,6,7,1,2,3]=>[7,2]=>25920
[8,3,4,5,6,7,1,9,2]=>[9]=>40320
[2,3,4,5,6,7,9,1,8]=>[9]=>40320
[2,3,4,5,6,9,8,1,7]=>[9]=>40320
[2,3,4,5,9,7,8,1,6]=>[9]=>40320
[2,3,4,9,6,7,8,1,5]=>[9]=>40320
[2,3,9,5,6,7,8,1,4]=>[9]=>40320
[2,9,4,5,6,7,8,1,3]=>[9]=>40320
[9,3,4,5,6,7,8,1,2]=>[9]=>40320
[2,3,4,5,6,7,8,9,1]=>[9]=>40320
[]=>[]=>1
[3,5,2,6,1,4,8,7]=>[4,2,2]=>1260
[3,5,2,6,4,1,8,7]=>[6,2]=>3360
[3,5,2,7,4,8,1,6]=>[6,2]=>3360
[3,5,2,7,4,8,6,1]=>[8]=>5040
[4,5,7,2,3,8,6,1]=>[8]=>5040
[4,5,7,2,3,8,1,6]=>[6,2]=>3360
[4,5,6,2,3,1,8,7]=>[6,2]=>3360
[4,5,6,2,1,3,8,7]=>[4,2,2]=>1260
[3,5,1,6,4,2,8,7]=>[4,2,2]=>1260
[4,5,6,1,3,2,8,7]=>[4,2,2]=>1260
[4,5,6,3,1,2,8,7]=>[6,2]=>3360
[4,5,7,3,2,8,1,6]=>[4,2,2]=>1260
[4,5,7,3,2,8,6,1]=>[6,2]=>3360
[4,6,7,3,8,2,5,1]=>[6,2]=>3360
[4,6,7,3,8,2,1,5]=>[4,2,2]=>1260
[4,6,7,3,8,1,2,5]=>[6,2]=>3360
[4,5,7,3,1,8,2,6]=>[6,2]=>3360
[4,5,7,1,3,8,2,6]=>[4,2,2]=>1260
[3,5,1,7,4,8,2,6]=>[4,2,2]=>1260
[2,1,5,7,4,8,3,6]=>[4,2,2]=>1260
[2,1,5,7,4,8,6,3]=>[6,2]=>3360
[3,5,1,7,4,8,6,2]=>[6,2]=>3360
[4,5,7,1,3,8,6,2]=>[6,2]=>3360
[4,5,7,3,1,8,6,2]=>[8]=>5040
[4,6,7,3,8,1,5,2]=>[8]=>5040
[4,6,7,3,8,5,1,2]=>[4,4]=>1260
[4,6,7,3,8,5,2,1]=>[8]=>5040
[5,6,7,8,3,1,4,2]=>[8]=>5040
[5,6,7,8,1,3,4,2]=>[6,2]=>3360
[4,6,7,1,8,3,5,2]=>[6,2]=>3360
[3,6,1,7,8,4,5,2]=>[6,2]=>3360
[2,1,6,7,8,4,5,3]=>[6,2]=>3360
[2,1,6,7,8,4,3,5]=>[4,2,2]=>1260
[3,6,1,7,8,4,2,5]=>[4,2,2]=>1260
[4,6,7,1,8,3,2,5]=>[4,2,2]=>1260
[5,6,7,8,1,3,2,4]=>[4,2,2]=>1260
[4,5,7,2,1,8,3,6]=>[4,2,2]=>1260
[4,6,7,2,8,1,3,5]=>[4,2,2]=>1260
[4,6,7,2,8,3,1,5]=>[6,2]=>3360
[4,6,7,2,8,3,5,1]=>[8]=>5040
[3,6,2,7,8,4,5,1]=>[8]=>5040
[3,6,2,7,8,4,1,5]=>[6,2]=>3360
[3,6,2,7,8,1,4,5]=>[4,2,2]=>1260
[3,5,2,7,1,8,4,6]=>[4,2,2]=>1260
[3,4,2,1,7,8,5,6]=>[4,2,2]=>1260
[3,4,1,2,7,8,6,5]=>[4,2,2]=>1260
[3,5,2,7,1,8,6,4]=>[4,4]=>1260
[3,6,2,7,8,1,5,4]=>[4,4]=>1260
[3,6,2,7,8,5,1,4]=>[8]=>5040
[3,6,2,7,8,5,4,1]=>[6,2]=>3360
[4,6,7,2,8,5,3,1]=>[6,2]=>3360
[4,6,7,2,8,5,1,3]=>[8]=>5040
[4,6,7,2,8,1,5,3]=>[4,4]=>1260
[4,5,7,2,1,8,6,3]=>[4,4]=>1260
[4,5,7,1,2,8,6,3]=>[4,2,2]=>1260
[3,5,1,7,2,8,6,4]=>[4,2,2]=>1260
[2,1,5,7,3,8,6,4]=>[4,2,2]=>1260
[2,1,6,7,8,3,5,4]=>[4,2,2]=>1260
[3,6,1,7,8,2,5,4]=>[4,2,2]=>1260
[4,6,7,1,8,2,5,3]=>[4,2,2]=>1260
[5,6,7,8,1,2,4,3]=>[4,2,2]=>1260
[5,6,7,8,2,1,4,3]=>[4,4]=>1260
[5,6,7,8,2,4,1,3]=>[8]=>5040
[5,6,7,8,2,4,3,1]=>[6,2]=>3360
[5,6,7,8,1,4,2,3]=>[6,2]=>3360
[4,6,7,1,8,5,2,3]=>[6,2]=>3360
[3,6,1,7,8,5,2,4]=>[6,2]=>3360
[2,1,6,7,8,5,3,4]=>[6,2]=>3360
[3,6,1,7,8,5,4,2]=>[4,2,2]=>1260
[4,6,7,1,8,5,3,2]=>[4,2,2]=>1260
[5,6,7,8,1,4,3,2]=>[4,2,2]=>1260
[5,6,7,8,4,1,3,2]=>[6,2]=>3360
[3,4,2,1,6,5,8,7,10,9]=>[4,2,2,2]=>18900
[3,5,2,6,4,1,8,7,10,9]=>[6,2,2]=>75600
[3,5,2,7,4,8,6,1,10,9]=>[8,2]=>226800
[3,5,2,7,4,9,6,10,8,1]=>[10]=>362880
[2,1,5,6,4,3,8,7,10,9]=>[4,2,2,2]=>18900
[4,5,6,3,2,1,8,7,10,9]=>[4,2,2,2]=>18900
[4,5,7,3,2,8,6,1,10,9]=>[6,2,2]=>75600
[4,5,7,3,2,9,6,10,8,1]=>[8,2]=>226800
[2,1,5,7,4,8,6,3,10,9]=>[6,2,2]=>75600
[4,6,7,3,8,5,2,1,10,9]=>[8,2]=>226800
[4,6,7,3,9,5,2,10,8,1]=>[10]=>362880
[2,1,5,7,4,9,6,10,8,3]=>[8,2]=>226800
[4,6,8,3,9,5,10,7,2,1]=>[6,4]=>151200
[2,1,4,3,7,8,6,5,10,9]=>[4,2,2,2]=>18900
[3,4,2,1,7,8,6,5,10,9]=>[4,4,2]=>56700
[3,6,2,7,8,5,4,1,10,9]=>[6,2,2]=>75600
[3,6,2,7,9,5,4,10,8,1]=>[8,2]=>226800
[2,1,6,7,8,5,4,3,10,9]=>[4,2,2,2]=>18900
[5,6,7,8,4,3,2,1,10,9]=>[4,4,2]=>56700
[5,6,7,9,4,3,2,10,8,1]=>[6,4]=>151200
[2,1,6,7,9,5,4,10,8,3]=>[6,2,2]=>75600
[5,6,8,9,4,3,10,7,2,1]=>[10]=>362880
[2,1,4,3,7,9,6,10,8,5]=>[6,2,2]=>75600
[3,4,2,1,7,9,6,10,8,5]=>[6,4]=>151200
[3,6,2,8,9,5,10,7,4,1]=>[10]=>362880
[2,1,6,8,9,5,10,7,4,3]=>[8,2]=>226800
[5,7,8,9,4,10,6,3,2,1]=>[8,2]=>226800
[6,7,8,9,10,1,4,5,3,2]=>[8,2]=>226800
[6,7,8,9,10,1,4,5,2,3]=>[4,4,2]=>56700
[6,7,8,9,10,1,3,4,5,2]=>[8,2]=>226800
[6,7,8,9,10,2,3,4,1,5]=>[8,2]=>226800
[2,1,4,3,6,5,9,10,8,7]=>[4,2,2,2]=>18900
[3,4,2,1,6,5,9,10,8,7]=>[4,4,2]=>56700
[3,5,2,6,4,1,9,10,8,7]=>[6,4]=>151200
[3,5,2,8,4,9,10,7,6,1]=>[8,2]=>226800
[2,1,5,6,4,3,9,10,8,7]=>[4,4,2]=>56700
[4,5,6,3,2,1,9,10,8,7]=>[4,4,2]=>56700
[4,5,8,3,2,9,10,7,6,1]=>[6,2,2]=>75600
[2,1,5,8,4,9,10,7,6,3]=>[6,2,2]=>75600
[4,7,8,3,9,10,6,5,2,1]=>[10]=>362880
[2,1,4,3,8,9,10,7,6,5]=>[4,2,2,2]=>18900
[3,4,2,1,8,9,10,7,6,5]=>[4,4,2]=>56700
[3,7,2,8,9,10,6,5,4,1]=>[6,4]=>151200
[2,1,7,8,9,10,6,5,4,3]=>[4,4,2]=>56700
[6,7,8,9,10,1,5,4,3,2]=>[4,4,2]=>56700
[6,7,8,9,10,5,4,3,2,1]=>[4,4,2]=>56700
[6,5,8,7,3,4,1,2]=>[4,4]=>1260
[3,6,7,4,5,8,1,2]=>[3,3,1,1]=>1120
[2,6,7,4,5,1,8,3]=>[3,3,1,1]=>1120
[1,6,7,4,5,2,3,8]=>[2,2,1,1,1,1]=>210
[1,5,4,7,6,2,3,8]=>[3,3,1,1]=>1120
[2,5,4,7,6,1,8,3]=>[4,4]=>1260
[3,5,4,7,6,8,1,2]=>[4,4]=>1260
[4,5,3,7,8,6,1,2]=>[3,3,1,1]=>1120
[5,4,3,8,7,6,1,2]=>[3,3,1,1]=>1120
[6,4,8,3,7,5,1,2]=>[4,4]=>1260
[6,3,8,4,5,7,1,2]=>[3,3,1,1]=>1120
[5,3,4,8,6,7,1,2]=>[4,4]=>1260
[4,3,5,6,8,7,1,2]=>[4,4]=>1260
[3,2,5,6,1,8,7,4]=>[3,3,1,1]=>1120
[4,2,5,6,8,1,7,3]=>[3,3,1,1]=>1120
[5,2,4,8,6,1,7,3]=>[3,3,1,1]=>1120
[6,2,8,4,5,1,7,3]=>[2,2,1,1,1,1]=>210
[7,8,2,4,5,1,6,3]=>[3,3,1,1]=>1120
[7,8,1,4,5,2,3,6]=>[3,3,1,1]=>1120
[6,1,8,4,5,2,3,7]=>[3,3,1,1]=>1120
[5,1,4,8,6,2,3,7]=>[4,4]=>1260
[4,1,3,2,8,6,5,7]=>[3,3,1,1]=>1120
[5,1,3,8,2,6,4,7]=>[3,3,1,1]=>1120
[6,1,8,3,2,5,4,7]=>[4,4]=>1260
[7,8,1,3,2,5,4,6]=>[4,4]=>1260
[7,8,2,3,1,5,6,4]=>[4,4]=>1260
[6,2,8,3,1,5,7,4]=>[3,3,1,1]=>1120
[5,2,3,8,1,6,7,4]=>[2,2,1,1,1,1]=>210
[6,3,8,2,1,7,5,4]=>[4,4]=>1260
[7,8,3,2,1,6,5,4]=>[3,3,1,1]=>1120
[7,8,4,2,6,1,5,3]=>[4,4]=>1260
[5,4,2,8,7,1,6,3]=>[4,4]=>1260
[4,5,2,7,8,1,6,3]=>[4,4]=>1260
[2,5,3,7,1,6,8,4]=>[3,3,1,1]=>1120
[1,5,3,7,2,6,4,8]=>[2,2,1,1,1,1]=>210
[1,6,7,3,2,5,4,8]=>[3,3,1,1]=>1120
[2,6,7,3,1,5,8,4]=>[4,4]=>1260
[3,6,7,2,1,8,5,4]=>[4,4]=>1260
[7,8,5,6,2,1,4,3]=>[4,4]=>1260
[6,5,8,7,1,2,3,4]=>[4,4]=>1260
[5,4,1,8,7,2,3,6]=>[4,4]=>1260
[6,4,8,1,7,2,3,5]=>[4,4]=>1260
[7,8,3,1,2,6,4,5]=>[3,3,1,1]=>1120
[5,3,1,8,2,7,4,6]=>[4,4]=>1260
[4,3,1,2,8,7,5,6]=>[4,4]=>1260
[4,2,1,3,8,5,7,6]=>[3,3,1,1]=>1120
[5,2,1,8,3,4,7,6]=>[3,3,1,1]=>1120
[6,2,8,1,3,4,7,5]=>[3,3,1,1]=>1120
[7,8,2,1,3,4,6,5]=>[4,4]=>1260
[4,3,1,2,6,5,8,7]=>[4,2,2]=>1260
[5,3,1,6,2,4,8,7]=>[4,2,2]=>1260
[6,3,1,5,2,4,8,7]=>[6,2]=>3360
[7,3,1,5,2,8,4,6]=>[6,2]=>3360
[8,4,5,1,2,7,3,6]=>[8]=>5040
[7,4,5,1,2,8,3,6]=>[6,2]=>3360
[6,4,5,1,2,3,8,7]=>[6,2]=>3360
[5,4,6,1,2,3,8,7]=>[4,2,2]=>1260
[2,1,6,5,3,4,8,7]=>[4,2,2]=>1260
[3,6,1,5,2,4,8,7]=>[4,2,2]=>1260
[4,6,5,1,2,3,8,7]=>[4,2,2]=>1260
[5,6,4,1,2,3,8,7]=>[6,2]=>3360
[6,5,4,1,2,3,8,7]=>[4,2,2]=>1260
[7,5,4,1,2,8,3,6]=>[4,2,2]=>1260
[8,6,4,1,7,2,3,5]=>[6,2]=>3360
[7,6,4,1,8,2,3,5]=>[4,2,2]=>1260
[6,7,4,1,8,2,3,5]=>[6,2]=>3360
[5,7,4,1,2,8,3,6]=>[6,2]=>3360
[4,7,5,1,2,8,3,6]=>[4,2,2]=>1260
[3,7,1,5,2,8,4,6]=>[4,2,2]=>1260
[2,1,7,5,3,8,4,6]=>[4,2,2]=>1260
[2,1,8,5,3,7,4,6]=>[6,2]=>3360
[3,8,1,5,2,7,4,6]=>[6,2]=>3360
[4,8,5,1,2,7,3,6]=>[6,2]=>3360
[5,8,4,1,2,7,3,6]=>[8]=>5040
[6,8,4,1,7,2,3,5]=>[8]=>5040
[8,7,4,1,6,2,3,5]=>[8]=>5040
[5,8,6,7,1,2,3,4]=>[6,2]=>3360
[4,8,6,1,7,2,3,5]=>[6,2]=>3360
[3,8,1,6,7,2,4,5]=>[6,2]=>3360
[2,1,8,6,7,3,4,5]=>[6,2]=>3360
[2,1,7,6,8,3,4,5]=>[4,2,2]=>1260
[3,7,1,6,8,2,4,5]=>[4,2,2]=>1260
[4,7,6,1,8,2,3,5]=>[4,2,2]=>1260
[5,7,6,8,1,2,3,4]=>[4,2,2]=>1260
[5,4,7,1,2,8,3,6]=>[4,2,2]=>1260
[6,4,7,1,8,2,3,5]=>[4,2,2]=>1260
[7,4,6,1,8,2,3,5]=>[6,2]=>3360
[8,4,6,1,7,2,3,5]=>[8]=>5040
[8,3,1,6,7,2,4,5]=>[8]=>5040
[7,3,1,6,8,2,4,5]=>[6,2]=>3360
[6,3,1,7,8,2,4,5]=>[4,2,2]=>1260
[5,3,1,7,2,8,4,6]=>[4,2,2]=>1260
[4,3,1,2,7,8,5,6]=>[4,2,2]=>1260
[2,1,4,3,8,7,5,6]=>[4,2,2]=>1260
[3,4,1,2,8,7,5,6]=>[4,2,2]=>1260
[6,3,1,8,7,2,4,5]=>[4,4]=>1260
[7,3,1,8,6,2,4,5]=>[8]=>5040
[8,4,7,1,6,2,3,5]=>[6,2]=>3360
[7,4,8,1,6,2,3,5]=>[8]=>5040
[5,4,8,1,2,7,3,6]=>[4,4]=>1260
[4,5,8,1,2,7,3,6]=>[4,2,2]=>1260
[3,5,1,8,2,7,4,6]=>[4,2,2]=>1260
[2,1,5,8,3,7,4,6]=>[4,2,2]=>1260
[2,1,6,8,7,3,4,5]=>[4,2,2]=>1260
[3,6,1,8,7,2,4,5]=>[4,2,2]=>1260
[4,6,8,1,7,2,3,5]=>[4,2,2]=>1260
[5,6,8,7,1,2,3,4]=>[4,2,2]=>1260
[7,5,8,6,1,2,3,4]=>[8]=>5040
[8,5,7,6,1,2,3,4]=>[6,2]=>3360
[5,7,8,6,1,2,3,4]=>[6,2]=>3360
[4,7,8,1,6,2,3,5]=>[6,2]=>3360
[3,7,1,8,6,2,4,5]=>[6,2]=>3360
[2,1,7,8,6,3,4,5]=>[6,2]=>3360
[2,1,8,7,6,3,4,5]=>[4,2,2]=>1260
[3,8,1,7,6,2,4,5]=>[4,2,2]=>1260
[4,8,7,1,6,2,3,5]=>[4,2,2]=>1260
[5,8,7,6,1,2,3,4]=>[4,2,2]=>1260
[6,8,7,5,1,2,3,4]=>[6,2]=>3360
[6,4,7,3,8,5,1,2]=>[8]=>5040
[6,4,7,3,5,8,1,2]=>[7,1]=>5760
[6,4,7,2,5,1,8,3]=>[3,2,2,1]=>1680
[5,4,3,7,6,8,1,2]=>[7,1]=>5760
[6,4,8,3,5,7,1,2]=>[4,3,1]=>3360
[5,4,3,6,8,7,1,2]=>[7,1]=>5760
[5,4,2,6,7,1,8,3]=>[8]=>5040
[5,4,2,6,7,1,3,8]=>[7,1]=>5760
[5,4,2,8,6,1,7,3]=>[4,3,1]=>3360
[6,4,8,2,5,1,7,3]=>[2,2,2,1,1]=>420
[7,8,4,2,5,1,6,3]=>[4,3,1]=>3360
[7,8,4,2,5,1,3,6]=>[7,1]=>5760
[5,4,2,8,6,1,3,7]=>[5,3]=>2688
[4,3,2,1,6,8,5,7]=>[4,2,2]=>1260
[4,3,2,1,8,6,5,7]=>[3,2,2,1]=>1680
[5,3,2,8,1,6,4,7]=>[3,2,2,1]=>1680
[7,8,3,2,1,5,4,6]=>[7,1]=>5760
[7,8,3,2,1,5,6,4]=>[4,3,1]=>3360
[6,3,8,2,1,5,7,4]=>[4,3,1]=>3360
[5,3,2,7,1,8,6,4]=>[4,2,2]=>1260
[5,3,2,7,1,6,8,4]=>[3,2,2,1]=>1680
[6,3,7,2,1,8,5,4]=>[8]=>5040
[6,4,7,2,8,1,5,3]=>[4,2,2]=>1260
[6,5,7,8,2,1,4,3]=>[4,2,2]=>1260
[6,5,8,7,2,1,3,4]=>[4,2,2]=>1260
[6,3,7,2,1,8,4,5]=>[4,4]=>1260
[6,3,7,2,1,4,5,8]=>[7,1]=>5760
[5,3,2,7,1,4,8,6]=>[4,2,2]=>1260
[7,8,3,2,1,6,4,5]=>[6,1,1]=>3360
[6,3,8,2,1,7,4,5]=>[8]=>5040
[4,3,2,1,8,7,5,6]=>[4,2,2]=>1260
[6,3,8,2,1,4,7,5]=>[7,1]=>5760
[7,8,3,2,1,4,6,5]=>[7,1]=>5760
[6,3,8,2,1,4,5,7]=>[8]=>5040
[4,3,2,1,8,5,6,7]=>[4,2,2]=>1260
[4,3,2,1,5,8,6,7]=>[3,2,2,1]=>1680
[7,8,5,6,1,2,4,3]=>[8]=>5040
[7,8,4,1,6,2,5,3]=>[8]=>5040
[7,8,1,4,6,2,5,3]=>[7,1]=>5760
[6,1,8,4,7,2,5,3]=>[3,2,2,1]=>1680
[1,6,8,4,7,2,5,3]=>[2,2,2,1,1]=>420
[1,6,8,3,2,7,5,4]=>[4,3,1]=>3360
[6,1,8,3,2,7,5,4]=>[5,3]=>2688
[7,8,1,3,2,6,5,4]=>[7,1]=>5760
[7,8,3,1,2,6,5,4]=>[6,1,1]=>3360
[7,8,3,4,6,5,1,2]=>[2,2,2,1,1]=>420
[7,8,2,4,6,1,5,3]=>[4,3,1]=>3360
[7,8,2,3,1,6,5,4]=>[4,3,1]=>3360
[7,8,2,1,3,6,5,4]=>[7,1]=>5760
[7,8,1,2,3,6,5,4]=>[4,3,1]=>3360
[6,1,8,2,3,7,5,4]=>[8]=>5040
[1,6,8,2,3,7,5,4]=>[7,1]=>5760
[1,5,2,8,3,7,6,4]=>[3,2,2,1]=>1680
[5,1,2,8,3,7,6,4]=>[4,2,2]=>1260
[5,2,1,8,3,7,6,4]=>[3,2,2,1]=>1680
[6,2,8,1,3,7,5,4]=>[7,1]=>5760
[6,2,8,3,1,7,5,4]=>[4,3,1]=>3360
[6,2,8,4,7,1,5,3]=>[2,2,2,1,1]=>420
[6,3,8,4,7,5,1,2]=>[4,3,1]=>3360
[3,6,8,4,7,5,1,2]=>[7,1]=>5760
[2,6,8,4,7,1,5,3]=>[3,2,2,1]=>1680
[2,6,8,3,1,7,5,4]=>[5,3]=>2688
[2,6,8,1,3,7,5,4]=>[8]=>5040
[2,5,1,8,3,7,6,4]=>[4,2,2]=>1260
[1,2,5,8,3,7,6,4]=>[2,2,2,1,1]=>420
[2,4,1,3,8,7,6,5]=>[4,2,2]=>1260
[2,5,3,8,1,7,6,4]=>[3,2,2,1]=>1680
[2,5,4,8,7,1,6,3]=>[5,3]=>2688
[3,5,4,8,7,6,1,2]=>[7,1]=>5760
[5,3,4,8,7,6,1,2]=>[4,3,1]=>3360
[5,2,4,8,7,1,6,3]=>[4,3,1]=>3360
[5,2,3,8,1,7,6,4]=>[2,2,2,1,1]=>420
[4,2,1,3,8,7,6,5]=>[3,2,2,1]=>1680
[4,1,2,3,8,7,6,5]=>[4,2,2]=>1260
[1,4,2,3,8,7,6,5]=>[3,2,2,1]=>1680
[4,1,3,2,8,7,6,5]=>[3,2,2,1]=>1680
[4,3,1,2,8,7,6,5]=>[4,2,2]=>1260
[6,3,8,1,2,7,5,4]=>[8]=>5040
[5,3,1,8,2,7,6,4]=>[4,2,2]=>1260
[5,1,3,8,2,7,6,4]=>[3,2,2,1]=>1680
[1,5,3,8,2,7,6,4]=>[2,2,2,1,1]=>420
[1,5,4,8,7,2,6,3]=>[4,3,1]=>3360
[5,1,4,8,7,2,6,3]=>[5,3]=>2688
[5,4,1,8,7,2,6,3]=>[8]=>5040
[6,4,8,1,7,2,5,3]=>[4,2,2]=>1260
[6,5,8,7,1,2,4,3]=>[4,2,2]=>1260
[5,6,8,7,3,4,1,2]=>[8]=>5040
[5,6,8,7,2,1,4,3]=>[4,2,2]=>1260
[4,5,1,8,7,2,6,3]=>[4,4]=>1260
[4,1,5,8,7,2,6,3]=>[8]=>5040
[1,4,5,8,7,2,6,3]=>[7,1]=>5760
[1,3,5,8,2,7,6,4]=>[3,2,2,1]=>1680
[3,1,5,8,2,7,6,4]=>[4,2,2]=>1260
[3,6,8,1,2,7,5,4]=>[4,4]=>1260
[3,6,8,2,1,7,5,4]=>[8]=>5040
[4,6,8,2,7,1,5,3]=>[4,2,2]=>1260
[4,6,8,3,7,5,1,2]=>[8]=>5040
[4,5,3,8,7,6,1,2]=>[6,1,1]=>3360
[4,5,2,8,7,1,6,3]=>[8]=>5040
[3,5,2,8,1,7,6,4]=>[4,2,2]=>1260
[3,1,4,2,8,7,6,5]=>[4,2,2]=>1260
[3,1,2,4,8,7,6,5]=>[3,2,2,1]=>1680
[3,2,5,8,1,7,6,4]=>[3,2,2,1]=>1680
[4,2,5,8,7,1,6,3]=>[7,1]=>5760
[4,3,5,8,7,6,1,2]=>[7,1]=>5760
[3,4,5,8,7,6,1,2]=>[4,3,1]=>3360
[2,4,5,8,7,1,6,3]=>[8]=>5040
[2,3,5,8,1,7,6,4]=>[4,2,2]=>1260
[4,1,3,2,6,5,8,7]=>[3,2,2,1]=>1680
[5,1,3,2,6,4,8,7]=>[5,2,1]=>4032
[6,1,3,2,5,4,8,7]=>[4,2,1,1]=>2520
[7,1,3,2,5,4,8,6]=>[6,1,1]=>3360
[8,1,3,2,5,4,7,6]=>[5,1,1,1]=>1344
[8,1,4,2,5,3,7,6]=>[6,1,1]=>3360
[7,1,4,2,5,3,8,6]=>[7,1]=>5760
[6,1,4,2,5,3,8,7]=>[5,2,1]=>4032
[5,1,4,2,6,3,8,7]=>[6,2]=>3360
[2,1,6,3,5,4,8,7]=>[3,2,2,1]=>1680
[3,1,6,2,5,4,8,7]=>[5,2,1]=>4032
[4,1,6,2,5,3,8,7]=>[3,2,2,1]=>1680
[6,2,5,1,4,3,8,7]=>[5,2,1]=>4032
[5,2,6,1,4,3,8,7]=>[3,2,2,1]=>1680
[5,2,7,1,4,3,8,6]=>[4,3,1]=>3360
[5,2,8,1,4,3,7,6]=>[3,3,1,1]=>1120
[6,2,8,1,4,3,7,5]=>[6,1,1]=>3360
[6,2,7,1,4,3,8,5]=>[7,1]=>5760
[7,2,6,1,4,3,8,5]=>[5,2,1]=>4032
[7,2,5,1,4,3,8,6]=>[7,1]=>5760
[4,1,7,2,5,3,8,6]=>[4,3,1]=>3360
[3,1,7,2,5,4,8,6]=>[7,1]=>5760
[2,1,7,3,5,4,8,6]=>[5,2,1]=>4032
[2,1,8,3,5,4,7,6]=>[4,2,1,1]=>2520
[3,1,8,2,5,4,7,6]=>[6,1,1]=>3360
[4,1,8,2,5,3,7,6]=>[3,3,1,1]=>1120
[8,2,5,1,4,3,7,6]=>[6,1,1]=>3360
[8,2,6,1,4,3,7,5]=>[4,2,1,1]=>2520
[7,1,4,3,8,2,6,5]=>[4,2,2]=>1260
[8,1,4,3,7,2,6,5]=>[6,2]=>3360
[8,1,5,3,7,2,6,4]=>[8]=>5040
[7,1,5,3,8,2,6,4]=>[4,4]=>1260
[8,2,6,1,5,3,7,4]=>[3,2,1,1,1]=>1120
[5,1,8,2,6,3,7,4]=>[7,1]=>5760
[4,1,8,2,6,3,7,5]=>[4,3,1]=>3360
[3,1,8,2,6,4,7,5]=>[7,1]=>5760
[2,1,8,3,6,4,7,5]=>[5,2,1]=>4032
[2,1,7,3,6,4,8,5]=>[6,2]=>3360
[4,1,7,2,6,3,8,5]=>[5,3]=>2688
[5,1,7,2,6,3,8,4]=>[8]=>5040
[7,2,6,1,5,3,8,4]=>[4,2,1,1]=>2520
[6,2,7,1,5,3,8,4]=>[6,1,1]=>3360
[6,2,8,1,5,3,7,4]=>[5,1,1,1]=>1344
[8,1,5,2,6,3,7,4]=>[4,3,1]=>3360
[6,1,5,2,7,3,8,4]=>[8]=>5040
[6,1,4,2,7,3,8,5]=>[5,3]=>2688
[8,1,4,2,6,3,7,5]=>[7,1]=>5760
[8,1,3,2,6,4,7,5]=>[6,1,1]=>3360
[7,1,3,2,6,4,8,5]=>[7,1]=>5760
[6,1,3,2,7,4,8,5]=>[4,3,1]=>3360
[5,1,3,2,7,4,8,6]=>[7,1]=>5760
[4,1,3,2,7,5,8,6]=>[4,3,1]=>3360
[2,1,4,3,8,5,7,6]=>[3,2,2,1]=>1680
[3,1,4,2,8,5,7,6]=>[4,3,1]=>3360
[4,1,3,2,8,5,7,6]=>[3,3,1,1]=>1120
[5,1,3,2,8,4,7,6]=>[6,1,1]=>3360
[6,1,3,2,8,4,7,5]=>[4,2,1,1]=>2520
[8,4,7,1,3,2,6,5]=>[8]=>5040
[7,4,8,1,3,2,6,5]=>[5,3]=>2688
[7,3,8,1,4,2,6,5]=>[8]=>5040
[8,3,7,1,4,2,6,5]=>[4,4]=>1260
[6,1,4,2,8,3,7,5]=>[5,2,1]=>4032
[5,1,4,2,8,3,7,6]=>[7,1]=>5760
[4,1,5,2,8,3,7,6]=>[4,3,1]=>3360
[3,1,5,2,8,4,7,6]=>[7,1]=>5760
[2,1,5,3,8,4,7,6]=>[5,2,1]=>4032
[2,1,6,3,8,4,7,5]=>[3,2,2,1]=>1680
[3,1,6,2,8,4,7,5]=>[5,2,1]=>4032
[4,1,6,2,8,3,7,5]=>[3,2,2,1]=>1680
[5,1,6,2,8,3,7,4]=>[5,2,1]=>4032
[6,1,5,2,8,3,7,4]=>[7,1]=>5760
[8,3,7,1,5,2,6,4]=>[4,3,1]=>3360
[7,3,8,1,5,2,6,4]=>[7,1]=>5760
[6,2,7,3,8,1,5,4]=>[5,2,1]=>4032
[6,2,8,3,7,1,5,4]=>[3,2,2,1]=>1680
[8,3,7,2,6,1,5,4]=>[8]=>5040
[5,1,8,3,7,2,6,4]=>[5,3]=>2688
[4,1,8,3,7,2,6,5]=>[8]=>5040
[3,1,8,4,7,2,6,5]=>[7,1]=>5760
[2,1,8,4,7,3,6,5]=>[5,2,1]=>4032
[2,1,7,4,8,3,6,5]=>[3,2,2,1]=>1680
[3,1,7,4,8,2,6,5]=>[5,2,1]=>4032
[4,1,7,3,8,2,6,5]=>[6,2]=>3360
[5,1,7,3,8,2,6,4]=>[8]=>5040
[7,3,8,2,6,1,5,4]=>[4,4]=>1260
[8,2,6,3,7,1,5,4]=>[5,2,1]=>4032
[7,2,6,3,8,1,5,4]=>[7,1]=>5760
[3,4,2,6,8,1,5,7]=>[5,3]=>2688
[5,3,6,2,8,1,4,7]=>[8]=>5040
[5,3,6,2,4,8,1,7]=>[8]=>5040
[5,7,3,8,2,4,1,6]=>[4,3,1]=>3360
[5,7,3,8,2,4,6,1]=>[7,1]=>5760
[7,4,2,5,8,3,6,1]=>[8]=>5040
[7,4,2,5,8,3,1,6]=>[6,2]=>3360
[4,5,2,6,3,8,1,7]=>[5,3]=>2688
[4,5,2,1,6,8,3,7]=>[6,2]=>3360
[5,3,1,6,8,2,4,7]=>[8]=>5040
[5,6,2,8,1,3,4,7]=>[3,3,2]=>1120
[3,5,6,1,4,8,2,7]=>[8]=>5040
[4,1,5,6,3,8,2,7]=>[6,2]=>3360
[4,5,1,6,3,8,2,7]=>[8]=>5040
[4,5,6,3,2,8,1,7]=>[6,2]=>3360
[7,4,5,3,8,2,1,6]=>[6,2]=>3360
[7,4,5,3,8,2,6,1]=>[8]=>5040
[6,7,4,8,3,2,5,1]=>[8]=>5040
[6,7,4,8,3,2,1,5]=>[4,4]=>1260
[6,7,4,1,8,3,2,5]=>[4,2,2]=>1260
[7,4,5,3,1,8,2,6]=>[6,2]=>3360
[4,7,1,5,8,3,2,6]=>[6,2]=>3360
[5,3,7,8,1,4,2,6]=>[3,3,2]=>1120
[7,5,8,2,4,6,1,3]=>[3,2,2,1]=>1680
[7,3,5,8,1,4,6,2]=>[8]=>5040
[4,5,1,7,8,3,6,2]=>[5,3]=>2688
[7,4,1,5,8,3,6,2]=>[4,4]=>1260
[6,7,4,3,8,1,5,2]=>[4,2,2]=>1260
[6,7,4,8,3,1,5,2]=>[6,2]=>3360
[6,7,4,8,3,5,2,1]=>[6,2]=>3360
[5,6,7,3,8,4,2,1]=>[5,3]=>2688
[5,6,7,3,1,8,4,2]=>[3,3,2]=>1120
[5,6,1,7,3,8,4,2]=>[3,3,2]=>1120
[5,1,6,7,3,8,4,2]=>[6,2]=>3360
[6,4,7,1,8,3,5,2]=>[8]=>5040
[6,7,8,3,1,4,5,2]=>[8]=>5040
[6,7,2,8,4,5,1,3]=>[8]=>5040
[6,7,2,8,4,1,3,5]=>[3,3,2]=>1120
[6,1,7,4,8,3,2,5]=>[5,2,1]=>4032
[5,1,6,7,3,2,8,4]=>[5,3]=>2688
[5,6,1,7,3,2,8,4]=>[3,3,2]=>1120
[5,6,7,3,2,1,8,4]=>[4,4]=>1260
[5,6,7,3,2,8,4,1]=>[5,3]=>2688
[5,6,2,7,3,8,4,1]=>[6,2]=>3360
[5,6,2,7,3,1,8,4]=>[5,3]=>2688
[5,6,2,1,7,3,8,4]=>[5,3]=>2688
[6,1,7,4,2,8,3,5]=>[5,2,1]=>4032
[6,7,2,1,8,3,4,5]=>[6,2]=>3360
[7,5,8,2,1,3,4,6]=>[5,3]=>2688
[5,7,3,1,8,2,4,6]=>[7,1]=>5760
[4,7,1,5,2,8,3,6]=>[6,2]=>3360
[7,4,2,5,1,8,3,6]=>[6,2]=>3360
[6,7,4,2,1,8,3,5]=>[4,4]=>1260
[6,7,4,2,8,3,1,5]=>[6,2]=>3360
[6,7,4,2,8,3,5,1]=>[8]=>5040
[3,6,7,2,8,4,5,1]=>[5,3]=>2688
[3,6,7,2,8,4,1,5]=>[3,3,2]=>1120
[3,6,7,2,1,8,4,5]=>[8]=>5040
[5,7,3,8,2,1,4,6]=>[7,1]=>5760
[3,4,7,8,2,1,5,6]=>[8]=>5040
[3,7,8,1,4,6,2,5]=>[5,2,1]=>4032
[3,4,7,8,2,6,1,5]=>[4,3,1]=>3360
[5,7,3,8,2,6,1,4]=>[4,2,1,1]=>2520
[3,6,7,2,8,5,1,4]=>[5,3]=>2688
[3,6,7,8,5,2,1,4]=>[3,2,2,1]=>1680
[3,6,7,8,5,2,4,1]=>[5,2,1]=>4032
[6,4,7,8,2,5,3,1]=>[6,2]=>3360
[6,4,7,8,2,1,5,3]=>[6,2]=>3360
[4,1,5,7,8,2,6,3]=>[5,3]=>2688
[5,3,7,8,1,6,2,4]=>[3,2,2,1]=>1680
[6,7,2,8,5,1,3,4]=>[3,2,2,1]=>1680
[6,4,1,7,8,2,5,3]=>[8]=>5040
[5,1,6,2,7,8,4,3]=>[5,3]=>2688
[5,6,2,1,7,8,4,3]=>[4,4]=>1260
[5,6,2,7,1,8,4,3]=>[4,2,2]=>1260
[5,6,2,7,8,4,3,1]=>[5,3]=>2688
[5,6,7,2,8,4,3,1]=>[3,3,2]=>1120
[5,6,7,2,1,8,4,3]=>[6,2]=>3360
[5,6,1,7,2,8,4,3]=>[6,2]=>3360
[5,1,6,7,2,8,4,3]=>[3,3,2]=>1120
[6,4,7,1,8,2,5,3]=>[4,4]=>1260
[3,6,7,1,8,5,2,4]=>[8]=>5040
[6,7,8,5,2,4,1,3]=>[6,2]=>3360
[6,7,8,3,5,1,4,2]=>[5,2,1]=>4032
[4,6,7,8,1,5,3,2]=>[6,2]=>3360
[5,1,6,7,8,4,3,2]=>[4,4]=>1260
[5,6,1,7,8,4,3,2]=>[8]=>5040
[5,6,7,1,8,4,3,2]=>[6,2]=>3360
[8,6,1,3,4,2,5,7]=>[6,2]=>3360
[8,3,2,5,1,6,4,7]=>[5,2,1]=>4032
[8,5,3,6,2,4,1,7]=>[3,2,2,1]=>1680
[5,3,2,7,4,1,8,6]=>[6,2]=>3360
[7,5,3,8,2,4,6,1]=>[5,2,1]=>4032
[7,2,4,5,8,3,6,1]=>[7,1]=>5760
[2,4,5,3,7,1,8,6]=>[8]=>5040
[8,2,4,5,6,3,1,7]=>[4,3,1]=>3360
[8,2,4,5,6,1,3,7]=>[7,1]=>5760
[8,1,2,4,5,6,3,7]=>[5,1,1,1]=>1344
[8,2,5,1,3,6,4,7]=>[4,2,1,1]=>2520
[8,5,6,2,1,4,3,7]=>[8]=>5040
[8,5,3,6,4,1,2,7]=>[7,1]=>5760
[8,4,1,5,6,3,2,7]=>[8]=>5040
[8,1,4,5,6,3,2,7]=>[4,4]=>1260
[4,5,3,7,2,1,8,6]=>[5,2,1]=>4032
[7,4,5,8,3,2,6,1]=>[6,2]=>3360
[4,3,6,7,2,8,5,1]=>[8]=>5040
[4,3,6,7,2,8,1,5]=>[5,3]=>2688
[1,4,3,6,7,2,8,5]=>[3,3,1,1]=>1120
[4,5,3,7,1,8,2,6]=>[5,2,1]=>4032
[4,1,5,3,7,2,8,6]=>[8]=>5040
[5,3,4,7,1,2,8,6]=>[6,2]=>3360
[7,5,8,2,1,4,6,3]=>[6,2]=>3360
[7,5,3,8,4,1,6,2]=>[4,3,1]=>3360
[7,4,5,8,3,6,1,2]=>[3,2,2,1]=>1680
[4,3,6,7,8,1,5,2]=>[8]=>5040
[1,6,4,7,8,3,5,2]=>[7,1]=>5760
[6,4,7,8,3,5,2,1]=>[8]=>5040
[3,5,6,7,8,4,1,2]=>[5,3]=>2688
[3,1,5,6,7,8,4,2]=>[8]=>5040
[4,6,1,7,8,3,5,2]=>[8]=>5040
[3,6,7,1,4,8,5,2]=>[5,3]=>2688
[6,2,4,1,7,8,5,3]=>[5,2,1]=>4032
[2,6,7,1,4,8,3,5]=>[6,2]=>3360
[4,3,6,7,8,1,2,5]=>[6,2]=>3360
[1,5,3,6,7,8,2,4]=>[3,3,1,1]=>1120
[3,5,6,7,8,2,1,4]=>[8]=>5040
[3,5,6,7,8,2,4,1]=>[6,2]=>3360
[5,2,7,1,3,8,4,6]=>[5,2,1]=>4032
[5,3,1,7,8,2,4,6]=>[6,2]=>3360
[4,5,2,7,8,1,3,6]=>[8]=>5040
[4,2,6,7,8,3,1,5]=>[3,2,2,1]=>1680
[4,2,6,7,8,3,5,1]=>[5,2,1]=>4032
[3,6,2,7,4,8,5,1]=>[5,3]=>2688
[3,6,2,7,4,8,1,5]=>[8]=>5040
[3,2,1,6,4,7,8,5]=>[5,2,1]=>4032
[3,7,4,2,1,5,8,6]=>[8]=>5040
[1,7,3,4,2,5,8,6]=>[5,1,1,1]=>1344
[4,7,2,1,3,5,8,6]=>[6,2]=>3360
[7,8,4,2,1,3,6,5]=>[8]=>5040
[7,8,1,3,4,2,6,5]=>[8]=>5040
[7,8,3,4,2,1,6,5]=>[3,3,1,1]=>1120
[6,3,2,7,1,8,5,4]=>[6,2]=>3360
[3,6,2,7,1,8,5,4]=>[8]=>5040
[6,7,3,8,2,5,4,1]=>[7,1]=>5760
[6,4,7,8,5,2,3,1]=>[5,2,1]=>4032
[2,6,4,7,8,1,5,3]=>[5,3]=>2688
[4,6,2,7,8,1,5,3]=>[8]=>5040
[7,4,5,8,6,2,1,3]=>[6,2]=>3360
[7,4,1,5,8,6,2,3]=>[7,1]=>5760
[7,5,3,8,6,1,2,4]=>[5,2,1]=>4032
[7,5,8,2,1,6,3,4]=>[7,1]=>5760
[6,2,7,1,3,8,5,4]=>[4,3,1]=>3360
[6,3,1,7,8,2,5,4]=>[4,4]=>1260
[4,6,1,7,8,5,2,3]=>[8]=>5040
[5,1,2,6,7,8,4,3]=>[8]=>5040
[5,2,6,7,8,4,1,3]=>[7,1]=>5760
[5,2,6,7,8,4,3,1]=>[4,3,1]=>3360
[2,5,6,7,8,4,1,3]=>[8]=>5040
[1,5,2,6,7,8,4,3]=>[7,1]=>5760
[1,6,4,7,8,5,2,3]=>[7,1]=>5760
[2,6,7,1,3,8,5,4]=>[5,3]=>2688
[6,7,8,2,1,5,4,3]=>[3,3,2]=>1120
[6,7,3,8,5,1,4,2]=>[4,2,1,1]=>2520
[6,4,7,8,5,3,1,2]=>[4,3,1]=>3360
[4,5,2,3,7,6,1,8]=>[6,1,1]=>3360
[6,4,3,7,2,5,1,8]=>[6,1,1]=>3360
[8,4,3,6,5,1,2,7]=>[6,1,1]=>3360
[1,5,6,3,4,8,7,2]=>[6,1,1]=>3360
[4,6,2,7,3,5,1,8]=>[4,3,1]=>3360
[3,2,6,7,4,5,1,8]=>[6,1,1]=>3360
[4,7,2,6,5,3,1,8]=>[6,1,1]=>3360
[5,7,6,2,4,3,1,8]=>[5,2,1]=>4032
[1,7,5,4,8,3,6,2]=>[6,1,1]=>3360
[8,7,5,4,1,3,2,6]=>[5,2,1]=>4032
[6,8,5,4,2,1,3,7]=>[5,2,1]=>4032
[5,8,6,2,4,1,3,7]=>[8]=>5040
[4,8,2,6,5,1,3,7]=>[4,3,1]=>3360
[3,2,8,6,5,1,4,7]=>[6,1,1]=>3360
[4,1,2,6,5,8,7,3]=>[6,1,1]=>3360
[5,1,6,2,4,8,7,3]=>[4,3,1]=>3360
[6,1,5,4,2,8,7,3]=>[6,1,1]=>3360
[7,1,5,4,8,2,6,3]=>[4,3,1]=>3360
[8,1,5,4,7,6,2,3]=>[6,1,1]=>3360
[1,8,6,7,4,5,3,2]=>[5,2,1]=>4032
[8,1,6,7,4,5,2,3]=>[8]=>5040
[7,1,6,8,4,2,5,3]=>[8]=>5040
[6,1,7,8,2,4,5,3]=>[8]=>5040
[5,1,7,2,8,4,6,3]=>[8]=>5040
[4,1,2,7,8,5,6,3]=>[8]=>5040
[3,2,1,7,8,5,6,4]=>[5,2,1]=>4032
[3,2,8,7,1,5,4,6]=>[5,2,1]=>4032
[4,8,2,7,1,5,3,6]=>[8]=>5040
[5,8,7,2,1,4,3,6]=>[4,2,2]=>1260
[6,8,7,1,2,4,3,5]=>[3,3,2]=>1120
[7,8,6,1,4,2,3,5]=>[8]=>5040
[8,7,6,1,4,3,2,5]=>[4,2,2]=>1260
[1,7,6,8,4,3,5,2]=>[5,2,1]=>4032
[1,6,7,8,3,4,5,2]=>[4,3,1]=>3360
[8,6,7,1,3,4,2,5]=>[8]=>5040
[7,6,8,1,3,2,4,5]=>[3,3,2]=>1120
[5,7,8,2,1,3,4,6]=>[3,3,2]=>1120
[4,7,2,8,1,3,5,6]=>[8]=>5040
[3,2,6,8,4,1,5,7]=>[4,3,1]=>3360
[4,6,2,8,3,1,5,7]=>[8]=>5040
[5,6,8,2,3,1,4,7]=>[8]=>5040
[6,5,8,3,2,1,4,7]=>[4,2,2]=>1260
[7,5,8,3,1,2,4,6]=>[8]=>5040
[8,5,7,3,1,4,2,6]=>[8]=>5040
[1,5,7,3,8,4,6,2]=>[4,3,1]=>3360
[1,4,3,7,8,5,6,2]=>[6,1,1]=>3360
[8,4,3,7,1,5,2,6]=>[4,3,1]=>3360
[6,4,3,8,2,1,5,7]=>[5,2,1]=>4032
[4,5,2,3,8,1,6,7]=>[8]=>5040
[3,2,5,4,8,1,6,7]=>[6,1,1]=>3360
[4,5,2,3,1,8,7,6]=>[5,2,1]=>4032
[6,4,3,1,2,8,7,5]=>[6,1,1]=>3360
[7,4,3,1,8,2,6,5]=>[5,2,1]=>4032
[8,4,3,1,7,6,2,5]=>[6,1,1]=>3360
[1,5,8,3,7,6,4,2]=>[6,1,1]=>3360
[8,5,1,3,7,6,2,4]=>[4,3,1]=>3360
[7,5,1,3,8,2,6,4]=>[8]=>5040
[6,5,1,3,2,8,7,4]=>[5,2,1]=>4032
[5,6,1,2,3,8,7,4]=>[4,3,1]=>3360
[4,6,2,1,3,8,7,5]=>[5,2,1]=>4032
[3,2,6,1,4,8,7,5]=>[6,1,1]=>3360
[3,2,7,1,8,4,6,5]=>[5,2,1]=>4032
[4,7,2,1,8,3,6,5]=>[4,2,2]=>1260
[5,7,1,2,8,3,6,4]=>[8]=>5040
[6,7,1,8,2,3,5,4]=>[3,3,2]=>1120
[7,6,1,8,3,2,5,4]=>[4,2,2]=>1260
[8,6,1,7,3,5,2,4]=>[8]=>5040
[1,6,8,7,3,5,4,2]=>[5,2,1]=>4032
[1,7,8,6,5,3,4,2]=>[6,1,1]=>3360
[8,7,1,6,5,3,2,4]=>[5,2,1]=>4032
[7,8,1,6,5,2,3,4]=>[4,3,1]=>3360
[6,8,1,7,2,5,3,4]=>[8]=>5040
[5,8,1,2,7,6,3,4]=>[4,3,1]=>3360
[4,8,2,1,7,6,3,5]=>[5,2,1]=>4032
[3,2,8,1,7,6,4,5]=>[6,1,1]=>3360
[4,1,2,8,7,6,5,3]=>[5,2,1]=>4032
[5,1,8,2,7,6,4,3]=>[5,2,1]=>4032
[6,1,8,7,2,5,4,3]=>[4,2,2]=>1260
[7,1,8,6,5,2,4,3]=>[5,2,1]=>4032
[8,1,7,6,5,4,2,3]=>[5,2,1]=>4032
[3,1,2,6,5,8,7,4]=>[3,3,1,1]=>1120
[3,1,6,2,4,8,7,5]=>[7,1]=>5760
[4,6,1,2,3,8,7,5]=>[7,1]=>5760
[6,1,5,2,4,8,7,3]=>[7,1]=>5760
[6,5,1,2,3,8,7,4]=>[7,1]=>5760
[6,4,1,2,3,8,7,5]=>[5,2,1]=>4032
[5,4,1,2,3,8,7,6]=>[3,2,2,1]=>1680
[6,4,1,7,2,3,5,8]=>[4,3,1]=>3360
[6,4,1,8,2,3,5,7]=>[5,3]=>2688
[7,4,1,2,8,3,6,5]=>[4,2,2]=>1260
[7,5,1,2,8,3,6,4]=>[4,4]=>1260
[7,1,5,2,8,4,6,3]=>[5,3]=>2688
[1,8,5,3,7,4,6,2]=>[5,2,1]=>4032
[8,1,5,2,7,4,6,3]=>[8]=>5040
[8,5,1,2,7,3,6,4]=>[8]=>5040
[8,4,1,2,7,3,6,5]=>[6,2]=>3360
[8,4,1,7,2,3,5,6]=>[4,4]=>1260
[7,4,1,6,2,3,5,8]=>[7,1]=>5760
[8,1,6,7,2,4,5,3]=>[8]=>5040
[1,8,6,7,3,4,5,2]=>[5,2,1]=>4032
[7,1,6,8,2,4,5,3]=>[4,4]=>1260
[7,6,1,8,2,3,5,4]=>[6,2]=>3360
[4,7,1,2,8,3,6,5]=>[6,2]=>3360
[3,1,7,2,8,4,6,5]=>[6,2]=>3360
[1,4,3,8,7,5,6,2]=>[3,3,1,1]=>1120
[4,1,2,8,7,5,6,3]=>[5,3]=>2688
[3,1,8,2,7,4,6,5]=>[8]=>5040
[3,1,8,7,2,4,5,6]=>[8]=>5040
[4,7,1,6,2,3,5,8]=>[4,3,1]=>3360
[4,8,1,6,2,3,5,7]=>[4,4]=>1260
[4,8,1,7,2,3,5,6]=>[8]=>5040
[4,8,1,2,7,3,6,5]=>[8]=>5040
[5,8,1,2,7,3,6,4]=>[5,3]=>2688
[1,5,8,3,7,4,6,2]=>[7,1]=>5760
[6,8,1,7,2,3,5,4]=>[5,3]=>2688
[6,8,7,1,2,3,4,5]=>[5,3]=>2688
[5,7,6,1,2,3,4,8]=>[5,2,1]=>4032
[1,7,8,6,3,4,5,2]=>[5,2,1]=>4032
[8,7,1,6,2,3,5,4]=>[5,3]=>2688
[3,2,5,1,6,4,8,7]=>[5,2,1]=>4032
[3,2,5,4,7,1,8,6]=>[6,1,1]=>3360
[4,2,5,3,7,6,8,1]=>[6,1,1]=>3360
[4,2,5,3,7,1,8,6]=>[7,1]=>5760
[4,2,5,3,6,1,8,7]=>[5,2,1]=>4032
[4,2,5,1,6,3,8,7]=>[3,2,2,1]=>1680
[3,1,5,4,6,2,8,7]=>[5,2,1]=>4032
[4,1,5,3,6,2,8,7]=>[6,2]=>3360
[4,3,5,1,6,2,8,7]=>[4,2,2]=>1260
[4,3,5,2,7,1,8,6]=>[8]=>5040
[4,3,6,2,7,5,8,1]=>[8]=>5040
[4,3,6,2,7,1,8,5]=>[5,3]=>2688
[4,3,6,1,7,2,8,5]=>[3,3,2]=>1120
[4,3,5,1,7,2,8,6]=>[6,2]=>3360
[3,1,5,4,7,2,8,6]=>[7,1]=>5760
[2,1,5,4,7,3,8,6]=>[5,2,1]=>4032
[3,1,5,4,7,6,8,2]=>[6,1,1]=>3360
[4,1,5,3,7,6,8,2]=>[7,1]=>5760
[4,3,5,1,7,6,8,2]=>[5,2,1]=>4032
[4,3,6,1,7,5,8,2]=>[6,2]=>3360
[4,3,6,5,7,1,8,2]=>[8]=>5040
[5,3,6,4,7,2,8,1]=>[4,3,1]=>3360
[5,3,6,4,7,1,8,2]=>[7,1]=>5760
[5,3,6,1,7,4,8,2]=>[8]=>5040
[5,1,6,3,7,4,8,2]=>[5,3]=>2688
[4,1,6,3,7,5,8,2]=>[8]=>5040
[3,1,6,4,7,5,8,2]=>[7,1]=>5760
[2,1,6,4,7,5,8,3]=>[5,2,1]=>4032
[2,1,6,4,7,3,8,5]=>[3,2,2,1]=>1680
[3,1,6,4,7,2,8,5]=>[4,3,1]=>3360
[4,1,6,3,7,2,8,5]=>[5,3]=>2688
[5,1,6,3,7,2,8,4]=>[8]=>5040
[5,3,6,1,7,2,8,4]=>[5,3]=>2688
[5,3,6,2,7,1,8,4]=>[8]=>5040
[5,3,6,2,7,4,8,1]=>[4,4]=>1260
[5,2,6,3,7,4,8,1]=>[4,3,1]=>3360
[5,2,6,3,7,1,8,4]=>[7,1]=>5760
[5,2,6,1,7,3,8,4]=>[5,2,1]=>4032
[4,2,5,1,7,3,8,6]=>[5,2,1]=>4032
[4,2,6,1,7,3,8,5]=>[3,2,2,1]=>1680
[4,2,6,3,7,1,8,5]=>[4,3,1]=>3360
[4,2,6,3,7,5,8,1]=>[7,1]=>5760
[3,2,6,4,7,5,8,1]=>[6,1,1]=>3360
[3,2,6,4,7,1,8,5]=>[3,3,1,1]=>1120
[3,2,6,1,7,4,8,5]=>[4,3,1]=>3360
[3,2,5,1,7,4,8,6]=>[7,1]=>5760
[3,2,4,1,7,5,8,6]=>[4,3,1]=>3360
[3,1,4,2,7,6,8,5]=>[4,3,1]=>3360
[3,2,5,1,7,6,8,4]=>[6,1,1]=>3360
[3,2,6,1,7,5,8,4]=>[7,1]=>5760
[3,2,6,5,7,1,8,4]=>[4,3,1]=>3360
[4,2,6,5,7,3,8,1]=>[5,2,1]=>4032
[4,2,6,5,7,1,8,3]=>[7,1]=>5760
[4,2,6,1,7,5,8,3]=>[5,2,1]=>4032
[4,2,5,1,7,6,8,3]=>[4,2,1,1]=>2520
[4,1,5,2,7,6,8,3]=>[4,3,1]=>3360
[3,1,5,2,7,6,8,4]=>[7,1]=>5760
[2,1,5,3,7,6,8,4]=>[5,2,1]=>4032
[2,1,6,3,7,5,8,4]=>[6,2]=>3360
[3,1,6,2,7,5,8,4]=>[8]=>5040
[4,1,6,2,7,5,8,3]=>[5,3]=>2688
[5,1,6,2,7,4,8,3]=>[8]=>5040
[5,2,6,1,7,4,8,3]=>[7,1]=>5760
[5,2,6,4,7,1,8,3]=>[6,1,1]=>3360
[5,2,6,4,7,3,8,1]=>[4,2,1,1]=>2520
[5,4,6,2,7,3,8,1]=>[4,2,2]=>1260
[5,4,6,2,7,1,8,3]=>[6,2]=>3360
[5,4,6,1,7,2,8,3]=>[8]=>5040
[5,1,6,4,7,2,8,3]=>[7,1]=>5760
[4,1,6,5,7,2,8,3]=>[8]=>5040
[3,1,6,5,7,2,8,4]=>[4,4]=>1260
[2,1,6,5,7,3,8,4]=>[4,2,2]=>1260
[3,1,6,5,7,4,8,2]=>[8]=>5040
[4,1,6,5,7,3,8,2]=>[6,2]=>3360
[5,1,6,4,7,3,8,2]=>[5,2,1]=>4032
[5,4,6,1,7,3,8,2]=>[6,2]=>3360
[5,4,6,3,7,1,8,2]=>[8]=>5040
[8,3,5,2,1,6,4,7]=>[7,1]=>5760
[8,6,3,5,2,4,1,7]=>[4,3,1]=>3360
[3,7,5,2,4,1,8,6]=>[8]=>5040
[8,3,7,5,2,4,6,1]=>[6,2]=>3360
[8,2,4,5,7,3,6,1]=>[5,2,1]=>4032
[2,4,5,7,3,1,8,6]=>[6,2]=>3360
[8,2,4,6,5,3,1,7]=>[3,3,1,1]=>1120
[8,2,5,4,6,1,3,7]=>[6,1,1]=>3360
[8,6,3,5,1,4,2,7]=>[7,1]=>5760
[8,6,1,4,5,3,2,7]=>[6,1,1]=>3360
[8,1,5,6,4,3,2,7]=>[4,4]=>1260
[5,7,4,3,2,1,8,6]=>[6,2]=>3360
[8,5,7,4,3,2,6,1]=>[5,2,1]=>4032
[4,6,8,3,2,7,5,1]=>[4,4]=>1260
[4,7,6,3,2,8,1,5]=>[8]=>5040
[1,4,6,7,3,2,8,5]=>[7,1]=>5760
[5,4,7,3,1,8,2,6]=>[4,2,2]=>1260
[1,7,4,5,3,2,8,6]=>[4,3,1]=>3360
[3,7,5,1,4,2,8,6]=>[4,4]=>1260
[5,7,4,2,1,3,8,6]=>[6,2]=>3360
[8,5,7,4,2,1,6,3]=>[5,2,1]=>4032
[8,3,7,5,1,4,6,2]=>[8]=>5040
[8,4,1,7,5,3,6,2]=>[7,1]=>5760
[4,6,3,8,7,1,5,2]=>[5,2,1]=>4032
[1,7,4,8,6,3,5,2]=>[7,1]=>5760
[8,4,7,6,3,5,2,1]=>[6,2]=>3360
[3,6,5,8,7,4,1,2]=>[4,4]=>1260
[3,1,5,8,6,7,4,2]=>[8]=>5040
[4,8,1,6,7,3,5,2]=>[4,2,2]=>1260
[3,6,4,1,8,7,5,2]=>[5,3]=>2688
[8,2,6,1,4,7,5,3]=>[7,1]=>5760
[2,7,6,8,1,4,3,5]=>[8]=>5040
[3,7,1,6,4,8,2,5]=>[4,2,2]=>1260
[1,7,3,5,6,8,2,4]=>[4,2,1,1]=>2520
[1,3,6,7,5,8,2,4]=>[6,1,1]=>3360
[3,7,6,5,8,2,1,4]=>[5,3]=>2688
[3,6,8,5,7,2,4,1]=>[3,3,2]=>1120
[2,3,5,7,6,8,1,4]=>[8]=>5040
[2,1,6,5,7,8,3,4]=>[6,2]=>3360
[4,2,7,6,8,3,1,5]=>[5,2,1]=>4032
[4,2,6,8,7,3,5,1]=>[3,2,2,1]=>1680
[3,8,2,4,6,7,5,1]=>[4,3,1]=>3360
[3,7,2,6,4,8,1,5]=>[4,4]=>1260
[3,2,6,1,4,7,8,5]=>[7,1]=>5760
[5,3,7,2,1,8,4,6]=>[4,2,2]=>1260
[4,7,3,2,1,5,8,6]=>[7,1]=>5760
[8,7,6,1,3,4,2,5]=>[6,2]=>3360
[8,5,7,3,2,1,6,4]=>[6,2]=>3360
[8,3,6,7,2,1,5,4]=>[8]=>5040
[3,7,8,6,2,1,5,4]=>[5,3]=>2688
[8,7,6,3,5,2,4,1]=>[5,2,1]=>4032
[2,7,4,8,1,6,5,3]=>[4,3,1]=>3360
[4,6,8,2,1,7,5,3]=>[6,2]=>3360
[8,4,1,5,7,2,6,3]=>[5,3]=>2688
[8,5,3,7,1,6,2,4]=>[6,1,1]=>3360
[8,5,7,2,1,3,6,4]=>[5,3]=>2688
[8,2,6,7,1,3,5,4]=>[5,2,1]=>4032
[8,3,6,1,7,5,2,4]=>[5,3]=>2688
[4,6,1,8,7,2,5,3]=>[4,2,2]=>1260
[8,1,2,5,6,7,4,3]=>[4,4]=>1260
[8,2,6,5,7,4,1,3]=>[7,1]=>5760
[2,1,7,8,5,6,4,3]=>[4,2,1,1]=>2520
[8,2,5,7,6,4,3,1]=>[5,2,1]=>4032
[2,7,6,8,5,4,1,3]=>[4,3,1]=>3360
[1,7,2,5,8,6,4,3]=>[6,1,1]=>3360
[1,7,4,8,2,6,5,3]=>[3,3,1,1]=>1120
[3,7,8,1,6,5,2,4]=>[4,2,2]=>1260
[2,7,8,6,1,3,5,4]=>[4,4]=>1260
[8,7,6,3,5,1,4,2]=>[7,1]=>5760
[8,4,7,6,5,1,3,2]=>[5,2,1]=>4032
[8,7,1,5,6,4,3,2]=>[5,3]=>2688
[8,1,6,7,5,4,3,2]=>[4,3,1]=>3360
[6,5,3,1,2,4,8,7]=>[3,2,2,1]=>1680
[4,6,3,5,1,2,8,7]=>[3,2,2,1]=>1680
[8,5,3,7,2,1,4,6]=>[3,2,2,1]=>1680
[6,8,1,4,5,7,3,2]=>[4,2,1,1]=>2520
[8,7,2,4,5,1,3,6]=>[3,3,1,1]=>1120
[3,6,2,4,5,1,8,7]=>[4,2,1,1]=>2520
[2,6,1,4,5,3,8,7]=>[4,2,1,1]=>2520
[6,1,2,4,5,3,8,7]=>[4,2,1,1]=>2520
[5,6,3,2,1,4,8,7]=>[3,2,2,1]=>1680
[5,4,3,6,1,2,8,7]=>[3,2,2,1]=>1680
[6,3,1,4,5,2,8,7]=>[4,2,1,1]=>2520
[3,1,6,4,5,2,8,7]=>[4,2,1,1]=>2520
[8,3,7,4,5,1,2,6]=>[3,3,1,1]=>1120
[5,8,7,4,2,6,3,1]=>[4,2,1,1]=>2520
[2,8,7,4,1,6,3,5]=>[4,2,1,1]=>2520
[8,1,7,4,2,6,3,5]=>[4,2,1,1]=>2520
[3,7,8,4,5,1,2,6]=>[4,2,1,1]=>2520
[2,1,8,7,5,3,4,6]=>[3,2,2,1]=>1680
[2,1,6,8,5,7,3,4]=>[3,2,2,1]=>1680
[5,6,3,8,1,7,2,4]=>[3,2,2,1]=>1680
[7,6,1,4,5,8,3,2]=>[3,3,1,1]=>1120
[3,7,6,4,5,8,2,1]=>[4,2,1,1]=>2520
[8,5,7,4,1,6,3,2]=>[4,2,1,1]=>2520
[5,1,8,4,7,6,2,3]=>[4,2,1,1]=>2520
[2,5,8,4,7,6,1,3]=>[4,2,1,1]=>2520
[2,4,8,3,5,6,7,1]=>[5,1,1,1]=>1344
[4,1,8,3,5,6,7,2]=>[5,1,1,1]=>1344
[3,8,4,2,5,6,7,1]=>[5,1,1,1]=>1344
[8,4,1,3,5,6,7,2]=>[5,1,1,1]=>1344
[7,5,8,4,3,6,1,2]=>[4,2,1,1]=>2520
[6,5,3,8,4,1,7,2]=>[4,2,1,1]=>2520
[2,1,5,8,4,6,7,3]=>[4,2,1,1]=>2520
[2,1,4,8,3,6,7,5]=>[4,2,1,1]=>2520
[6,4,3,8,2,1,7,5]=>[4,2,1,1]=>2520
[7,3,8,4,2,6,1,5]=>[4,2,1,1]=>2520
[8,3,1,2,5,6,7,4]=>[5,1,1,1]=>1344
[3,1,8,2,5,6,7,4]=>[5,1,1,1]=>1344
[2,3,8,1,5,6,7,4]=>[5,1,1,1]=>1344
[4,3,8,2,5,6,7,1]=>[5,1,1,1]=>1344
[4,8,2,3,5,6,7,1]=>[5,1,1,1]=>1344
[3,8,2,1,5,6,7,4]=>[5,1,1,1]=>1344
[2,8,1,3,5,6,7,4]=>[5,1,1,1]=>1344
[8,1,2,3,5,6,7,4]=>[5,1,1,1]=>1344
[7,8,2,4,3,6,1,5]=>[4,2,1,1]=>2520
[6,8,3,2,4,1,7,5]=>[4,2,1,1]=>2520
[2,1,8,3,4,6,7,5]=>[4,2,1,1]=>2520
[2,1,7,8,5,4,3,6]=>[3,2,2,1]=>1680
[5,7,3,8,1,4,2,6]=>[3,2,2,1]=>1680
[7,1,8,4,5,3,2,6]=>[3,3,1,1]=>1120
[2,7,8,4,5,3,1,6]=>[3,3,1,1]=>1120
[8,7,1,4,3,6,2,5]=>[4,2,1,1]=>2520
[3,8,7,4,2,6,1,5]=>[3,3,1,1]=>1120
[5,7,8,4,3,6,2,1]=>[4,2,1,1]=>2520
[5,6,3,8,4,2,7,1]=>[4,2,1,1]=>2520
[4,8,3,6,2,1,7,5]=>[3,3,1,1]=>1120
[8,6,3,1,4,2,7,5]=>[4,2,1,1]=>2520
[7,5,3,8,2,4,1,6]=>[3,2,2,1]=>1680
[2,4,3,1,8,5,7,6]=>[3,3,1,1]=>1120
[4,1,3,2,6,8,7,5]=>[3,3,1,1]=>1120
[7,5,3,6,2,8,1,4]=>[3,2,2,1]=>1680
[8,6,3,5,1,2,7,4]=>[4,2,1,1]=>2520
[5,8,3,2,6,1,7,4]=>[3,3,1,1]=>1120
[4,5,3,8,6,2,7,1]=>[3,3,1,1]=>1120
[3,5,8,4,7,6,2,1]=>[3,3,1,1]=>1120
[5,8,2,4,7,6,1,3]=>[3,3,1,1]=>1120
[8,7,5,4,1,6,2,3]=>[4,2,1,1]=>2520
[2,7,6,4,5,8,1,3]=>[3,3,1,1]=>1120
[7,1,6,4,5,8,2,3]=>[3,3,1,1]=>1120
[5,7,3,6,1,8,2,4]=>[3,2,2,1]=>1680
[2,1,7,6,5,8,3,4]=>[3,2,2,1]=>1680
[2,1,8,5,3,6,7,4]=>[4,2,1,1]=>2520
[6,8,3,5,2,1,7,4]=>[4,2,1,1]=>2520
[7,8,5,4,2,6,1,3]=>[4,2,1,1]=>2520
[8,1,4,2,5,6,7,3]=>[5,1,1,1]=>1344
[2,8,4,1,5,6,7,3]=>[5,1,1,1]=>1344
[4,8,1,2,5,6,7,3]=>[5,1,1,1]=>1344
[3,4,8,1,5,6,7,2]=>[5,1,1,1]=>1344
[3,4,2,8,5,6,7,1]=>[5,1,1,1]=>1344
[2,4,1,8,5,6,7,3]=>[5,1,1,1]=>1344
[4,1,2,8,5,6,7,3]=>[5,1,1,1]=>1344
[8,4,2,1,5,6,7,3]=>[5,1,1,1]=>1344
[7,5,2,4,8,6,1,3]=>[4,2,1,1]=>2520
[6,5,3,2,8,1,7,4]=>[4,2,1,1]=>2520
[2,1,5,3,8,6,7,4]=>[4,2,1,1]=>2520
[6,4,3,5,8,1,7,2]=>[4,2,1,1]=>2520
[7,3,5,4,8,6,1,2]=>[4,2,1,1]=>2520
[8,3,4,1,5,6,7,2]=>[5,1,1,1]=>1344
[4,3,1,8,5,6,7,2]=>[5,1,1,1]=>1344
[3,1,4,8,5,6,7,2]=>[5,1,1,1]=>1344
[6,5,3,7,2,8,4,1]=>[3,2,2,1]=>1680
[6,3,7,4,5,8,2,1]=>[3,3,1,1]=>1120
[6,7,2,4,5,8,3,1]=>[3,3,1,1]=>1120
[5,1,7,4,8,6,3,2]=>[4,2,1,1]=>2520
[2,5,7,4,8,6,3,1]=>[4,2,1,1]=>2520
[5,6,3,7,1,8,4,2]=>[3,2,2,1]=>1680
[3,8,7,4,5,2,1,6]=>[3,3,1,1]=>1120
[3,7,5,4,8,6,2,1]=>[4,2,1,1]=>2520
[5,7,1,4,8,6,2,3]=>[4,2,1,1]=>2520
[5,6,3,1,8,2,7,4]=>[4,2,1,1]=>2520
[4,6,3,5,8,2,7,1]=>[4,2,1,1]=>2520
[4,6,3,8,1,2,7,5]=>[4,2,1,1]=>2520
[3,7,8,4,1,6,2,5]=>[4,2,1,1]=>2520
[3,2,5,1,6,8,4,7]=>[7,1]=>5760
[3,6,2,5,4,8,1,7]=>[6,2]=>3360
[3,5,2,4,7,1,8,6]=>[7,1]=>5760
[3,5,8,2,4,7,6,1]=>[3,3,2]=>1120
[4,2,5,8,3,7,6,1]=>[3,2,2,1]=>1680
[4,2,6,5,3,8,1,7]=>[7,1]=>5760
[5,4,2,1,6,8,3,7]=>[8]=>5040
[6,3,5,1,4,8,2,7]=>[8]=>5040
[4,6,1,5,3,8,2,7]=>[4,4]=>1260
[5,1,6,4,3,8,2,7]=>[7,1]=>5760
[5,4,3,2,7,1,8,6]=>[5,2,1]=>4032
[5,4,3,8,2,7,6,1]=>[5,2,1]=>4032
[4,3,6,2,8,7,5,1]=>[8]=>5040
[4,3,7,6,2,1,8,5]=>[5,3]=>2688
[6,4,3,1,7,2,8,5]=>[4,3,1]=>3360
[7,5,4,3,1,8,2,6]=>[4,2,2]=>1260
[1,4,7,5,8,3,2,6]=>[7,1]=>5760
[7,1,3,5,8,4,2,6]=>[4,3,1]=>3360
[7,2,5,8,4,1,3,6]=>[7,1]=>5760
[2,8,5,7,4,6,1,3]=>[7,1]=>5760
[3,5,8,7,1,4,6,2]=>[5,3]=>2688
[1,4,5,8,7,3,6,2]=>[4,3,1]=>3360
[1,5,4,8,7,3,6,2]=>[7,1]=>5760
[6,4,3,8,1,7,5,2]=>[4,3,1]=>3360
[4,3,7,1,8,6,5,2]=>[5,2,1]=>4032
[4,8,3,7,6,5,2,1]=>[5,2,1]=>4032
[5,3,8,7,6,4,2,1]=>[8]=>5040
[7,5,3,1,8,6,4,2]=>[3,3,1,1]=>1120
[1,8,6,5,3,7,4,2]=>[5,2,1]=>4032
[1,5,8,6,3,7,4,2]=>[4,3,1]=>3360
[4,6,1,8,7,3,5,2]=>[6,2]=>3360
[6,8,7,3,1,4,5,2]=>[6,2]=>3360
[6,2,8,7,4,5,1,3]=>[5,2,1]=>4032
[7,6,2,8,4,1,3,5]=>[5,3]=>2688
[7,3,1,6,8,4,2,5]=>[4,2,2]=>1260
[1,7,6,4,8,3,2,5]=>[2,2,2,1,1]=>420
[5,7,1,6,3,2,8,4]=>[5,3]=>2688
[6,1,7,5,3,2,8,4]=>[5,3]=>2688
[7,6,5,3,2,1,8,4]=>[8]=>5040
[6,5,3,2,8,7,4,1]=>[7,1]=>5760
[5,2,6,3,8,7,4,1]=>[4,3,1]=>3360
[5,2,7,6,3,1,8,4]=>[7,1]=>5760
[6,5,2,1,7,3,8,4]=>[8]=>5040
[5,2,7,4,1,8,3,6]=>[2,2,2,1,1]=>420
[4,7,2,6,3,1,8,5]=>[5,3]=>2688
[2,4,8,6,3,7,5,1]=>[8]=>5040
[3,8,6,2,4,7,5,1]=>[8]=>5040
[7,3,6,2,4,1,8,5]=>[8]=>5040
[3,6,7,2,1,4,8,5]=>[5,3]=>2688
[4,3,7,8,2,1,5,6]=>[4,4]=>1260
[8,3,7,1,4,6,2,5]=>[4,3,1]=>3360
[3,8,2,5,7,1,6,4]=>[8]=>5040
[8,3,6,2,7,1,5,4]=>[6,2]=>3360
[7,8,3,6,2,1,5,4]=>[7,1]=>5760
[8,7,3,6,2,5,4,1]=>[5,2,1]=>4032
[4,7,8,2,1,6,5,3]=>[5,2,1]=>4032
[4,2,6,8,1,7,5,3]=>[7,1]=>5760
[5,4,8,2,7,1,6,3]=>[4,2,2]=>1260
[4,8,1,5,7,2,6,3]=>[8]=>5040
[5,8,3,7,1,6,2,4]=>[4,2,1,1]=>2520
[5,8,7,2,6,1,3,4]=>[3,3,2]=>1120
[8,6,2,7,5,1,3,4]=>[7,1]=>5760
[3,6,8,1,7,5,2,4]=>[4,4]=>1260
[5,1,6,8,2,7,4,3]=>[5,3]=>2688
[6,5,2,8,1,7,4,3]=>[8]=>5040
[5,2,7,1,8,6,4,3]=>[6,1,1]=>3360
[5,8,2,7,6,4,3,1]=>[8]=>5040
[6,2,8,7,5,4,3,1]=>[6,1,1]=>3360
[7,6,2,1,8,5,4,3]=>[5,3]=>2688
[6,1,7,2,8,5,4,3]=>[8]=>5040
[7,5,1,8,2,6,4,3]=>[5,2,1]=>4032
[4,7,1,8,6,2,5,3]=>[4,4]=>1260
[7,8,3,1,6,5,2,4]=>[5,2,1]=>4032
[8,7,4,6,1,5,3,2]=>[8]=>5040
[8,5,7,1,6,4,3,2]=>[6,2]=>3360
[6,8,1,7,5,4,3,2]=>[5,2,1]=>4032
[7,1,8,6,5,4,3,2]=>[5,2,1]=>4032
[5,4,2,3,7,6,1,8]=>[3,3,1,1]=>1120
[6,4,2,7,3,5,1,8]=>[7,1]=>5760
[7,4,2,6,3,5,1,8]=>[5,2,1]=>4032
[8,4,2,6,3,1,5,7]=>[8]=>5040
[3,2,7,6,4,5,1,8]=>[3,3,1,1]=>1120
[4,7,2,6,3,5,1,8]=>[7,1]=>5760
[5,7,6,2,3,4,1,8]=>[7,1]=>5760
[1,6,5,2,3,8,4,7]=>[5,2,1]=>4032
[1,7,5,2,8,3,4,6]=>[4,3,1]=>3360
[6,8,5,2,3,1,4,7]=>[4,2,2]=>1260
[5,8,6,2,3,1,4,7]=>[4,4]=>1260
[4,8,2,6,3,1,5,7]=>[5,3]=>2688
[3,2,8,6,4,1,5,7]=>[7,1]=>5760
[3,2,1,6,4,8,5,7]=>[5,2,1]=>4032
[7,1,5,2,8,3,4,6]=>[4,4]=>1260
[1,8,5,2,7,3,4,6]=>[7,1]=>5760
[1,8,6,7,2,3,4,5]=>[3,2,2,1]=>1680
[8,1,6,7,2,3,4,5]=>[4,2,2]=>1260
[7,1,6,8,2,3,4,5]=>[6,2]=>3360
[3,2,1,7,8,4,5,6]=>[5,2,1]=>4032
[3,2,8,7,1,4,5,6]=>[7,1]=>5760
[5,8,7,2,1,3,4,6]=>[6,2]=>3360
[1,7,6,8,2,3,4,5]=>[5,2,1]=>4032
[6,5,8,2,3,1,4,7]=>[6,2]=>3360
[8,5,7,2,1,3,4,6]=>[8]=>5040
[6,4,2,8,3,1,5,7]=>[6,2]=>3360
[5,4,2,3,8,1,6,7]=>[5,3]=>2688
[3,2,5,4,1,8,6,7]=>[3,3,1,1]=>1120
[4,5,2,3,1,8,6,7]=>[5,3]=>2688
[5,4,2,3,1,8,6,7]=>[3,3,2]=>1120
[6,4,2,1,3,8,5,7]=>[8]=>5040
[7,4,2,1,8,3,5,6]=>[8]=>5040
[8,4,2,1,7,3,5,6]=>[6,2]=>3360
[1,4,2,8,7,3,5,6]=>[5,2,1]=>4032
[1,5,8,2,7,3,4,6]=>[4,3,1]=>3360
[8,5,1,2,7,3,4,6]=>[4,4]=>1260
[7,5,1,2,8,3,4,6]=>[8]=>5040
[6,5,1,2,3,8,4,7]=>[8]=>5040
[4,6,2,1,3,8,5,7]=>[6,2]=>3360
[3,2,6,1,4,8,5,7]=>[7,1]=>5760
[3,2,7,1,8,4,5,6]=>[7,1]=>5760
[4,7,2,1,8,3,5,6]=>[6,2]=>3360
[7,6,1,8,2,3,4,5]=>[8]=>5040
[8,6,1,7,2,3,4,5]=>[6,2]=>3360
[1,6,8,7,2,3,4,5]=>[5,2,1]=>4032
[1,7,8,6,2,3,4,5]=>[7,1]=>5760
[7,8,1,6,2,3,4,5]=>[5,3]=>2688
[6,8,1,7,2,3,4,5]=>[3,3,2]=>1120
[4,8,2,1,7,3,5,6]=>[4,2,2]=>1260
[3,2,8,1,7,4,5,6]=>[5,2,1]=>4032
[3,2,1,8,7,4,5,6]=>[3,2,2,1]=>1680
[5,1,8,2,7,3,4,6]=>[5,3]=>2688
[6,1,8,7,2,3,4,5]=>[6,2]=>3360
[8,1,7,6,2,3,4,5]=>[4,4]=>1260
[1,8,7,6,2,3,4,5]=>[4,3,1]=>3360
[6,3,5,1,2,4,8,7]=>[3,3,2]=>1120
[4,3,5,6,1,2,8,7]=>[6,2]=>3360
[8,3,7,5,2,1,4,6]=>[5,3]=>2688
[6,3,7,5,1,8,4,2]=>[8]=>5040
[6,5,2,7,1,8,3,4]=>[8]=>5040
[8,5,2,7,4,1,3,6]=>[5,3]=>2688
[2,6,1,5,4,3,8,7]=>[4,2,2]=>1260
[6,4,3,5,1,2,8,7]=>[5,2,1]=>4032
[5,3,1,4,6,2,8,7]=>[5,2,1]=>4032
[3,1,4,6,5,2,8,7]=>[5,2,1]=>4032
[5,7,4,6,2,8,3,1]=>[8]=>5040
[8,1,4,7,2,6,3,5]=>[4,3,1]=>3360
[3,4,7,8,5,2,1,6]=>[4,3,1]=>3360
[2,1,8,5,7,3,4,6]=>[3,3,2]=>1120
[8,6,3,5,1,7,4,2]=>[7,1]=>5760
[5,8,2,4,6,7,3,1]=>[7,1]=>5760
[3,4,8,6,5,7,1,2]=>[7,1]=>5760
[7,5,4,8,1,6,3,2]=>[7,1]=>5760
[5,1,4,6,8,2,7,3]=>[7,1]=>5760
[2,5,4,6,7,1,8,3]=>[8]=>5040
[2,4,6,3,7,5,8,1]=>[8]=>5040
[4,1,6,3,8,5,7,2]=>[7,1]=>5760
[3,7,4,2,8,6,5,1]=>[7,1]=>5760
[7,4,1,3,5,8,6,2]=>[7,1]=>5760
[6,5,8,4,1,7,3,2]=>[7,1]=>5760
[8,5,3,7,4,1,6,2]=>[7,1]=>5760
[2,1,4,8,3,7,6,5]=>[4,2,2]=>1260
[7,4,3,8,2,1,6,5]=>[4,3,1]=>3360
[6,3,7,4,1,8,2,5]=>[4,3,1]=>3360
[8,3,1,2,5,7,6,4]=>[5,2,1]=>4032
[3,1,8,2,7,6,5,4]=>[5,2,1]=>4032
[2,3,8,1,6,7,5,4]=>[5,3]=>2688
[4,3,7,2,6,8,5,1]=>[8]=>5040
[4,7,2,3,8,5,6,1]=>[8]=>5040
[3,8,2,1,7,5,6,4]=>[5,3]=>2688
[2,8,1,3,6,5,7,4]=>[5,2,1]=>4032
[2,7,8,5,4,3,1,6]=>[3,3,2]=>1120
[8,7,1,6,3,4,2,5]=>[4,2,2]=>1260
[3,8,6,7,2,4,1,5]=>[5,3]=>2688
[5,3,8,7,4,2,6,1]=>[8]=>5040
[4,3,8,7,2,1,6,5]=>[4,4]=>1260
[8,3,6,1,4,2,7,5]=>[4,3,1]=>3360
[7,3,5,8,2,4,1,6]=>[3,3,2]=>1120
[2,3,4,1,8,5,7,6]=>[4,3,1]=>3360
[4,1,3,2,6,7,8,5]=>[4,3,1]=>3360
[8,3,5,6,2,7,1,4]=>[5,3]=>2688
[5,3,6,1,8,7,2,4]=>[4,4]=>1260
[5,6,2,8,7,4,1,3]=>[5,3]=>2688
[7,8,5,6,1,4,2,3]=>[6,2]=>3360
[2,8,6,5,4,7,1,3]=>[6,2]=>3360
[8,1,6,4,5,7,2,3]=>[6,1,1]=>3360
[5,8,3,6,1,7,2,4]=>[5,2,1]=>4032
[2,1,8,6,5,7,3,4]=>[5,2,1]=>4032
[2,1,7,5,3,6,8,4]=>[5,2,1]=>4032
[6,7,3,5,2,1,8,4]=>[5,2,1]=>4032
[7,1,4,2,5,6,8,3]=>[6,1,1]=>3360
[2,7,4,1,6,5,8,3]=>[6,2]=>3360
[4,6,1,2,8,7,3,5]=>[6,2]=>3360
[2,4,1,5,8,7,6,3]=>[6,2]=>3360
[4,1,2,5,8,6,7,3]=>[6,1,1]=>3360
[6,4,2,1,5,8,7,3]=>[6,1,1]=>3360
[8,5,2,4,6,1,7,3]=>[6,1,1]=>3360
[7,5,3,2,6,8,1,4]=>[5,2,1]=>4032
[2,1,5,3,6,8,7,4]=>[5,2,1]=>4032
[7,3,5,4,6,1,8,2]=>[7,1]=>5760
[6,3,4,1,5,7,8,2]=>[7,1]=>5760
[4,3,1,5,7,6,8,2]=>[7,1]=>5760
[3,1,4,5,6,8,7,2]=>[7,1]=>5760
[4,5,2,6,3,1,8,7]=>[3,3,2]=>1120
[6,5,2,1,4,3,8,7]=>[6,2]=>3360
[6,5,2,7,4,8,3,1]=>[5,3]=>2688
[8,5,2,7,4,1,6,3]=>[8]=>5040
[8,3,7,5,2,1,6,4]=>[8]=>5040
[6,3,7,5,2,8,4,1]=>[5,3]=>2688
[3,1,6,5,4,2,8,7]=>[4,2,2]=>1260
[5,6,3,2,4,1,8,7]=>[5,2,1]=>4032
[3,6,2,4,1,5,8,7]=>[5,2,1]=>4032
[2,6,1,3,5,4,8,7]=>[5,2,1]=>4032
[6,7,2,3,4,8,5,1]=>[5,3]=>2688
[8,7,2,3,4,1,6,5]=>[8]=>5040
[5,1,7,3,8,4,6,2]=>[4,4]=>1260
[2,5,7,3,8,6,4,1]=>[4,3,1]=>3360
[7,6,1,3,5,8,4,2]=>[4,3,1]=>3360
[3,6,7,4,1,8,5,2]=>[4,3,1]=>3360
[5,6,3,7,4,8,1,2]=>[4,3,1]=>3360
[2,1,6,7,4,8,5,3]=>[3,3,2]=>1120
[2,1,8,7,4,3,6,5]=>[6,2]=>3360
[5,8,3,7,4,2,6,1]=>[7,1]=>5760
[3,8,7,4,1,2,6,5]=>[7,1]=>5760
[7,8,1,3,5,2,6,4]=>[7,1]=>5760
[5,8,7,3,2,6,1,4]=>[7,1]=>5760
[2,8,6,3,1,5,7,4]=>[7,1]=>5760
[8,1,6,3,2,5,4,7]=>[8]=>5040
[2,8,4,1,6,3,7,5]=>[7,1]=>5760
[4,8,1,2,7,6,3,5]=>[7,1]=>5760
[3,8,4,2,5,7,1,6]=>[7,1]=>5760
[6,8,3,5,2,7,4,1]=>[7,1]=>5760
[2,1,5,3,8,7,6,4]=>[4,2,2]=>1260
[6,5,3,2,8,7,1,4]=>[4,3,1]=>3360
[7,5,2,4,8,1,6,3]=>[4,3,1]=>3360
[3,4,2,8,5,7,6,1]=>[5,2,1]=>4032
[2,4,1,8,7,6,5,3]=>[5,2,1]=>4032
[8,4,2,1,7,5,3,6]=>[8]=>5040
[4,3,1,8,6,7,5,2]=>[5,3]=>2688
[3,1,4,8,6,5,7,2]=>[5,2,1]=>4032
[7,1,6,5,4,8,2,3]=>[3,3,2]=>1120
[3,7,5,6,8,4,2,1]=>[4,2,2]=>1260
[5,7,1,6,8,2,4,3]=>[4,4]=>1260
[8,6,2,5,1,7,4,3]=>[8]=>5040
[5,6,2,1,8,7,3,4]=>[4,4]=>1260
[4,6,2,5,8,3,7,1]=>[4,3,1]=>3360
[7,5,2,6,3,8,1,4]=>[3,3,2]=>1120
[4,1,2,3,6,8,7,5]=>[4,3,1]=>3360
[2,4,3,1,8,5,6,7]=>[4,3,1]=>3360
[7,5,2,8,3,4,6,1]=>[5,3]=>2688
[5,6,2,8,4,3,1,7]=>[5,3]=>2688
[4,7,2,8,1,5,3,6]=>[5,3]=>2688
[8,7,2,1,4,5,6,3]=>[8]=>5040
[3,6,8,7,1,5,4,2]=>[6,2]=>3360
[5,7,8,6,3,4,1,2]=>[6,2]=>3360
[7,1,8,5,4,3,6,2]=>[6,2]=>3360
[2,7,8,4,5,3,6,1]=>[6,1,1]=>3360
[5,7,3,8,1,4,6,2]=>[5,2,1]=>4032
[2,1,7,8,5,4,6,3]=>[5,2,1]=>4032
[2,1,5,8,4,6,3,7]=>[5,2,1]=>4032
[6,5,3,8,4,1,2,7]=>[5,2,1]=>4032
[7,5,8,4,3,6,2,1]=>[6,1,1]=>3360
[2,4,8,3,5,6,1,7]=>[6,1,1]=>3360
[4,1,8,3,6,5,2,7]=>[6,2]=>3360
[3,4,8,1,7,2,5,6]=>[6,2]=>3360
[8,4,1,3,7,2,6,5]=>[8]=>5040
[3,1,8,2,4,7,6,5]=>[6,2]=>3360
[2,3,8,1,4,6,7,5]=>[6,1,1]=>3360
[4,3,8,2,5,1,7,6]=>[6,1,1]=>3360
[6,3,8,4,2,5,7,1]=>[6,1,1]=>3360
[7,4,3,8,2,5,1,6]=>[5,2,1]=>4032
[2,1,4,8,3,5,7,6]=>[5,2,1]=>4032
[6,8,2,4,3,5,1,7]=>[7,1]=>5760
[4,8,2,3,5,1,6,7]=>[7,1]=>5760
[3,8,2,1,4,6,5,7]=>[7,1]=>5760
[2,8,1,3,4,5,7,6]=>[7,1]=>5760
[2,8,4,1,6,5,3,7]=>[6,2]=>3360
[2,8,4,1,6,5,7,3]=>[5,2,1]=>4032
[2,8,7,6,1,4,3,5]=>[4,2,2]=>1260
[2,8,5,6,7,4,3,1]=>[3,3,2]=>1120
[7,5,8,6,1,4,2,3]=>[4,2,2]=>1260
[3,5,7,6,1,4,2,8]=>[5,2,1]=>4032
[3,5,7,2,4,1,6,8]=>[4,3,1]=>3360
[7,5,8,2,4,1,6,3]=>[3,3,2]=>1120
[2,8,5,3,4,7,6,1]=>[3,3,2]=>1120
[2,8,5,3,4,1,7,6]=>[4,3,1]=>3360
[2,8,5,3,4,1,6,7]=>[5,3]=>2688
[2,8,7,6,1,4,5,3]=>[6,2]=>3360
[2,8,5,3,6,1,7,4]=>[7,1]=>5760
[2,8,5,6,7,4,1,3]=>[6,2]=>3360
[2,8,5,3,4,7,1,6]=>[5,3]=>2688
[2,8,5,3,4,6,1,7]=>[4,3,1]=>3360
[2,8,5,3,4,6,7,1]=>[3,3,1,1]=>1120
[3,5,7,2,4,6,1,8]=>[3,3,1,1]=>1120
[6,5,2,7,3,1,4,8]=>[3,2,2,1]=>1680
[6,5,2,8,3,1,7,4]=>[3,2,2,1]=>1680
[6,5,2,8,3,1,4,7]=>[3,3,2]=>1120
[7,5,8,2,4,6,3,1]=>[4,3,1]=>3360
[7,5,8,6,1,4,3,2]=>[6,2]=>3360
[6,5,8,2,1,3,7,4]=>[7,1]=>5760
[3,5,6,2,1,8,7,4]=>[7,1]=>5760
[3,5,7,6,1,4,8,2]=>[6,2]=>3360
[3,5,7,2,4,1,8,6]=>[5,3]=>2688
[3,5,7,2,4,6,8,1]=>[4,3,1]=>3360
[6,5,2,7,3,1,8,4]=>[3,3,2]=>1120
[4,5,2,6,3,1,7,8]=>[3,3,1,1]=>1120
[4,1,2,3,7,6,8,5]=>[4,3,1]=>3360
[6,5,2,7,3,4,8,1]=>[5,3]=>2688
[5,1,6,7,4,3,8,2]=>[6,2]=>3360
[5,1,2,6,4,8,7,3]=>[7,1]=>5760
[5,1,2,8,6,4,7,3]=>[7,1]=>5760
[5,1,6,8,7,3,4,2]=>[6,2]=>3360
[6,5,2,8,3,7,4,1]=>[5,3]=>2688
[4,1,2,3,8,7,5,6]=>[4,4]=>1260
[4,1,2,3,8,6,5,7]=>[4,3,1]=>3360
[4,1,2,3,8,6,7,5]=>[4,2,1,1]=>2520
[4,1,2,3,7,6,5,8]=>[4,2,1,1]=>2520
[4,1,2,3,8,5,7,6]=>[4,3,1]=>3360
[7,1,6,8,4,3,5,2]=>[6,2]=>3360
[6,1,2,8,4,5,7,3]=>[7,1]=>5760
[5,6,8,2,3,1,7,4]=>[7,1]=>5760
[6,5,8,2,4,3,1,7]=>[5,3]=>2688
[6,5,8,2,4,3,7,1]=>[4,3,1]=>3360
[7,5,2,8,3,4,1,6]=>[3,3,2]=>1120
[6,5,2,8,3,7,1,4]=>[3,3,2]=>1120
[6,5,2,7,3,4,1,8]=>[4,3,1]=>3360
[5,1,6,7,4,3,2,8]=>[5,2,1]=>4032
[5,1,6,8,7,3,2,4]=>[4,2,2]=>1260
[7,1,6,8,4,3,2,5]=>[3,3,2]=>1120
[5,7,8,6,3,4,2,1]=>[4,2,2]=>1260
[4,1,8,3,6,5,7,2]=>[5,2,1]=>4032
[4,1,8,3,6,2,7,5]=>[7,1]=>5760
[3,1,4,8,6,2,7,5]=>[7,1]=>5760
[3,1,4,8,6,5,2,7]=>[6,2]=>3360
[7,1,6,5,8,3,2,4]=>[3,3,2]=>1120
[4,1,6,7,8,3,2,5]=>[4,2,2]=>1260
[4,1,6,5,7,3,2,8]=>[5,2,1]=>4032
[4,5,2,6,3,7,1,8]=>[4,3,1]=>3360
[4,5,2,7,3,8,1,6]=>[3,3,2]=>1120
[3,5,6,2,4,8,7,1]=>[4,3,1]=>3360
[3,5,6,2,4,8,1,7]=>[5,3]=>2688
[3,7,5,6,8,4,1,2]=>[6,2]=>3360
[3,6,5,2,8,1,7,4]=>[7,1]=>5760
[6,1,2,5,8,4,7,3]=>[7,1]=>5760
[7,1,6,5,8,3,4,2]=>[6,2]=>3360
[7,5,2,6,3,8,4,1]=>[5,3]=>2688
[4,1,2,3,5,8,7,6]=>[4,2,1,1]=>2520
[4,1,2,3,7,8,6,5]=>[4,4]=>1260
[4,5,2,7,3,8,6,1]=>[5,3]=>2688
[4,1,6,7,8,3,5,2]=>[6,2]=>3360
[4,1,2,6,8,5,7,3]=>[7,1]=>5760
[4,1,2,5,6,8,7,3]=>[7,1]=>5760
[4,5,2,6,3,7,8,1]=>[5,3]=>2688
[7,8,5,6,1,4,3,2]=>[4,2,2]=>1260
[7,8,4,2,1,5,3,6]=>[8]=>5040
[7,8,2,1,6,5,3,4]=>[6,2]=>3360
[6,4,1,2,5,7,3,8]=>[4,2,1,1]=>2520
[2,4,8,1,5,7,3,6]=>[4,3,1]=>3360
[4,3,8,1,7,2,5,6]=>[4,2,2]=>1260
[6,3,1,4,7,2,5,8]=>[4,2,1,1]=>2520
[7,8,3,4,5,1,6,2]=>[3,2,1,1,1]=>1120
[7,8,3,5,4,2,1,6]=>[3,2,2,1]=>1680
[7,8,4,1,2,3,6,5]=>[5,3]=>2688
[7,8,3,6,5,4,1,2]=>[2,2,2,1,1]=>420
[7,8,2,1,5,3,4,6]=>[4,3,1]=>3360
[7,8,2,6,4,1,3,5]=>[8]=>5040
[7,8,2,5,6,4,1,3]=>[3,3,2]=>1120
[7,8,1,6,5,4,3,2]=>[3,2,2,1]=>1680
[6,2,1,7,5,4,3,8]=>[5,1,1,1]=>1344
[2,1,8,7,5,4,3,6]=>[5,2,1]=>4032
[1,3,8,2,6,4,7,5]=>[6,1,1]=>3360
[5,3,7,1,6,4,8,2]=>[4,4]=>1260
[5,3,6,2,7,4,1,8]=>[4,3,1]=>3360
[6,1,2,5,8,7,4,3]=>[8]=>5040
[6,3,1,8,4,2,7,5]=>[4,3,1]=>3360
[6,4,2,1,5,3,8,7]=>[5,2,1]=>4032
[6,4,3,7,5,8,1,2]=>[6,1,1]=>3360
[4,3,8,7,5,6,1,2]=>[3,3,1,1]=>1120
[2,4,7,1,5,3,6,8]=>[3,3,1,1]=>1120
[1,3,7,6,4,2,8,5]=>[7,1]=>5760
[2,1,7,5,6,8,4,3]=>[6,2]=>3360
[3,7,2,8,6,4,1,5]=>[4,4]=>1260
[3,8,1,7,6,4,5,2]=>[4,2,2]=>1260
[1,8,5,7,3,6,4,2]=>[2,2,2,1,1]=>420
[2,7,5,8,3,6,1,4]=>[3,2,2,1]=>1680
[1,5,6,8,2,4,7,3]=>[4,2,1,1]=>2520
[2,6,8,5,3,1,4,7]=>[5,3]=>2688
[2,6,1,4,7,3,5,8]=>[4,2,1,1]=>2520
[5,6,7,3,8,4,1,2]=>[8]=>5040
[5,2,8,1,4,7,3,6]=>[4,3,1]=>3360
[4,6,7,5,2,1,3,8]=>[5,2,1]=>4032
[4,5,6,7,2,8,1,3]=>[3,3,2]=>1120
[4,5,7,6,1,8,3,2]=>[6,2]=>3360
[1,5,8,6,2,7,3,4]=>[5,2,1]=>4032
[1,6,5,8,3,2,7,4]=>[2,2,2,1,1]=>420
[4,6,5,7,1,2,8,3]=>[6,2]=>3360
[4,7,5,6,3,1,8,2]=>[3,3,2]=>1120
[5,1,6,3,4,2,8,7]=>[6,2]=>3360
[5,7,1,4,2,3,8,6]=>[7,1]=>5760
[5,7,6,4,3,8,1,2]=>[7,1]=>5760
[6,3,4,5,8,7,1,2]=>[5,3]=>2688
[6,2,4,1,8,3,7,5]=>[4,2,1,1]=>2520
[6,2,3,5,4,8,1,7]=>[4,2,1,1]=>2520
[6,1,3,4,5,8,7,2]=>[4,1,1,1,1]=>420
[5,1,4,2,7,6,8,3]=>[7,1]=>5760
[1,6,2,4,7,8,3,5]=>[6,1,1]=>3360
[5,7,2,4,1,6,3,8]=>[3,2,1,1,1]=>1120
[6,1,4,2,8,5,3,7]=>[8]=>5040
[6,7,5,8,1,4,3,2]=>[8]=>5040
[5,8,7,6,3,4,1,2]=>[4,2,2]=>1260
[5,8,7,6,2,3,1,4]=>[8]=>5040
[4,1,7,2,6,5,3,8]=>[3,2,2,1]=>1680
[4,8,2,1,5,6,3,7]=>[4,2,1,1]=>2520
[4,2,7,8,1,6,3,5]=>[4,2,1,1]=>2520
[2,1,8,7,6,5,3,4]=>[4,2,2]=>1260
[3,1,4,7,8,2,6,5]=>[6,2]=>3360
[3,1,7,4,5,6,8,2]=>[5,1,1,1]=>1344
[4,2,7,1,6,3,8,5]=>[5,2,1]=>4032
[4,3,7,5,6,8,1,2]=>[8]=>5040
[4,8,6,3,5,7,1,2]=>[5,2,1]=>4032
[4,8,1,2,5,3,7,6]=>[6,1,1]=>3360
[3,8,6,5,2,4,1,7]=>[8]=>5040
[3,8,5,6,1,4,7,2]=>[3,2,2,1]=>1680
[5,3,7,8,2,1,6,4]=>[6,2]=>3360
[5,2,8,7,1,6,4,3]=>[2,2,2,1,1]=>420
[1,6,8,7,5,2,4,3]=>[2,2,2,1,1]=>420
[3,6,7,8,5,1,4,2]=>[7,1]=>5760
[3,7,6,8,5,2,1,4]=>[5,2,1]=>4032
[3,7,8,5,1,2,4,6]=>[8]=>5040
[3,7,1,6,4,2,5,8]=>[5,2,1]=>4032
[4,1,8,6,2,3,5,7]=>[8]=>5040
[4,7,8,6,3,5,1,2]=>[8]=>5040
[3,8,7,6,5,4,1,2]=>[3,2,2,1]=>1680
[2,1,7,6,5,3,4,8]=>[4,2,1,1]=>2520
[2,8,1,6,4,5,3,7]=>[5,3]=>2688
[2,8,7,5,1,4,3,6]=>[6,2]=>3360
[2,8,6,7,5,1,3,4]=>[7,1]=>5760
[2,7,8,6,5,4,1,3]=>[3,2,2,1]=>1680
[6,4,2,7,1,3,8,5]=>[8]=>5040
[7,4,2,5,1,3,8,6]=>[8]=>5040
[8,5,3,6,1,7,2,4]=>[7,1]=>5760
[7,3,6,2,4,8,1,5]=>[6,2]=>3360
[3,6,2,7,1,4,8,5]=>[8]=>5040
[5,3,6,7,1,2,8,4]=>[3,3,2]=>1120
[6,3,7,4,1,2,8,5]=>[7,1]=>5760
[4,7,1,5,2,3,8,6]=>[8]=>5040
[7,6,4,2,3,8,1,5]=>[6,2]=>3360
[8,6,4,2,3,7,1,5]=>[8]=>5040
[4,7,6,3,8,1,2,5]=>[4,2,2]=>1260
[5,7,4,2,3,8,1,6]=>[6,2]=>3360
[3,7,6,1,4,8,2,5]=>[6,2]=>3360
[6,4,7,5,2,8,1,3]=>[5,3]=>2688
[7,4,8,5,2,6,1,3]=>[3,2,2,1]=>1680
[5,8,2,6,3,7,1,4]=>[8]=>5040
[3,8,6,2,4,7,1,5]=>[4,4]=>1260
[4,8,6,2,7,1,3,5]=>[8]=>5040
[2,6,5,8,1,3,4,7]=>[5,3]=>2688
[2,5,7,4,8,1,3,6]=>[5,2,1]=>4032
[5,4,6,7,2,8,1,3]=>[5,3]=>2688
[3,5,7,1,4,8,2,6]=>[6,2]=>3360
[5,3,7,2,4,8,1,6]=>[6,2]=>3360
[5,4,7,3,8,1,2,6]=>[4,4]=>1260
[7,4,6,3,8,1,2,5]=>[6,2]=>3360
[8,4,6,3,7,1,2,5]=>[8]=>5040
[8,4,1,6,7,2,3,5]=>[5,3]=>2688
[7,4,1,6,8,2,3,5]=>[3,3,2]=>1120
[6,5,3,7,1,8,2,4]=>[7,1]=>5760
[6,5,1,2,7,8,3,4]=>[8]=>5040
[5,3,6,4,7,8,1,2]=>[4,3,1]=>3360
[6,3,7,4,8,5,1,2]=>[7,1]=>5760
[4,7,1,5,8,6,2,3]=>[5,2,1]=>4032
[7,5,1,2,8,6,3,4]=>[4,3,1]=>3360
[7,6,1,8,5,2,3,4]=>[3,2,2,1]=>1680
[8,6,1,7,5,2,3,4]=>[5,2,1]=>4032
[5,7,2,8,1,6,3,4]=>[3,2,2,1]=>1680
[6,3,7,8,5,1,2,4]=>[3,2,2,1]=>1680
[3,6,8,2,7,1,4,5]=>[8]=>5040
[2,4,8,7,1,3,5,6]=>[5,3]=>2688
[4,3,8,7,1,2,5,6]=>[4,4]=>1260
[5,3,8,7,1,2,4,6]=>[4,2,2]=>1260
[8,3,7,6,1,2,4,5]=>[5,3]=>2688
[8,4,7,6,1,2,3,5]=>[3,3,2]=>1120
[3,5,8,7,1,2,4,6]=>[6,2]=>3360
[2,5,8,7,1,3,4,6]=>[3,3,2]=>1120
[5,8,7,1,6,2,3,4]=>[6,2]=>3360
[2,8,7,6,1,3,4,5]=>[4,4]=>1260
[3,8,7,6,1,2,4,5]=>[8]=>5040
[4,8,7,6,1,2,3,5]=>[6,2]=>3360
[5,6,3,1,4,2,8,7]=>[3,2,2,1]=>1680
[3,8,7,4,5,1,6,2]=>[4,2,1,1]=>2520
[2,1,7,8,5,3,6,4]=>[3,2,2,1]=>1680
[5,7,3,8,1,2,6,4]=>[3,2,2,1]=>1680
[8,7,1,4,5,3,2,6]=>[4,2,1,1]=>2520
[2,7,8,4,1,6,5,3]=>[4,2,1,1]=>2520
[7,1,8,4,2,6,5,3]=>[4,2,1,1]=>2520
[7,5,1,4,8,6,3,2]=>[3,3,1,1]=>1120
[6,5,3,1,8,4,7,2]=>[3,3,1,1]=>1120
[8,6,3,1,2,5,7,4]=>[3,3,1,1]=>1120
[8,7,1,4,2,6,5,3]=>[3,3,1,1]=>1120
[2,3,4,5,6,7,8,1,9]=>[8,1]=>45360
[2,3,4,5,6,8,9,1,7]=>[7,2]=>25920
[2,3,4,5,7,8,9,1,6]=>[9]=>40320
[2,3,4,6,7,8,9,1,5]=>[6,3]=>20160
[2,3,5,6,7,8,9,1,4]=>[9]=>40320
[2,4,5,6,7,8,9,1,3]=>[5,4]=>18144
[3,4,5,6,7,8,9,1,2]=>[9]=>40320
[2,3,4,5,6,7,8,9,10,1]=>[10]=>362880
[2,3,4,5,6,7,8,9,1,10]=>[9,1]=>403200
[2,3,4,5,6,7,1,8,9]=>[7,1,1]=>25920
[2,3,4,5,6,7,8,10,1,9]=>[10]=>362880
[2,3,4,5,6,1,9,7,8]=>[6,3]=>20160
[2,3,4,5,6,7,9,10,1,8]=>[8,2]=>226800
[2,3,4,5,1,8,9,6,7]=>[5,2,2]=>9072
[2,3,4,5,6,8,9,10,1,7]=>[10]=>362880
[2,3,4,1,7,8,9,5,6]=>[5,4]=>18144
[2,3,4,5,7,8,9,10,1,6]=>[7,3]=>172800
[2,3,1,6,7,8,9,4,5]=>[3,3,3]=>2240
[2,3,4,6,7,8,9,10,1,5]=>[10]=>362880
[2,1,5,6,7,8,9,3,4]=>[7,2]=>25920
[2,3,5,6,7,8,9,10,1,4]=>[6,4]=>151200
[1,4,5,6,7,8,9,2,3]=>[4,4,1]=>11340
[2,4,5,6,7,8,9,10,1,3]=>[10]=>362880
[3,4,5,6,7,8,9,10,1,2]=>[5,5]=>72576
[3,6,4,5,7,2,8,1]=>[6,2]=>3360
[5,3,2,7,4,6,8,1]=>[5,2,1]=>4032
[7,5,3,6,2,4,8,1]=>[3,2,2,1]=>1680
[6,3,2,5,1,8,4,7]=>[6,2]=>3360
[8,5,3,6,2,7,1,4]=>[5,2,1]=>4032
[8,2,6,3,4,7,1,5]=>[7,1]=>5760
[7,2,6,3,4,5,8,1]=>[4,3,1]=>3360
[6,2,7,3,4,5,8,1]=>[7,1]=>5760
[4,2,5,7,3,6,8,1]=>[4,2,1,1]=>2520
[5,4,7,6,2,3,8,1]=>[8]=>5040
[6,7,3,5,2,4,8,1]=>[7,1]=>5760
[3,7,6,2,4,5,8,1]=>[8]=>5040
[2,7,6,3,4,5,8,1]=>[4,4]=>1260
[6,5,3,1,2,8,4,7]=>[5,2,1]=>4032
[8,6,5,2,3,7,1,4]=>[6,2]=>3360
[8,5,2,1,7,3,4,6]=>[8]=>5040
[7,5,2,1,8,3,4,6]=>[5,3]=>2688
[1,6,3,2,8,4,5,7]=>[3,3,1,1]=>1120
[5,6,2,3,1,8,4,7]=>[6,2]=>3360
[5,4,8,6,2,7,1,3]=>[6,2]=>3360
[6,8,3,5,2,7,1,4]=>[4,3,1]=>3360
[7,8,5,2,3,6,1,4]=>[3,2,2,1]=>1680
[6,8,2,1,7,3,4,5]=>[8]=>5040
[1,8,6,3,7,2,4,5]=>[7,1]=>5760
[1,8,2,7,3,4,5,6]=>[7,1]=>5760
[2,8,1,7,3,4,5,6]=>[8]=>5040
[3,8,6,1,7,2,4,5]=>[8]=>5040
[4,8,1,5,7,2,3,6]=>[5,3]=>2688
[4,2,8,3,7,1,5,6]=>[5,2,1]=>4032
[8,1,2,7,3,4,5,6]=>[8]=>5040
[3,6,2,7,1,8,4,5]=>[6,2]=>3360
[6,3,7,1,2,8,4,5]=>[8]=>5040
[7,3,1,5,8,2,4,6]=>[8]=>5040
[3,2,1,5,8,4,6,7]=>[5,2,1]=>4032
[5,4,1,3,6,8,2,7]=>[8]=>5040
[1,5,3,4,6,8,2,7]=>[5,1,1,1]=>1344
[4,3,5,1,6,8,2,7]=>[6,2]=>3360
[5,4,6,3,8,7,1,2]=>[8]=>5040
[3,6,4,5,8,7,1,2]=>[8]=>5040
[6,5,3,4,8,7,1,2]=>[3,3,1,1]=>1120
[5,3,2,8,7,1,4,6]=>[6,2]=>3360
[5,3,1,8,7,2,4,6]=>[8]=>5040
[8,5,3,7,6,1,2,4]=>[7,1]=>5760
[6,1,8,3,7,2,4,5]=>[5,3]=>2688
[6,3,8,1,7,2,4,5]=>[8]=>5040
[7,6,8,2,3,5,1,4]=>[6,2]=>3360
[3,7,8,2,4,6,1,5]=>[7,1]=>5760
[6,7,3,8,2,5,1,4]=>[5,2,1]=>4032
[5,4,7,8,2,6,1,3]=>[7,1]=>5760
[4,2,5,8,7,1,3,6]=>[4,3,1]=>3360
[2,3,8,7,1,4,5,6]=>[8]=>5040
[7,2,8,6,1,3,4,5]=>[7,1]=>5760
[2,1,8,7,3,4,5,6]=>[6,2]=>3360
[8,2,7,6,1,3,4,5]=>[4,3,1]=>3360
[1,2,8,7,3,4,5,6]=>[6,1,1]=>3360
[1,3,8,7,2,4,5,6]=>[7,1]=>5760
[1,7,8,3,6,2,4,5]=>[7,1]=>5760
[4,1,5,8,7,2,3,6]=>[5,3]=>2688
[5,4,8,7,6,1,2,3]=>[3,3,2]=>1120
[6,8,3,7,5,1,2,4]=>[4,2,1,1]=>2520
[7,8,6,2,5,1,3,4]=>[4,3,1]=>3360
[8,1,6,7,3,2,5,4]=>[8]=>5040
[8,1,6,7,3,2,4,5]=>[6,2]=>3360
[8,1,5,3,7,2,4,6]=>[4,4]=>1260
[8,1,5,3,6,2,4,7]=>[8]=>5040
[7,5,1,3,6,2,4,8]=>[4,3,1]=>3360
[7,5,8,3,6,2,4,1]=>[5,3]=>2688
[7,4,8,3,2,6,5,1]=>[7,1]=>5760
[7,4,1,3,2,6,5,8]=>[6,1,1]=>3360
[8,1,4,3,2,6,5,7]=>[5,2,1]=>4032
[8,1,4,3,2,7,5,6]=>[6,2]=>3360
[8,1,4,3,2,7,6,5]=>[4,2,2]=>1260
[8,1,5,4,6,7,2,3]=>[7,1]=>5760
[8,1,5,3,6,2,7,4]=>[7,1]=>5760
[8,1,4,3,2,6,7,5]=>[4,2,1,1]=>2520
[8,1,4,3,2,5,7,6]=>[5,2,1]=>4032
[8,1,4,3,2,5,6,7]=>[6,2]=>3360
[7,4,1,3,2,5,6,8]=>[7,1]=>5760
[7,4,8,3,2,5,6,1]=>[8]=>5040
[6,4,3,8,2,5,7,1]=>[6,1,1]=>3360
[6,4,3,1,2,5,8,7]=>[5,2,1]=>4032
[7,4,1,3,2,5,8,6]=>[8]=>5040
[7,4,1,3,2,6,8,5]=>[7,1]=>5760
[7,5,1,3,6,2,8,4]=>[5,3]=>2688
[7,5,1,4,6,8,2,3]=>[7,1]=>5760
[7,5,8,3,6,2,1,4]=>[3,3,2]=>1120
[7,4,8,3,2,6,1,5]=>[5,2,1]=>4032
[7,4,8,3,2,5,1,6]=>[6,2]=>3360
[6,4,3,8,2,5,1,7]=>[7,1]=>5760
[6,4,3,7,2,5,8,1]=>[7,1]=>5760
[5,4,3,2,8,6,1,7]=>[4,2,1,1]=>2520
[5,4,3,2,8,7,1,6]=>[5,2,1]=>4032
[6,5,3,8,7,2,1,4]=>[5,2,1]=>4032
[6,5,4,8,7,1,2,3]=>[3,3,2]=>1120
[6,5,4,1,7,8,2,3]=>[5,3]=>2688
[6,5,3,1,7,2,8,4]=>[7,1]=>5760
[6,4,3,1,2,7,8,5]=>[7,1]=>5760
[5,4,3,2,1,8,6,7]=>[3,2,2,1]=>1680
[6,5,3,1,8,2,7,4]=>[6,1,1]=>3360
[6,5,4,1,8,7,2,3]=>[8]=>5040
[7,5,1,4,8,6,2,3]=>[6,1,1]=>3360
[7,4,1,3,2,8,6,5]=>[8]=>5040
[7,4,1,3,2,8,5,6]=>[6,2]=>3360
[6,4,3,1,2,8,5,7]=>[7,1]=>5760
[6,4,3,1,2,7,5,8]=>[6,1,1]=>3360
[6,4,3,8,2,7,5,1]=>[7,1]=>5760
[6,5,3,8,7,2,4,1]=>[7,1]=>5760
[6,5,3,1,7,2,4,8]=>[6,1,1]=>3360
[6,5,3,1,8,2,4,7]=>[7,1]=>5760
[7,5,1,3,8,2,4,6]=>[4,4]=>1260
[7,6,1,8,3,2,4,5]=>[6,2]=>3360
[7,6,1,8,4,5,2,3]=>[8]=>5040
[7,6,8,1,4,5,2,3]=>[6,2]=>3360
[7,6,8,1,3,2,5,4]=>[6,2]=>3360
[6,5,3,7,8,2,4,1]=>[5,2,1]=>4032
[6,4,3,7,2,8,5,1]=>[4,3,1]=>3360
[6,4,3,7,2,1,5,8]=>[4,2,1,1]=>2520
[7,4,8,3,2,1,5,6]=>[8]=>5040
[7,4,8,3,2,1,6,5]=>[5,3]=>2688
[7,5,8,3,1,2,6,4]=>[5,3]=>2688
[7,5,8,4,1,6,2,3]=>[4,2,1,1]=>2520
[6,5,4,8,1,7,2,3]=>[5,3]=>2688
[6,5,3,8,1,2,7,4]=>[4,2,1,1]=>2520
[5,4,3,2,8,1,7,6]=>[4,2,1,1]=>2520
[6,4,3,7,2,1,8,5]=>[5,2,1]=>4032
[6,5,3,7,1,2,8,4]=>[4,3,1]=>3360
[6,5,4,7,1,8,2,3]=>[8]=>5040
[6,5,3,7,8,2,1,4]=>[7,1]=>5760
[6,4,3,7,2,8,1,5]=>[7,1]=>5760
[5,4,3,2,7,8,1,6]=>[3,2,2,1]=>1680
[5,4,3,2,6,8,1,7]=>[5,2,1]=>4032
[5,6,2,1,3,4,8,7]=>[6,2]=>3360
[5,3,7,8,2,1,4,6]=>[8]=>5040
[7,6,1,2,5,8,3,4]=>[4,3,1]=>3360
[2,1,7,8,4,3,5,6]=>[6,2]=>3360
[7,8,1,2,5,4,6,3]=>[7,1]=>5760
[8,4,1,3,7,6,2,5]=>[7,1]=>5760
[6,5,2,1,8,7,4,3]=>[4,4]=>1260
[4,7,2,8,1,3,6,5]=>[4,4]=>1260
[3,4,7,1,8,2,6,5]=>[6,2]=>3360
[1,8,2,4,3,5,6,7]=>[6,1,1]=>3360
[1,7,2,4,3,5,6,8]=>[5,1,1,1]=>1344
[1,6,2,4,3,5,7,8]=>[4,1,1,1,1]=>420
[1,5,2,4,3,6,7,8]=>[3,1,1,1,1,1]=>112
[1,6,2,5,3,4,7,8]=>[5,1,1,1]=>1344
[1,7,2,5,3,4,6,8]=>[6,1,1]=>3360
[1,8,2,5,3,4,6,7]=>[7,1]=>5760
[1,8,2,6,3,4,5,7]=>[5,2,1]=>4032
[1,7,2,6,3,4,5,8]=>[4,2,1,1]=>2520
[1,8,2,7,3,5,4,6]=>[5,2,1]=>4032
[1,7,2,8,3,5,4,6]=>[7,1]=>5760
[1,6,2,8,3,5,4,7]=>[4,3,1]=>3360
[1,5,2,8,3,6,4,7]=>[3,3,1,1]=>1120
[1,4,2,8,3,6,5,7]=>[6,1,1]=>3360
[1,3,2,8,4,6,5,7]=>[4,2,1,1]=>2520
[1,2,3,8,4,6,5,7]=>[4,1,1,1,1]=>420
[1,2,3,7,4,6,5,8]=>[3,1,1,1,1,1]=>112
[1,3,2,7,4,6,5,8]=>[3,2,1,1,1]=>1120
[1,4,2,7,3,6,5,8]=>[5,1,1,1]=>1344
[1,5,2,7,3,6,4,8]=>[3,2,1,1,1]=>1120
[1,6,2,7,3,5,4,8]=>[4,2,1,1]=>2520
[1,7,2,6,3,5,4,8]=>[6,1,1]=>3360
[1,8,2,6,3,5,4,7]=>[7,1]=>5760
[1,8,2,5,3,6,4,7]=>[6,1,1]=>3360
[1,7,2,5,3,6,4,8]=>[5,1,1,1]=>1344
[1,6,2,5,3,7,4,8]=>[6,1,1]=>3360
[1,5,2,4,3,7,6,8]=>[3,2,1,1,1]=>1120
[1,6,2,4,3,7,5,8]=>[5,1,1,1]=>1344
[1,7,2,4,3,6,5,8]=>[4,1,1,1,1]=>420
[1,8,2,4,3,6,5,7]=>[5,1,1,1]=>1344
[1,8,2,3,4,6,5,7]=>[6,1,1]=>3360
[1,7,2,3,4,6,5,8]=>[5,1,1,1]=>1344
[1,8,2,3,4,7,5,6]=>[7,1]=>5760
[1,8,2,4,3,7,5,6]=>[6,1,1]=>3360
[1,7,2,4,3,8,5,6]=>[4,2,1,1]=>2520
[1,6,2,4,3,8,5,7]=>[6,1,1]=>3360
[1,5,2,4,3,8,6,7]=>[3,3,1,1]=>1120
[1,6,2,5,3,8,4,7]=>[7,1]=>5760
[1,7,2,5,3,8,4,6]=>[5,2,1]=>4032
[1,8,2,5,3,7,4,6]=>[7,1]=>5760
[1,8,2,6,3,7,4,5]=>[4,3,1]=>3360
[1,7,2,6,3,8,4,5]=>[7,1]=>5760
[1,2,3,8,4,7,5,6]=>[5,1,1,1]=>1344
[1,3,2,8,4,7,5,6]=>[5,2,1]=>4032
[1,4,2,8,3,7,5,6]=>[7,1]=>5760
[1,5,2,8,3,7,4,6]=>[4,3,1]=>3360
[1,6,2,8,3,7,4,5]=>[7,1]=>5760
[1,7,2,8,3,6,4,5]=>[6,1,1]=>3360
[1,8,2,7,3,6,4,5]=>[4,2,1,1]=>2520
[4,6,3,7,2,5,1,8]=>[3,3,1,1]=>1120
[4,6,3,7,5,2,1,8]=>[3,2,1,1,1]=>1120
[4,6,3,8,5,1,7,2]=>[5,1,1,1]=>1344
[4,6,3,8,5,1,2,7]=>[6,1,1]=>3360
[5,6,8,3,4,1,2,7]=>[8]=>5040
[5,6,8,3,4,1,7,2]=>[7,1]=>5760
[4,6,2,7,5,3,1,8]=>[3,3,1,1]=>1120
[5,6,7,2,4,3,1,8]=>[7,1]=>5760
[5,6,8,4,3,1,7,2]=>[6,1,1]=>3360
[5,6,8,4,3,1,2,7]=>[7,1]=>5760
[5,7,8,4,1,6,2,3]=>[2,2,2,1,1]=>420
[5,7,8,4,1,6,3,2]=>[4,2,1,1]=>2520
[5,7,8,4,1,3,6,2]=>[5,2,1]=>4032
[5,6,8,4,2,1,7,3]=>[4,2,1,1]=>2520
[5,6,8,2,4,1,7,3]=>[5,2,1]=>4032
[4,6,2,8,5,1,7,3]=>[6,1,1]=>3360
[3,2,6,8,5,1,7,4]=>[3,2,1,1,1]=>1120
[3,2,6,8,5,1,4,7]=>[3,3,1,1]=>1120
[4,6,2,8,5,1,3,7]=>[7,1]=>5760
[5,6,8,2,4,1,3,7]=>[5,3]=>2688
[5,6,8,4,2,1,3,7]=>[4,3,1]=>3360
[5,7,8,4,1,3,2,6]=>[3,2,2,1]=>1680
[5,7,8,4,1,2,6,3]=>[3,2,2,1]=>1680
[5,7,8,4,1,2,3,6]=>[5,2,1]=>4032
[6,7,8,1,5,2,3,4]=>[7,1]=>5760
[6,7,8,1,5,2,4,3]=>[5,2,1]=>4032
[6,7,8,1,5,3,2,4]=>[5,2,1]=>4032
[6,7,8,1,3,5,2,4]=>[6,2]=>3360
[5,7,8,2,1,6,3,4]=>[5,2,1]=>4032
[4,7,2,8,1,6,3,5]=>[4,3,1]=>3360
[3,2,7,8,1,6,4,5]=>[6,1,1]=>3360
[3,2,7,8,1,6,5,4]=>[4,2,1,1]=>2520
[4,7,2,8,1,6,5,3]=>[7,1]=>5760
[5,7,8,2,1,6,4,3]=>[3,2,2,1]=>1680
[6,7,8,1,3,5,4,2]=>[8]=>5040
[6,7,8,1,5,3,4,2]=>[7,1]=>5760
[6,7,8,1,5,4,3,2]=>[4,3,1]=>3360
[6,7,8,1,5,4,2,3]=>[3,2,2,1]=>1680
[6,7,8,1,4,5,2,3]=>[4,2,2]=>1260
[6,7,8,1,4,5,3,2]=>[4,4]=>1260
[6,7,8,1,4,3,5,2]=>[8]=>5040
[6,7,8,1,3,4,5,2]=>[5,3]=>2688
[5,7,8,2,1,4,6,3]=>[4,2,2]=>1260
[4,7,2,8,1,5,6,3]=>[8]=>5040
[3,2,7,8,1,5,6,4]=>[5,2,1]=>4032
[3,2,6,8,4,1,7,5]=>[3,3,1,1]=>1120
[4,6,2,8,3,1,7,5]=>[7,1]=>5760
[5,6,8,3,2,1,7,4]=>[4,3,1]=>3360
[5,7,8,3,1,4,6,2]=>[6,2]=>3360
[5,7,8,3,1,6,4,2]=>[5,2,1]=>4032
[5,7,8,3,1,6,2,4]=>[3,2,2,1]=>1680
[4,7,3,8,1,6,2,5]=>[4,2,1,1]=>2520
[4,7,3,8,1,6,5,2]=>[6,1,1]=>3360
[4,7,3,8,1,5,6,2]=>[7,1]=>5760
[4,6,3,8,2,1,7,5]=>[6,1,1]=>3360
[4,5,3,2,8,1,7,6]=>[6,1,1]=>3360
[4,5,2,3,8,1,7,6]=>[7,1]=>5760
[3,2,5,4,8,1,7,6]=>[5,1,1,1]=>1344
[4,5,3,2,8,1,6,7]=>[7,1]=>5760
[4,6,3,8,2,1,5,7]=>[7,1]=>5760
[4,7,3,8,1,5,2,6]=>[5,2,1]=>4032
[4,7,3,8,1,2,6,5]=>[4,3,1]=>3360
[4,7,3,8,1,2,5,6]=>[7,1]=>5760
[5,7,8,3,1,2,4,6]=>[6,2]=>3360
[5,7,8,3,1,2,6,4]=>[3,3,2]=>1120
[5,7,8,3,1,4,2,6]=>[4,2,2]=>1260
[5,6,8,3,2,1,4,7]=>[4,4]=>1260
[3,2,7,8,1,5,4,6]=>[7,1]=>5760
[5,7,8,2,1,4,3,6]=>[6,2]=>3360
[6,7,8,1,3,4,2,5]=>[3,3,2]=>1120
[6,7,8,1,4,3,2,5]=>[6,2]=>3360
[6,7,8,1,4,2,5,3]=>[6,2]=>3360
[6,7,8,1,4,2,3,5]=>[8]=>5040
[6,7,8,1,2,5,3,4]=>[8]=>5040
[6,7,8,1,2,5,4,3]=>[6,2]=>3360
[6,7,8,1,2,4,5,3]=>[3,3,2]=>1120
[6,7,8,1,3,2,5,4]=>[8]=>5040
[5,7,8,2,1,3,6,4]=>[6,2]=>3360
[3,2,7,8,1,4,6,5]=>[7,1]=>5760
[6,7,8,1,3,2,4,5]=>[5,3]=>2688
[6,7,8,1,2,4,3,5]=>[5,3]=>2688
[6,7,8,1,2,3,5,4]=>[5,3]=>2688
[7,2,8,5,1,6,4,3]=>[4,2,1,1]=>2520
[1,3,7,5,2,6,4,8]=>[5,1,1,1]=>1344
[1,3,7,5,4,2,6,8]=>[4,2,1,1]=>2520
[7,2,8,5,4,1,6,3]=>[3,2,2,1]=>1680
[2,8,5,4,3,1,7,6]=>[4,2,1,1]=>2520
[2,8,4,5,6,1,7,3]=>[7,1]=>5760
[2,8,6,5,7,3,1,4]=>[6,2]=>3360
[2,8,4,5,3,7,1,6]=>[5,3]=>2688
[2,8,4,3,5,6,1,7]=>[4,2,1,1]=>2520
[7,2,8,4,5,6,1,3]=>[2,2,1,1,1,1]=>210
[1,6,3,7,5,2,4,8]=>[2,2,1,1,1,1]=>210
[6,2,3,8,5,1,7,4]=>[2,2,1,1,1,1]=>210
[6,3,2,8,5,1,4,7]=>[3,2,2,1]=>1680
[7,4,8,2,5,6,3,1]=>[4,2,1,1]=>2520
[7,4,8,5,2,1,3,6]=>[5,3]=>2688
[6,4,8,5,1,3,7,2]=>[7,1]=>5760
[6,3,7,5,2,1,8,4]=>[6,2]=>3360
[4,3,7,5,1,2,8,6]=>[5,3]=>2688
[4,3,7,1,5,6,8,2]=>[4,2,1,1]=>2520
[3,6,1,7,5,2,8,4]=>[3,2,2,1]=>1680
[3,4,1,2,7,6,8,5]=>[3,2,2,1]=>1680
[3,4,2,1,7,5,8,6]=>[4,4]=>1260
[3,6,5,7,1,4,8,2]=>[5,3]=>2688
[6,5,2,7,4,1,8,3]=>[6,2]=>3360
[3,5,2,6,4,8,7,1]=>[7,1]=>5760
[5,3,1,8,6,4,7,2]=>[7,1]=>5760
[5,6,1,8,7,2,4,3]=>[6,2]=>3360
[6,3,5,8,2,7,4,1]=>[5,3]=>2688
[6,5,8,4,2,3,7,1]=>[4,2,1,1]=>2520
[6,2,5,8,3,7,1,4]=>[3,2,2,1]=>1680
[1,6,5,7,3,4,2,8]=>[4,2,1,1]=>2520
[1,5,2,7,4,6,3,8]=>[5,1,1,1]=>1344
[5,2,1,8,7,6,3,4]=>[4,2,1,1]=>2520
[7,1,3,8,4,6,2,5]=>[3,3,1,1]=>1120
[2,3,4,8,6,1,7,5]=>[7,1]=>5760
[2,3,4,8,6,5,1,7]=>[6,2]=>3360
[2,7,3,5,8,6,1,4]=>[3,3,1,1]=>1120
[3,2,4,7,8,6,1,5]=>[4,2,1,1]=>2520
[1,5,4,6,2,7,3,8]=>[4,2,1,1]=>2520
[5,2,4,7,1,8,3,6]=>[3,2,2,1]=>1680
[5,3,6,4,1,8,7,2]=>[4,2,1,1]=>2520
[5,3,6,1,4,8,2,7]=>[5,3]=>2688
[7,3,5,6,8,4,2,1]=>[6,2]=>3360
[6,3,5,1,8,2,7,4]=>[7,1]=>5760
[2,6,1,5,8,4,7,3]=>[7,1]=>5760
[2,7,6,5,8,3,4,1]=>[6,2]=>3360
[5,7,1,6,3,8,4,2]=>[5,3]=>2688
[3,2,4,1,7,8,5,6]=>[3,2,2,1]=>1680
[3,1,4,2,7,8,6,5]=>[4,4]=>1260
[5,1,4,7,2,8,6,3]=>[5,3]=>2688
[3,6,4,7,8,2,5,1]=>[6,2]=>3360
[3,1,4,6,8,5,7,2]=>[7,1]=>5760
[6,3,4,5,7,1,8,2]=>[6,2]=>3360
[2,5,4,6,1,7,8,3]=>[5,3]=>2688
[7,2,1,4,3,6,5,8]=>[4,1,1,1,1]=>420
[7,3,4,1,2,6,5,8]=>[6,1,1]=>3360
[7,6,3,2,5,4,1,8]=>[3,2,1,1,1]=>1120
[1,8,3,2,5,4,7,6]=>[4,1,1,1,1]=>420
[1,8,4,5,2,3,7,6]=>[6,1,1]=>3360
[7,2,1,5,6,3,4,8]=>[6,1,1]=>3360
[7,2,1,6,5,4,3,8]=>[3,2,1,1,1]=>1120
[1,8,5,4,3,2,7,6]=>[3,2,1,1,1]=>1120
[1,8,6,4,3,7,2,5]=>[6,1,1]=>3360
[6,5,7,4,3,1,8,2]=>[5,2,1]=>4032
[6,4,7,5,1,3,8,2]=>[8]=>5040
[6,3,7,1,5,4,8,2]=>[4,3,1]=>3360
[3,2,1,8,5,4,7,6]=>[3,2,1,1,1]=>1120
[2,3,8,1,5,4,7,6]=>[6,1,1]=>3360
[2,5,8,4,3,1,7,6]=>[6,1,1]=>3360
[2,6,8,4,3,7,1,5]=>[4,3,1]=>3360
[2,7,8,4,3,6,5,1]=>[6,1,1]=>3360
[1,8,7,4,3,6,5,2]=>[3,2,1,1,1]=>1120
[1,8,7,5,6,3,4,2]=>[5,2,1]=>4032
[2,7,8,5,6,3,4,1]=>[8]=>5040
[2,5,8,6,7,1,3,4]=>[8]=>5040
[2,4,8,6,1,7,3,5]=>[8]=>5040
[3,2,1,8,6,7,4,5]=>[5,2,1]=>4032
[5,3,7,1,6,8,4,2]=>[8]=>5040
[5,4,7,6,1,8,3,2]=>[4,2,2]=>1260
[4,6,7,5,8,3,1,2]=>[8]=>5040
[1,8,6,5,7,3,2,4]=>[5,2,1]=>4032
[1,8,5,6,7,2,3,4]=>[4,3,1]=>3360
[5,4,6,7,1,8,2,3]=>[3,3,2]=>1120
[5,3,6,1,7,8,2,4]=>[8]=>5040
[5,2,1,6,7,8,3,4]=>[4,3,1]=>3360
[6,2,1,5,7,3,8,4]=>[4,3,1]=>3360
[6,3,5,1,7,2,8,4]=>[8]=>5040
[5,6,4,7,2,8,1,3]=>[8]=>5040
[1,8,4,6,2,7,3,5]=>[4,3,1]=>3360
[1,8,3,2,6,7,4,5]=>[6,1,1]=>3360
[5,7,3,2,6,8,4,1]=>[4,3,1]=>3360
[5,6,3,2,7,8,1,4]=>[4,3,1]=>3360
[6,5,3,2,7,1,8,4]=>[5,2,1]=>4032
[6,2,1,4,3,7,8,5]=>[6,1,1]=>3360
[4,6,3,2,8,7,1,5]=>[5,2,1]=>4032
[4,7,3,2,8,6,5,1]=>[6,1,1]=>3360
[1,8,3,2,7,6,5,4]=>[3,2,1,1,1]=>1120
[1,8,4,7,2,6,5,3]=>[6,1,1]=>3360
[3,6,4,8,2,7,1,5]=>[8]=>5040
[3,4,5,8,1,2,7,6]=>[4,3,1]=>3360
[4,3,5,1,8,2,7,6]=>[5,2,1]=>4032
[4,2,1,6,8,7,3,5]=>[5,2,1]=>4032
[3,4,6,8,1,7,2,5]=>[8]=>5040
[3,6,5,8,7,2,1,4]=>[4,2,2]=>1260
[1,8,5,7,6,2,4,3]=>[5,2,1]=>4032
[1,8,6,7,5,4,2,3]=>[6,1,1]=>3360
[3,6,7,8,5,4,1,2]=>[4,3,1]=>3360
[3,4,7,8,1,6,5,2]=>[4,3,1]=>3360
[2,4,8,7,1,6,5,3]=>[5,2,1]=>4032
[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,2,2,2,2,2]=>10395
[6,5,4,3,2,1,12,11,10,9,8,7]=>[2,2,2,2,2,2]=>10395
[12,11,10,9,8,7,6,5,4,3,2,1]=>[2,2,2,2,2,2]=>10395
[7,4,6,1,8,3,5,2]=>[6,2]=>3360
[8,3,5,1,7,4,6,2]=>[8]=>5040
[8,3,4,1,7,5,6,2]=>[5,3]=>2688
[4,8,3,1,7,5,6,2]=>[3,2,2,1]=>1680
[4,6,2,1,7,5,8,3]=>[6,2]=>3360
[1,4,6,2,7,5,8,3]=>[5,2,1]=>4032
[1,7,5,2,6,8,4,3]=>[4,3,1]=>3360
[7,5,2,1,6,8,4,3]=>[5,3]=>2688
[6,8,4,3,1,7,5,2]=>[4,2,2]=>1260
[3,6,8,4,1,7,5,2]=>[7,1]=>5760
[3,6,7,5,1,8,4,2]=>[5,3]=>2688
[7,5,6,1,8,3,4,2]=>[3,3,2]=>1120
[3,4,6,5,7,1,8,2]=>[5,3]=>2688
[4,7,5,6,1,8,3,2]=>[8]=>5040
[6,7,5,1,8,4,3,2]=>[5,3]=>2688
[6,8,4,1,7,5,3,2]=>[6,2]=>3360
[6,7,5,3,1,8,4,2]=>[8]=>5040
[8,4,2,1,6,7,5,3]=>[5,3]=>2688
[1,8,4,2,6,7,5,3]=>[4,3,1]=>3360
[1,5,3,2,7,6,8,4]=>[5,1,1,1]=>1344
[5,3,2,1,7,6,8,4]=>[5,2,1]=>4032
[2,5,3,1,7,6,8,4]=>[6,1,1]=>3360
[2,8,4,1,6,7,5,3]=>[5,3]=>2688
[2,7,5,1,6,8,4,3]=>[4,4]=>1260
[2,4,6,1,7,5,8,3]=>[5,3]=>2688
[4,7,1,6,5,8,2,3]=>[5,2,1]=>4032
[4,8,2,6,5,7,1,3]=>[4,3,1]=>3360
[4,6,1,2,7,5,8,3]=>[8]=>5040
[7,5,1,2,6,8,4,3]=>[8]=>5040
[8,4,1,2,6,7,5,3]=>[3,3,2]=>1120
[5,3,1,2,7,6,8,4]=>[7,1]=>5760
[1,2,5,3,7,6,8,4]=>[5,1,1,1]=>1344
[4,3,1,2,7,6,8,5]=>[4,3,1]=>3360
[3,5,1,2,7,6,8,4]=>[5,2,1]=>4032
[6,7,1,5,8,2,3,4]=>[5,3]=>2688
[2,7,6,1,5,8,3,4]=>[7,1]=>5760
[2,3,5,1,7,6,8,4]=>[7,1]=>5760
[7,6,1,5,8,3,2,4]=>[5,3]=>2688
[3,6,7,1,5,8,2,4]=>[7,1]=>5760
[7,1,6,5,8,2,4,3]=>[8]=>5040
[7,5,1,6,8,4,2,3]=>[6,2]=>3360
[8,4,1,6,7,5,2,3]=>[5,3]=>2688
[5,2,3,1,7,6,8,4]=>[5,1,1,1]=>1344
[3,5,2,1,7,6,8,4]=>[7,1]=>5760
[1,3,5,2,7,6,8,4]=>[6,1,1]=>3360
[1,7,6,2,5,8,3,4]=>[6,1,1]=>3360
[7,6,2,1,5,8,3,4]=>[7,1]=>5760
[8,3,1,5,7,6,2,4]=>[7,1]=>5760
[6,2,4,1,7,5,8,3]=>[7,1]=>5760
[6,2,5,1,7,4,8,3]=>[4,3,1]=>3360
[7,1,6,4,8,2,5,3]=>[7,1]=>5760
[8,2,6,4,7,1,5,3]=>[4,2,1,1]=>2520
[6,1,5,2,7,4,8,3]=>[4,4]=>1260
[7,6,2,5,8,3,1,4]=>[3,3,2]=>1120
[8,3,5,7,6,2,1,4]=>[4,4]=>1260
[1,8,3,5,7,6,2,4]=>[5,1,1,1]=>1344
[1,5,2,3,7,6,8,4]=>[6,1,1]=>3360
[5,2,1,3,7,6,8,4]=>[6,1,1]=>3360
[7,5,2,6,8,4,1,3]=>[4,2,2]=>1260
[8,4,2,6,7,5,1,3]=>[8]=>5040
[6,1,4,2,7,5,8,3]=>[8]=>5040
[8,2,6,5,7,1,4,3]=>[4,3,1]=>3360
[3,6,8,2,5,7,1,4]=>[7,1]=>5760
[8,3,2,5,7,6,1,4]=>[5,2,1]=>4032
[5,1,3,2,7,6,8,4]=>[6,1,1]=>3360
[4,1,3,2,7,6,8,5]=>[3,3,1,1]=>1120
[4,2,1,3,7,6,8,5]=>[3,3,1,1]=>1120
[1,4,2,3,7,6,8,5]=>[3,3,1,1]=>1120
[2,4,1,3,7,6,8,5]=>[4,3,1]=>3360
[2,5,1,3,7,6,8,4]=>[7,1]=>5760
[2,8,3,5,7,6,1,4]=>[6,1,1]=>3360
[6,8,2,3,5,7,1,4]=>[4,3,1]=>3360
[6,7,1,3,5,8,2,4]=>[5,2,1]=>4032
[8,3,5,7,6,1,2,4]=>[8]=>5040
[5,1,2,3,7,6,8,4]=>[7,1]=>5760
[3,1,2,4,7,6,8,5]=>[3,3,1,1]=>1120
[10,8,9,5,6,7,1,2,3,4]=>[6,2,2]=>75600
[10,8,9,4,5,6,1,2,3,7]=>[3,2,2,1,1,1]=>25200
[10,7,8,5,6,9,1,2,3,4]=>[10]=>362880
[10,7,8,4,5,9,1,2,3,6]=>[8,1,1]=>226800
[10,6,7,4,5,8,1,2,3,9]=>[5,3,1,1]=>120960
[10,7,8,3,4,9,1,2,5,6]=>[10]=>362880
[10,6,7,3,4,8,1,2,5,9]=>[7,3]=>172800
[9,8,10,5,6,7,1,2,3,4]=>[8,2]=>226800
[9,8,10,4,5,6,1,2,3,7]=>[5,2,1,1,1]=>60480
[9,7,10,5,6,8,1,2,3,4]=>[10]=>362880
[9,7,10,4,5,8,1,2,3,6]=>[8,1,1]=>226800
[9,6,10,4,5,7,1,2,3,8]=>[8,1,1]=>226800
[9,7,10,3,4,8,1,2,5,6]=>[10]=>362880
[9,6,10,3,4,7,1,2,5,8]=>[10]=>362880
[8,7,9,5,6,10,1,2,3,4]=>[4,4,2]=>56700
[8,7,9,4,5,10,1,2,3,6]=>[4,2,2,1,1]=>56700
[8,6,9,4,5,10,1,2,3,7]=>[6,2,1,1]=>151200
[7,6,8,4,5,9,1,2,3,10]=>[5,2,1,1,1]=>60480
[8,7,9,3,4,10,1,2,5,6]=>[4,4,2]=>56700
[8,6,9,3,4,10,1,2,5,7]=>[6,4]=>151200
[7,6,8,3,4,9,1,2,5,10]=>[7,2,1]=>259200
[9,6,10,5,7,8,1,2,3,4]=>[7,3]=>172800
[9,6,10,4,7,8,1,2,3,5]=>[6,3,1]=>201600
[9,5,10,4,6,7,1,2,3,8]=>[9,1]=>403200
[9,6,10,3,7,8,1,2,4,5]=>[7,3]=>172800
[9,5,10,3,6,7,1,2,4,8]=>[10]=>362880
[8,6,9,5,7,10,1,2,3,4]=>[8,2]=>226800
[8,6,9,4,7,10,1,2,3,5]=>[7,2,1]=>259200
[8,5,9,4,6,10,1,2,3,7]=>[7,2,1]=>259200
[7,5,8,4,6,9,1,2,3,10]=>[6,2,1,1]=>151200
[8,6,9,3,7,10,1,2,4,5]=>[7,3]=>172800
[8,5,9,3,6,10,1,2,4,7]=>[7,3]=>172800
[7,5,8,3,6,9,1,2,4,10]=>[7,2,1]=>259200
[8,4,9,3,5,10,1,2,6,7]=>[9,1]=>403200
[7,4,8,3,5,9,1,2,6,10]=>[4,2,2,1,1]=>56700
[9,6,10,2,7,8,1,3,4,5]=>[10]=>362880
[9,5,10,2,6,7,1,3,4,8]=>[7,3]=>172800
[8,6,9,2,7,10,1,3,4,5]=>[10]=>362880
[8,5,9,2,6,10,1,3,4,7]=>[10]=>362880
[7,5,8,2,6,9,1,3,4,10]=>[5,2,2,1]=>90720
[8,4,9,2,5,10,1,3,6,7]=>[7,2,1]=>259200
[7,4,8,2,5,9,1,3,6,10]=>[2,2,2,2,1,1]=>4725
[8,1,2,4,3,6,5,7]=>[6,1,1]=>3360
[8,1,3,5,6,2,7,4]=>[6,1,1]=>3360
[8,1,3,4,2,6,7,5]=>[4,1,1,1,1]=>420
[8,1,3,2,4,5,7,6]=>[6,1,1]=>3360
[2,7,8,3,4,5,6,1]=>[8]=>5040
[2,6,3,8,4,5,7,1]=>[6,1,1]=>3360
[6,3,2,1,4,5,8,7]=>[4,2,2]=>1260
[7,3,1,4,2,6,8,5]=>[6,1,1]=>3360
[7,4,1,5,6,8,2,3]=>[8]=>5040
[4,7,8,5,6,1,2,3]=>[4,2,2]=>1260
[3,7,8,5,6,2,1,4]=>[8]=>5040
[3,7,8,4,2,6,1,5]=>[6,1,1]=>3360
[3,7,8,2,4,5,1,6]=>[8]=>5040
[3,6,2,8,4,5,1,7]=>[8]=>5040
[2,3,6,7,4,5,8,1]=>[8]=>5040
[3,5,2,4,8,6,1,7]=>[6,1,1]=>3360
[3,5,4,2,8,7,1,6]=>[8]=>5040
[4,6,5,8,7,1,2,3]=>[8]=>5040
[6,4,5,1,7,8,2,3]=>[8]=>5040
[7,4,1,2,3,8,5,6]=>[4,2,2]=>1260
[6,2,4,1,3,7,5,8]=>[6,1,1]=>3360
[2,6,4,8,3,7,5,1]=>[8]=>5040
[2,6,5,8,7,3,4,1]=>[8]=>5040
[6,2,5,1,7,3,4,8]=>[6,1,1]=>3360
[6,5,2,1,8,3,4,7]=>[8]=>5040
[2,5,6,7,8,3,4,1]=>[4,2,2]=>1260
[2,4,6,7,3,8,5,1]=>[8]=>5040
[4,2,6,7,3,1,5,8]=>[6,1,1]=>3360
[4,7,8,2,3,1,5,6]=>[8]=>5040
[4,7,8,3,2,1,6,5]=>[8]=>5040
[5,6,4,8,1,7,2,3]=>[3,3,2]=>1120
[5,6,3,8,1,2,7,4]=>[2,2,2,1,1]=>420
[4,2,5,3,7,1,6,8]=>[6,1,1]=>3360
[4,3,6,7,2,1,8,5]=>[8]=>5040
[3,4,6,7,2,8,1,5]=>[8]=>5040
[3,4,5,2,7,8,1,6]=>[4,2,2]=>1260
[3,4,2,5,6,8,1,7]=>[8]=>5040
[5,2,7,8,6,4,1,3]=>[7,1]=>5760
[5,1,2,7,8,6,4,3]=>[5,2,1]=>4032
[4,7,1,8,6,5,2,3]=>[4,2,2]=>1260
[4,7,1,2,8,6,5,3]=>[7,1]=>5760
[4,6,8,1,2,7,5,3]=>[4,2,2]=>1260
[6,8,7,1,5,3,2,4]=>[7,1]=>5760
[6,8,7,3,5,1,2,4]=>[5,2,1]=>4032
[7,8,1,6,3,5,2,4]=>[8]=>5040
[7,8,1,3,6,5,2,4]=>[6,2]=>3360
[7,8,3,6,5,2,1,4]=>[4,2,1,1]=>2520
[4,7,2,8,6,1,5,3]=>[8]=>5040
[1,7,3,4,8,6,5,2]=>[4,1,1,1,1]=>420
[4,2,7,1,8,6,5,3]=>[4,2,1,1]=>2520
[7,8,2,3,6,5,1,4]=>[4,2,2]=>1260
[8,5,7,1,6,2,3,4]=>[3,3,2]=>1120
[8,5,7,1,2,6,3,4]=>[3,2,2,1]=>1680
[6,8,2,7,1,3,5,4]=>[8]=>5040
[6,8,7,2,5,3,1,4]=>[4,3,1]=>3360
[6,2,4,8,7,1,5,3]=>[3,2,2,1]=>1680
[1,6,8,3,7,4,5,2]=>[5,2,1]=>4032
[1,6,8,3,4,7,5,2]=>[7,1]=>5760
[6,2,4,8,1,7,5,3]=>[4,3,1]=>3360
[6,8,7,2,3,5,1,4]=>[5,3]=>2688
[6,8,2,1,7,3,5,4]=>[6,2]=>3360
[8,5,7,2,1,6,3,4]=>[5,2,1]=>4032
[8,5,7,1,2,3,6,4]=>[3,3,2]=>1120
[8,7,6,2,1,4,3,5]=>[5,3]=>2688
[8,5,7,2,3,1,6,4]=>[8]=>5040
[5,8,4,2,7,1,6,3]=>[4,4]=>1260
[1,8,7,5,3,4,6,2]=>[5,2,1]=>4032
[1,8,7,3,5,4,6,2]=>[4,2,1,1]=>2520
[8,2,5,4,7,1,6,3]=>[6,1,1]=>3360
[8,5,2,7,3,1,6,4]=>[5,3]=>2688
[8,7,6,2,4,3,1,5]=>[6,2]=>3360
[8,7,6,1,2,4,3,5]=>[8]=>5040
[8,7,6,1,4,2,3,5]=>[4,4]=>1260
[8,7,6,4,1,3,2,5]=>[3,2,2,1]=>1680
[5,8,4,7,2,1,6,3]=>[8]=>5040
[1,8,7,5,4,3,6,2]=>[3,2,2,1]=>1680
[1,6,8,4,3,7,5,2]=>[6,1,1]=>3360
[6,8,7,3,2,5,1,4]=>[8]=>5040
[6,8,1,7,3,2,5,4]=>[8]=>5040
[8,5,7,3,1,6,2,4]=>[7,1]=>5760
[8,5,7,1,3,2,6,4]=>[5,3]=>2688
[8,5,7,3,1,2,6,4]=>[8]=>5040
[5,8,4,7,1,2,6,3]=>[6,2]=>3360
[5,8,4,1,7,2,6,3]=>[8]=>5040
[5,8,4,7,1,6,2,3]=>[5,2,1]=>4032
[8,1,2,6,5,7,4,3]=>[4,3,1]=>3360
[8,2,5,6,7,4,1,3]=>[5,2,1]=>4032
[4,8,5,7,1,6,2,3]=>[7,1]=>5760
[4,8,5,7,1,2,6,3]=>[8]=>5040
[4,8,5,1,7,2,6,3]=>[6,2]=>3360
[8,5,3,1,7,2,6,4]=>[4,3,1]=>3360
[8,5,3,7,1,2,6,4]=>[7,1]=>5760
[6,8,1,3,7,2,5,4]=>[6,2]=>3360
[4,6,2,8,1,7,5,3]=>[8]=>5040
[1,6,4,8,3,7,5,2]=>[7,1]=>5760
[1,8,7,4,5,3,6,2]=>[3,2,1,1,1]=>1120
[4,8,5,7,2,1,6,3]=>[4,4]=>1260
[8,5,3,7,2,1,6,4]=>[5,2,1]=>4032
[8,7,6,3,1,4,2,5]=>[3,3,2]=>1120
[8,7,6,1,3,2,4,5]=>[8]=>5040
[8,5,3,2,7,1,6,4]=>[7,1]=>5760
[4,8,5,2,7,1,6,3]=>[8]=>5040
[1,8,7,4,3,5,6,2]=>[4,2,1,1]=>2520
[1,8,7,3,4,5,6,2]=>[5,2,1]=>4032
[8,2,4,5,7,1,6,3]=>[7,1]=>5760
[8,5,2,3,7,1,6,4]=>[8]=>5040
[6,3,1,5,4,2,8,7]=>[4,2,2]=>1260
[8,3,1,5,2,7,6,4]=>[6,2]=>3360
[8,5,4,2,1,7,3,6]=>[8]=>5040
[8,5,4,2,1,7,6,3]=>[6,2]=>3360
[6,5,4,2,1,3,8,7]=>[6,2]=>3360
[6,5,4,2,3,1,8,7]=>[4,2,2]=>1260
[6,3,2,5,1,4,8,7]=>[4,2,2]=>1260
[6,5,4,3,1,2,8,7]=>[4,2,2]=>1260
[6,5,4,1,3,2,8,7]=>[6,2]=>3360
[8,5,4,1,2,7,6,3]=>[4,2,2]=>1260
[8,7,4,1,6,3,2,5]=>[6,2]=>3360
[8,7,4,1,6,3,5,2]=>[8]=>5040
[8,7,4,1,6,5,3,2]=>[6,2]=>3360
[8,5,4,1,3,7,6,2]=>[6,2]=>3360
[8,5,4,3,1,7,6,2]=>[4,2,2]=>1260
[8,3,2,5,1,7,6,4]=>[4,2,2]=>1260
[2,1,8,5,3,7,6,4]=>[4,2,2]=>1260
[8,3,2,5,1,7,4,6]=>[6,2]=>3360
[8,5,4,3,1,7,2,6]=>[6,2]=>3360
[8,5,4,1,3,7,2,6]=>[8]=>5040
[8,7,4,1,6,5,2,3]=>[4,2,2]=>1260
[8,7,4,1,6,2,5,3]=>[4,4]=>1260
[8,7,6,5,2,1,4,3]=>[4,4]=>1260
[8,7,4,3,6,2,1,5]=>[6,2]=>3360
[8,3,2,7,6,4,1,5]=>[6,2]=>3360
[2,1,8,7,6,4,3,5]=>[6,2]=>3360
[2,1,8,7,6,4,5,3]=>[4,2,2]=>1260
[8,3,2,7,6,4,5,1]=>[4,2,2]=>1260
[8,7,4,3,6,2,5,1]=>[4,2,2]=>1260
[8,7,6,5,2,4,3,1]=>[6,2]=>3360
[8,5,4,2,3,7,6,1]=>[4,2,2]=>1260
[8,7,4,2,6,5,3,1]=>[4,2,2]=>1260
[8,7,4,2,6,3,5,1]=>[6,2]=>3360
[8,7,4,2,6,3,1,5]=>[8]=>5040
[8,3,1,7,6,4,2,5]=>[8]=>5040
[8,3,1,7,6,4,5,2]=>[4,4]=>1260
[8,3,1,7,6,5,4,2]=>[4,2,2]=>1260
[8,3,1,5,4,7,6,2]=>[4,2,2]=>1260
[8,3,1,5,4,7,2,6]=>[6,2]=>3360
[8,3,1,7,6,5,2,4]=>[6,2]=>3360
[8,3,1,7,6,2,5,4]=>[8]=>5040
[8,7,4,2,6,1,5,3]=>[8]=>5040
[8,7,4,2,6,5,1,3]=>[6,2]=>3360
[8,5,4,2,3,7,1,6]=>[4,4]=>1260
[8,3,2,5,4,7,1,6]=>[4,2,2]=>1260
[2,1,8,5,4,7,3,6]=>[4,2,2]=>1260
[8,3,2,7,6,5,1,4]=>[4,2,2]=>1260
[8,7,4,3,6,5,1,2]=>[4,2,2]=>1260
[8,7,6,5,3,1,4,2]=>[8]=>5040
[8,7,6,5,1,3,2,4]=>[4,2,2]=>1260
[8,7,6,5,1,3,4,2]=>[6,2]=>3360
[8,7,6,5,1,4,3,2]=>[8]=>5040
[8,7,6,5,4,1,3,2]=>[6,2]=>3360
[8,7,4,3,6,1,5,2]=>[6,2]=>3360
[8,3,2,7,6,1,5,4]=>[6,2]=>3360
[2,1,8,7,6,3,5,4]=>[6,2]=>3360
[8,3,2,7,6,1,4,5]=>[4,2,2]=>1260
[8,7,6,5,1,4,2,3]=>[6,2]=>3360
[8,7,6,5,1,2,4,3]=>[8]=>5040
[7,3,5,1,8,4,6,2]=>[4,4]=>1260
[7,3,4,1,8,5,6,2]=>[8]=>5040
[4,5,6,2,1,8,7,3]=>[4,3,1]=>3360
[1,6,5,2,7,4,3,8]=>[3,3,1,1]=>1120
[7,4,3,1,8,6,5,2]=>[6,1,1]=>3360
[7,6,5,1,8,4,3,2]=>[8]=>5040
[7,6,4,1,8,5,3,2]=>[4,4]=>1260
[6,4,2,1,8,7,5,3]=>[8]=>5040
[1,6,4,2,7,5,3,8]=>[6,1,1]=>3360
[1,5,3,2,7,6,4,8]=>[4,1,1,1,1]=>420
[5,3,2,1,8,7,6,4]=>[4,2,2]=>1260
[2,5,3,1,7,8,6,4]=>[7,1]=>5760
[2,6,4,1,7,8,5,3]=>[6,2]=>3360
[2,6,5,1,7,8,4,3]=>[8]=>5040
[4,5,7,1,6,8,2,3]=>[6,2]=>3360
[6,5,1,2,8,4,3,7]=>[8]=>5040
[6,4,1,2,8,5,3,7]=>[6,2]=>3360
[5,3,1,2,8,6,4,7]=>[7,1]=>5760
[4,3,1,2,8,6,5,7]=>[4,3,1]=>3360
[6,1,2,5,8,3,4,7]=>[4,4]=>1260
[7,1,3,4,8,2,5,6]=>[6,1,1]=>3360
[7,1,5,6,8,2,3,4]=>[8]=>5040
[2,6,1,5,7,8,3,4]=>[8]=>5040
[7,4,1,6,8,5,2,3]=>[8]=>5040
[5,2,3,1,8,6,7,4]=>[4,1,1,1,1]=>420
[3,5,2,1,6,8,7,4]=>[7,1]=>5760
[1,6,2,5,7,3,4,8]=>[3,3,1,1]=>1120
[6,2,1,5,8,7,3,4]=>[4,3,1]=>3360
[7,3,1,5,8,6,2,4]=>[4,3,1]=>3360
[6,2,4,1,8,5,7,3]=>[6,1,1]=>3360
[6,2,5,1,8,4,7,3]=>[3,3,1,1]=>1120
[7,3,1,4,8,6,2,5]=>[4,2,1,1]=>2520
[6,2,1,4,8,7,3,5]=>[4,2,1,1]=>2520
[1,6,2,4,7,3,5,8]=>[3,2,1,1,1]=>1120
[5,2,1,3,8,7,4,6]=>[7,1]=>5760
[7,4,1,3,8,5,2,6]=>[5,3]=>2688
[7,5,1,3,8,4,2,6]=>[8]=>5040
[3,6,7,1,4,8,2,5]=>[8]=>5040
[7,6,1,4,8,3,2,5]=>[5,2,1]=>4032
[4,2,1,3,8,7,5,6]=>[4,3,1]=>3360
[2,6,1,4,7,8,3,5]=>[7,1]=>5760
[7,1,4,6,8,2,3,5]=>[6,2]=>3360
[7,1,3,5,8,2,4,6]=>[7,1]=>5760
[6,1,2,4,8,3,5,7]=>[4,3,1]=>3360
[5,2,3,1,6,4,8,7]=>[4,2,1,1]=>2520
[7,4,5,2,3,1,8,6]=>[4,2,2]=>1260
[8,6,7,3,5,2,4,1]=>[3,2,2,1]=>1680
[7,3,5,2,4,1,8,6]=>[4,4]=>1260
[6,3,5,2,4,1,8,7]=>[4,2,2]=>1260
[5,2,4,1,6,3,8,7]=>[5,2,1]=>4032
[4,1,6,3,5,2,8,7]=>[5,2,1]=>4032
[6,3,4,1,5,2,8,7]=>[5,2,1]=>4032
[5,2,6,3,4,1,8,7]=>[5,2,1]=>4032
[5,2,7,3,4,1,8,6]=>[7,1]=>5760
[5,2,8,6,7,3,4,1]=>[7,1]=>5760
[6,2,8,5,7,3,4,1]=>[4,3,1]=>3360
[6,2,7,3,4,1,8,5]=>[5,2,1]=>4032
[7,3,4,1,5,2,8,6]=>[7,1]=>5760
[4,1,7,3,5,2,8,6]=>[7,1]=>5760
[3,1,7,4,5,2,8,6]=>[6,1,1]=>3360
[2,1,7,4,5,3,8,6]=>[4,2,1,1]=>2520
[3,1,8,6,7,4,5,2]=>[4,2,2]=>1260
[4,1,8,6,7,3,5,2]=>[6,2]=>3360
[8,6,7,3,4,1,5,2]=>[4,4]=>1260
[8,5,7,3,4,1,6,2]=>[8]=>5040
[8,5,6,2,7,3,4,1]=>[4,2,2]=>1260
[8,4,7,3,5,1,6,2]=>[7,1]=>5760
[5,1,8,4,7,3,6,2]=>[7,1]=>5760
[4,1,8,5,7,3,6,2]=>[8]=>5040
[3,1,8,5,7,4,6,2]=>[4,4]=>1260
[2,1,8,5,7,4,6,3]=>[4,2,2]=>1260
[2,1,7,4,6,3,8,5]=>[5,2,1]=>4032
[3,1,7,4,6,2,8,5]=>[7,1]=>5760
[4,1,7,3,6,2,8,5]=>[8]=>5040
[5,1,7,3,6,2,8,4]=>[4,4]=>1260
[6,2,7,3,5,1,8,4]=>[4,2,1,1]=>2520
[6,2,8,4,7,3,5,1]=>[4,2,1,1]=>2520
[8,4,7,3,6,2,5,1]=>[6,2]=>3360
[7,3,6,2,5,1,8,4]=>[7,1]=>5760
[6,2,5,1,7,3,8,4]=>[7,1]=>5760
[5,2,4,1,7,3,8,6]=>[7,1]=>5760
[6,2,4,1,7,3,8,5]=>[4,3,1]=>3360
[8,5,7,3,6,2,4,1]=>[3,3,2]=>1120
[8,5,7,4,6,2,3,1]=>[3,2,2,1]=>1680
[7,4,6,2,3,1,8,5]=>[6,2]=>3360
[6,2,3,1,7,4,8,5]=>[3,3,1,1]=>1120
[5,2,3,1,7,4,8,6]=>[6,1,1]=>3360
[4,2,3,1,7,5,8,6]=>[4,2,1,1]=>2520
[3,1,4,2,8,6,7,5]=>[4,2,1,1]=>2520
[6,2,3,1,8,5,7,4]=>[5,1,1,1]=>1344
[8,5,6,2,3,1,7,4]=>[7,1]=>5760
[7,4,8,5,6,2,3,1]=>[4,4]=>1260
[7,3,8,5,6,2,4,1]=>[8]=>5040
[8,5,6,2,4,1,7,3]=>[4,3,1]=>3360
[5,2,4,1,8,6,7,3]=>[5,1,1,1]=>1344
[4,1,5,2,8,6,7,3]=>[3,3,1,1]=>1120
[3,1,5,2,8,6,7,4]=>[6,1,1]=>3360
[2,1,6,3,8,5,7,4]=>[5,2,1]=>4032
[3,1,6,2,8,5,7,4]=>[7,1]=>5760
[4,1,6,2,8,5,7,3]=>[4,3,1]=>3360
[5,1,6,2,8,4,7,3]=>[7,1]=>5760
[8,4,6,2,5,1,7,3]=>[4,2,1,1]=>2520
[7,3,8,4,6,2,5,1]=>[7,1]=>5760
[6,2,7,3,8,4,5,1]=>[7,1]=>5760
[8,4,5,1,6,2,7,3]=>[7,1]=>5760
[5,1,8,4,6,2,7,3]=>[4,2,1,1]=>2520
[4,1,8,5,6,2,7,3]=>[5,2,1]=>4032
[3,1,8,5,6,2,7,4]=>[7,1]=>5760
[2,1,8,5,6,3,7,4]=>[5,2,1]=>4032
[2,1,7,4,8,5,6,3]=>[5,2,1]=>4032
[3,1,7,4,8,5,6,2]=>[7,1]=>5760
[4,1,7,3,8,5,6,2]=>[8]=>5040
[7,3,8,4,5,1,6,2]=>[3,3,1,1]=>1120
[8,4,5,1,7,3,6,2]=>[4,4]=>1260
[7,3,6,2,8,4,5,1]=>[4,4]=>1260
[7,8,5,6,1,3,4,2]=>[6,2]=>3360
[7,8,1,3,6,2,5,4]=>[8]=>5040
[1,3,8,4,7,2,5,6]=>[4,2,1,1]=>2520
[3,6,1,4,7,2,5,8]=>[2,2,2,1,1]=>420
[4,6,1,2,5,7,3,8]=>[6,1,1]=>3360
[1,4,8,2,5,7,3,6]=>[4,2,1,1]=>2520
[7,8,2,4,5,6,1,3]=>[3,2,1,1,1]=>1120
[7,8,1,5,4,6,3,2]=>[3,2,2,1]=>1680
[7,8,2,1,6,3,4,5]=>[5,3]=>2688
[7,8,3,5,6,4,1,2]=>[3,2,2,1]=>1680
[7,8,1,4,2,3,6,5]=>[4,3,1]=>3360
[7,8,5,1,4,2,6,3]=>[8]=>5040
[7,8,4,5,3,1,6,2]=>[3,3,2]=>1120
[1,5,8,4,3,2,7,6]=>[5,1,1,1]=>1344
[5,6,1,4,3,2,7,8]=>[3,2,1,1,1]=>1120
[2,6,4,8,3,7,1,5]=>[4,4]=>1260
[1,4,6,8,3,7,5,2]=>[4,3,1]=>3360
[2,4,8,5,3,1,6,7]=>[8]=>5040
[2,5,8,1,4,7,6,3]=>[4,2,2]=>1260
[3,5,8,4,7,6,1,2]=>[6,1,1]=>3360
[1,6,2,4,7,3,8,5]=>[3,3,1,1]=>1120
[5,6,2,1,4,7,8,3]=>[5,3]=>2688
[4,6,2,5,3,1,8,7]=>[6,2]=>3360
[4,7,5,1,3,6,8,2]=>[3,2,2,1]=>1680
[7,5,3,6,2,4,1,8]=>[2,2,2,1,1]=>420
[5,7,3,6,1,4,8,2]=>[3,2,2,1]=>1680
[5,3,6,7,2,1,8,4]=>[5,3]=>2688
[6,1,7,5,2,4,8,3]=>[5,3]=>2688
[6,3,1,2,4,5,8,7]=>[6,2]=>3360
[1,4,7,2,5,3,8,6]=>[4,2,1,1]=>2520
[4,6,7,8,3,5,1,2]=>[8]=>5040
[3,6,1,8,4,2,5,7]=>[4,2,2]=>1260
[1,6,7,5,8,2,4,3]=>[5,2,1]=>4032
[3,5,6,7,8,1,4,2]=>[3,3,2]=>1120
[3,6,5,7,8,2,1,4]=>[6,2]=>3360
[5,2,7,6,1,4,3,8]=>[2,2,2,1,1]=>420
[2,5,7,6,8,1,3,4]=>[6,2]=>3360
[2,7,5,6,8,4,1,3]=>[3,3,2]=>1120
[2,1,6,8,4,5,3,7]=>[6,2]=>3360
[2,7,1,8,5,3,4,6]=>[7,1]=>5760
[3,7,6,8,5,4,1,2]=>[7,1]=>5760
[4,3,8,5,6,7,1,2]=>[5,3]=>2688
[4,2,8,1,6,3,7,5]=>[4,2,1,1]=>2520
[3,1,8,5,4,6,7,2]=>[4,2,1,1]=>2520
[3,2,8,4,5,6,1,7]=>[4,1,1,1,1]=>420
[3,4,2,8,6,1,7,5]=>[7,1]=>5760
[3,4,7,1,5,2,6,8]=>[6,1,1]=>3360
[4,3,7,8,1,2,6,5]=>[4,4]=>1260
[1,7,3,8,5,2,6,4]=>[3,2,1,1,1]=>1120
[4,1,8,3,6,2,5,7]=>[8]=>5040
[5,7,8,6,3,2,1,4]=>[8]=>5040
[5,7,8,6,1,3,4,2]=>[6,2]=>3360
[7,6,5,8,1,3,4,2]=>[8]=>5040
[1,6,4,3,8,2,5,7]=>[3,2,2,1]=>1680
[7,1,3,4,8,2,6,5]=>[4,2,1,1]=>2520
[3,6,5,4,1,2,7,8]=>[3,2,1,1,1]=>1120
[2,4,5,1,7,8,6,3]=>[5,3]=>2688
[2,6,3,4,5,8,1,7]=>[5,1,1,1]=>1344
[2,6,4,1,8,3,7,5]=>[5,2,1]=>4032
[7,3,6,4,8,5,1,2]=>[5,2,1]=>4032
[7,2,1,4,8,3,5,6]=>[6,1,1]=>3360
[7,1,6,5,3,8,4,2]=>[8]=>5040
[7,2,5,6,3,8,1,4]=>[3,2,2,1]=>1680
[6,5,2,7,1,8,4,3]=>[6,2]=>3360
[5,6,2,7,3,1,4,8]=>[5,2,1]=>4032
[5,6,7,4,2,8,1,3]=>[7,1]=>5760
[5,7,6,4,1,8,3,2]=>[5,2,1]=>4032
[6,7,1,5,2,8,3,4]=>[8]=>5040
[1,7,5,2,4,8,3,6]=>[5,2,1]=>4032
[6,1,5,2,8,3,4,7]=>[8]=>5040
[6,7,5,3,8,4,1,2]=>[8]=>5040
[1,6,5,4,2,3,8,7]=>[4,2,1,1]=>2520
[7,1,5,3,4,2,8,6]=>[5,3]=>2688
[7,6,1,5,3,2,8,4]=>[6,2]=>3360
[7,5,6,4,1,2,8,3]=>[7,1]=>5760
[6,7,5,4,3,1,8,2]=>[3,2,2,1]=>1680
[7,5,2,4,3,1,6,8]=>[3,3,1,1]=>1120
[7,4,6,1,2,5,3,8]=>[7,1]=>5760
[7,1,4,2,5,3,6,8]=>[6,1,1]=>3360
[6,8,1,4,2,5,7,3]=>[6,1,1]=>3360
[1,6,4,2,5,7,3,8]=>[5,1,1,1]=>1344
[1,6,3,7,5,4,2,8]=>[4,1,1,1,1]=>420
[6,8,1,3,7,5,4,2]=>[6,2]=>3360
[7,1,3,5,6,4,2,8]=>[3,3,1,1]=>1120
[7,3,1,6,4,5,2,8]=>[4,3,1]=>3360
[7,4,2,6,5,1,3,8]=>[6,1,1]=>3360
[7,4,6,3,1,5,2,8]=>[7,1]=>5760
[7,2,4,1,5,3,6,8]=>[5,1,1,1]=>1344
[7,2,3,5,4,1,6,8]=>[3,2,1,1,1]=>1120
[6,8,1,2,3,4,7,5]=>[7,1]=>5760
[1,5,7,2,3,8,6,4]=>[7,1]=>5760
[5,1,8,2,3,6,7,4]=>[6,1,1]=>3360
[5,8,2,3,7,6,4,1]=>[7,1]=>5760
[6,2,8,1,3,7,4,5]=>[4,3,1]=>3360
[6,8,2,3,5,4,7,1]=>[6,1,1]=>3360
[6,8,2,4,1,5,7,3]=>[3,3,1,1]=>1120
[6,8,3,1,2,4,7,5]=>[3,3,1,1]=>1120
[2,6,4,1,5,7,3,8]=>[6,1,1]=>3360
[2,6,3,5,7,1,4,8]=>[3,3,1,1]=>1120
[2,5,1,7,8,3,6,4]=>[8]=>5040
[2,5,3,6,8,4,7,1]=>[4,2,1,1]=>2520
[2,1,4,7,8,5,6,3]=>[6,2]=>3360
[2,4,7,6,8,5,1,3]=>[8]=>5040
[2,5,3,7,6,1,8,4]=>[4,3,1]=>3360
[2,5,7,8,1,4,6,3]=>[5,3]=>2688
[3,5,7,4,1,6,2,8]=>[5,1,1,1]=>1344
[5,3,4,1,8,6,7,2]=>[6,1,1]=>3360
[5,2,8,4,6,1,7,3]=>[3,2,1,1,1]=>1120
[5,2,1,8,6,3,7,4]=>[4,2,1,1]=>2520
[4,2,8,6,5,3,7,1]=>[5,1,1,1]=>1344
[4,2,8,5,7,6,3,1]=>[6,1,1]=>3360
[1,4,2,7,5,8,6,3]=>[6,1,1]=>3360
[4,1,8,6,7,5,3,2]=>[8]=>5040
[5,3,8,7,6,2,4,1]=>[6,2]=>3360
[5,8,4,7,6,2,1,3]=>[8]=>5040
[5,8,7,4,3,6,1,2]=>[4,2,1,1]=>2520
[6,4,8,3,1,7,2,5]=>[8]=>5040
[6,4,2,8,7,1,3,5]=>[6,2]=>3360
[6,3,8,7,2,5,1,4]=>[8]=>5040
[5,8,3,7,1,6,4,2]=>[2,2,2,1,1]=>420
[5,1,3,8,6,7,2,4]=>[5,2,1]=>4032
[1,5,3,7,8,6,2,4]=>[5,1,1,1]=>1344
[1,5,7,6,4,2,8,3]=>[4,3,1]=>3360
[5,8,7,4,1,6,2,3]=>[4,2,1,1]=>2520
[6,4,8,1,2,7,3,5]=>[8]=>5040
[6,8,5,1,2,3,7,4]=>[7,1]=>5760
[6,8,5,2,4,3,7,1]=>[7,1]=>5760
[6,8,5,3,1,2,7,4]=>[7,1]=>5760
[4,5,1,2,7,6,3,8]=>[6,1,1]=>3360
[4,5,1,2,6,8,7,3]=>[7,1]=>5760
[3,5,6,1,8,4,7,2]=>[4,3,1]=>3360
[3,5,7,1,2,8,6,4]=>[6,2]=>3360
[3,6,2,7,5,1,4,8]=>[4,2,1,1]=>2520
[4,2,6,1,7,3,5,8]=>[2,2,2,1,1]=>420
[4,6,3,1,2,7,5,8]=>[4,2,1,1]=>2520
[4,5,3,1,7,6,2,8]=>[3,2,1,1,1]=>1120
[4,2,5,7,1,6,3,8]=>[5,1,1,1]=>1344
[3,5,2,7,8,1,6,4]=>[8]=>5040
[3,1,4,7,5,6,2,8]=>[5,1,1,1]=>1344
[3,4,6,5,8,7,1,2]=>[4,4]=>1260
[3,1,4,5,8,6,7,2]=>[6,1,1]=>3360
[3,4,6,8,5,2,7,1]=>[6,1,1]=>3360
[3,5,6,2,8,4,7,1]=>[7,1]=>5760
[4,2,5,6,1,8,7,3]=>[6,1,1]=>3360
[4,5,3,1,6,8,7,2]=>[4,2,1,1]=>2520
[2,1,7,5,8,6,4,3]=>[5,2,1]=>4032
[1,2,7,5,3,8,6,4]=>[6,1,1]=>3360
[4,1,2,7,3,8,6,5]=>[8]=>5040
[6,4,1,7,5,2,3,8]=>[6,1,1]=>3360
[6,1,3,7,5,2,4,8]=>[3,2,1,1,1]=>1120
[3,1,2,6,8,5,4,7]=>[5,3]=>2688
[3,7,1,2,5,4,8,6]=>[5,2,1]=>4032
[1,3,7,2,4,8,6,5]=>[7,1]=>5760
[2,4,1,7,8,6,5,3]=>[7,1]=>5760
[3,4,7,5,1,8,6,2]=>[8]=>5040
[2,7,4,1,5,8,6,3]=>[7,1]=>5760
[2,3,7,1,5,8,6,4]=>[7,1]=>5760
[5,2,8,1,3,7,4,6]=>[7,1]=>5760
[2,1,6,8,3,4,7,5]=>[5,2,1]=>4032
[2,6,8,3,1,5,7,4]=>[4,3,1]=>3360
[2,8,6,4,1,5,7,3]=>[6,1,1]=>3360
[3,6,4,8,5,1,7,2]=>[6,1,1]=>3360
[6,3,7,4,5,1,8,2]=>[4,2,1,1]=>2520
[2,6,3,7,5,8,1,4]=>[6,1,1]=>3360
[5,2,1,7,8,3,4,6]=>[5,2,1]=>4032
[4,7,2,3,6,8,1,5]=>[5,3]=>2688
[5,2,7,3,6,8,1,4]=>[7,1]=>5760
[5,7,4,6,2,8,1,3]=>[4,4]=>1260
[5,7,3,4,6,1,8,2]=>[3,3,1,1]=>1120
[5,3,8,4,6,1,7,2]=>[3,3,1,1]=>1120
[8,5,2,4,1,6,7,3]=>[5,1,1,1]=>1344
[8,2,3,5,1,6,7,4]=>[4,1,1,1,1]=>420
[4,2,8,3,6,7,1,5]=>[7,1]=>5760
[2,4,8,1,7,3,5,6]=>[3,3,2]=>1120
[8,4,1,3,6,2,5,7]=>[8]=>5040
[4,8,3,1,7,2,5,6]=>[3,2,2,1]=>1680
[5,2,8,4,7,1,6,3]=>[4,2,1,1]=>2520
[5,8,4,7,3,1,6,2]=>[6,2]=>3360
[4,6,8,3,1,7,5,2]=>[8]=>5040
[6,3,8,2,7,1,5,4]=>[4,2,2]=>1260
[6,3,1,8,2,4,7,5]=>[7,1]=>5760
[5,3,8,1,2,6,4,7]=>[7,1]=>5760
[5,7,4,1,6,2,3,8]=>[7,1]=>5760
[8,5,4,1,2,6,3,7]=>[5,2,1]=>4032
[5,1,8,4,2,7,3,6]=>[4,3,1]=>3360
[1,6,2,8,5,3,7,4]=>[3,2,1,1,1]=>1120
[6,8,5,3,1,7,4,2]=>[6,2]=>3360
[8,4,5,1,2,6,3,7]=>[7,1]=>5760
[5,6,3,7,1,2,4,8]=>[2,2,2,1,1]=>420
[1,6,3,7,2,8,4,5]=>[4,2,1,1]=>2520
[6,3,2,7,8,5,1,4]=>[6,2]=>3360
[4,5,7,8,3,1,6,2]=>[8]=>5040
[4,7,2,5,8,1,6,3]=>[8]=>5040
[8,1,3,4,6,2,5,7]=>[6,1,1]=>3360
[3,8,2,4,6,7,1,5]=>[7,1]=>5760
[3,5,6,8,2,7,1,4]=>[4,2,2]=>1260
[2,4,5,6,8,1,7,3]=>[4,3,1]=>3360
[4,8,3,5,6,1,7,2]=>[4,2,1,1]=>2520
[5,6,2,3,7,8,1,4]=>[5,3]=>2688
[6,8,7,3,4,1,2,5]=>[6,2]=>3360
[6,8,4,7,1,5,3,2]=>[3,3,2]=>1120
[6,8,4,7,2,5,3,1]=>[5,3]=>2688
[5,4,8,7,1,6,3,2]=>[5,2,1]=>4032
[4,3,8,7,6,1,2,5]=>[8]=>5040
[3,8,4,7,5,1,2,6]=>[7,1]=>5760
[3,4,8,7,6,1,2,5]=>[5,3]=>2688
[4,5,8,7,6,1,2,3]=>[6,2]=>3360
[4,5,8,7,2,6,3,1]=>[5,2,1]=>4032
[3,5,8,2,7,6,4,1]=>[4,3,1]=>3360
[3,5,8,1,7,6,4,2]=>[7,1]=>5760
[2,5,8,1,7,6,4,3]=>[5,2,1]=>4032
[2,5,8,7,1,6,3,4]=>[4,3,1]=>3360
[8,1,4,6,2,5,3,7]=>[8]=>5040
[1,8,4,7,2,5,3,6]=>[4,3,1]=>3360
[1,4,8,7,2,6,3,5]=>[6,1,1]=>3360
[1,5,8,2,7,6,4,3]=>[4,2,1,1]=>2520
[2,5,8,3,7,6,4,1]=>[7,1]=>5760
[1,4,2,8,7,6,5,3]=>[4,2,1,1]=>2520
[1,8,3,2,7,5,4,6]=>[6,1,1]=>3360
[8,1,3,2,6,5,4,7]=>[5,2,1]=>4032
[2,8,3,1,7,5,4,6]=>[7,1]=>5760
[3,4,1,8,7,6,5,2]=>[3,2,2,1]=>1680
[4,3,1,8,7,6,5,2]=>[5,2,1]=>4032
[4,2,1,8,7,6,5,3]=>[4,2,1,1]=>2520
[3,8,2,1,7,5,4,6]=>[8]=>5040
[8,4,2,6,1,5,3,7]=>[8]=>5040
[5,2,8,1,7,6,4,3]=>[4,2,1,1]=>2520
[5,3,8,1,7,6,4,2]=>[4,3,1]=>3360
[5,3,8,2,7,6,4,1]=>[7,1]=>5760
[6,8,2,1,7,5,4,3]=>[5,3]=>2688
[6,8,2,7,1,5,3,4]=>[5,3]=>2688
[5,8,7,1,2,4,3,6]=>[6,2]=>3360
[5,2,8,3,7,6,4,1]=>[6,1,1]=>3360
[5,1,8,3,7,6,4,2]=>[7,1]=>5760
[4,1,8,7,2,6,3,5]=>[7,1]=>5760
[8,4,1,6,2,5,3,7]=>[4,4]=>1260
[3,1,8,2,7,6,4,5]=>[7,1]=>5760
[3,1,2,8,7,6,5,4]=>[3,2,2,1]=>1680
[4,1,3,8,7,6,5,2]=>[4,2,1,1]=>2520
[3,1,4,8,7,6,5,2]=>[5,2,1]=>4032
[2,1,8,3,7,6,4,5]=>[5,2,1]=>4032
[2,8,1,3,7,5,4,6]=>[8]=>5040
[8,1,2,3,6,5,4,7]=>[6,2]=>3360
[1,8,2,3,7,5,4,6]=>[7,1]=>5760
[1,4,3,6,8,2,5,7]=>[3,3,1,1]=>1120
[3,1,6,2,5,8,4,7]=>[7,1]=>5760
[3,5,1,8,2,4,7,6]=>[3,2,2,1]=>1680
[1,4,5,2,8,3,7,6]=>[4,2,1,1]=>2520
[1,4,2,6,5,8,3,7]=>[6,1,1]=>3360
[1,5,4,2,6,8,3,7]=>[7,1]=>5760
[3,1,6,5,8,2,4,7]=>[4,4]=>1260
[1,6,4,2,5,8,3,7]=>[6,1,1]=>3360
[1,5,2,6,4,8,3,7]=>[7,1]=>5760
[1,2,6,5,4,8,3,7]=>[4,2,1,1]=>2520
[1,2,5,4,7,3,8,6]=>[5,1,1,1]=>1344
[4,1,2,6,3,8,7,5]=>[7,1]=>5760
[7,1,5,4,2,8,3,6]=>[5,2,1]=>4032
[1,4,7,5,2,8,3,6]=>[3,2,2,1]=>1680
[7,1,3,5,2,8,4,6]=>[5,2,1]=>4032
[7,2,5,1,8,3,4,6]=>[4,3,1]=>3360
[1,4,5,2,8,7,3,6]=>[5,2,1]=>4032
[1,6,4,2,8,3,7,5]=>[4,2,1,1]=>2520
[1,4,2,8,3,7,6,5]=>[5,2,1]=>4032
[1,2,5,3,8,7,6,4]=>[4,2,1,1]=>2520
[1,2,8,6,5,3,7,4]=>[4,1,1,1,1]=>420
[1,5,2,8,6,3,7,4]=>[4,2,1,1]=>2520
[1,6,4,2,8,7,3,5]=>[5,2,1]=>4032
[6,2,1,8,7,3,4,5]=>[4,3,1]=>3360
[7,6,2,1,8,3,4,5]=>[3,3,2]=>1120
[7,3,1,6,2,8,4,5]=>[8]=>5040
[1,7,6,4,2,8,3,5]=>[6,1,1]=>3360
[1,7,5,2,6,3,8,4]=>[4,3,1]=>3360
[1,6,2,7,5,3,8,4]=>[3,3,1,1]=>1120
[1,2,7,6,5,3,8,4]=>[5,1,1,1]=>1344
[1,2,6,5,3,8,7,4]=>[5,1,1,1]=>1344
[1,5,2,6,3,8,7,4]=>[3,3,1,1]=>1120
[1,5,2,7,6,3,8,4]=>[4,3,1]=>3360
[1,6,5,2,7,3,8,4]=>[7,1]=>5760
[1,5,7,4,2,8,3,6]=>[2,2,2,1,1]=>420
[4,1,2,8,6,3,7,5]=>[7,1]=>5760
[3,1,8,6,2,4,7,5]=>[5,2,1]=>4032
[4,3,7,1,8,2,5,6]=>[6,2]=>3360
[8,3,1,6,2,4,7,5]=>[5,2,1]=>4032
[7,1,8,3,2,4,6,5]=>[8]=>5040
[1,8,7,3,2,4,6,5]=>[4,3,1]=>3360
[1,4,2,8,7,3,6,5]=>[7,1]=>5760
[1,7,4,2,8,3,6,5]=>[5,2,1]=>4032
[8,1,5,4,2,7,3,6]=>[7,1]=>5760
[1,4,8,5,2,7,3,6]=>[4,3,1]=>3360
[8,5,3,1,7,2,4,6]=>[7,1]=>5760
[8,6,2,1,7,3,4,5]=>[5,3]=>2688
[1,8,6,4,2,7,3,5]=>[3,3,1,1]=>1120
[1,8,5,2,6,3,7,4]=>[3,3,1,1]=>1120
[1,5,2,7,3,8,6,4]=>[4,3,1]=>3360
[1,2,8,5,3,7,6,4]=>[4,2,1,1]=>2520
[1,2,6,3,8,7,5,4]=>[6,1,1]=>3360
[1,2,7,6,3,8,5,4]=>[3,3,1,1]=>1120
[1,6,2,7,3,8,5,4]=>[7,1]=>5760
[1,7,2,8,5,3,6,4]=>[4,2,1,1]=>2520
[1,7,4,2,8,6,3,5]=>[4,2,1,1]=>2520
[7,1,8,3,2,6,4,5]=>[7,1]=>5760
[7,2,1,8,6,3,4,5]=>[7,1]=>5760
[1,8,7,3,2,6,4,5]=>[3,3,1,1]=>1120
[1,4,2,8,7,6,3,5]=>[6,1,1]=>3360
[1,2,8,7,5,3,6,4]=>[5,1,1,1]=>1344
[1,2,8,6,3,7,5,4]=>[6,1,1]=>3360
[1,2,7,3,8,6,5,4]=>[5,1,1,1]=>1344
[4,1,7,3,6,5,8,2]=>[6,2]=>3360
[5,1,8,7,6,2,4,3]=>[4,2,2]=>1260
[8,1,7,6,3,4,5,2]=>[3,3,2]=>1120
[5,7,8,6,2,4,1,3]=>[4,2,2]=>1260
[5,7,1,6,2,4,3,8]=>[5,2,1]=>4032
[6,4,1,5,2,7,3,8]=>[4,3,1]=>3360
[8,1,4,5,3,7,6,2]=>[3,3,2]=>1120
[6,1,4,5,3,8,7,2]=>[4,3,1]=>3360
[6,1,4,5,3,7,8,2]=>[5,3]=>2688
[5,1,7,8,6,2,4,3]=>[4,4]=>1260
[6,1,4,8,3,5,7,2]=>[7,1]=>5760
[7,1,8,6,3,4,5,2]=>[6,2]=>3360
[7,1,4,5,3,8,6,2]=>[5,3]=>2688
[7,1,4,5,3,6,8,2]=>[4,3,1]=>3360
[8,1,4,5,3,6,7,2]=>[3,3,1,1]=>1120
[7,4,1,5,2,6,3,8]=>[3,3,1,1]=>1120
[6,3,5,7,2,1,4,8]=>[3,2,2,1]=>1680
[6,3,5,8,2,1,7,4]=>[3,2,2,1]=>1680
[6,3,5,7,2,1,8,4]=>[3,3,2]=>1120
[8,4,5,7,3,6,1,2]=>[5,2,1]=>4032
[6,4,5,8,3,7,2,1]=>[6,2]=>3360
[5,8,7,6,2,4,1,3]=>[6,2]=>3360
[5,4,8,6,3,1,7,2]=>[7,1]=>5760
[5,4,1,8,2,3,7,6]=>[7,1]=>5760
[5,8,1,6,2,4,3,7]=>[6,2]=>3360
[8,4,1,5,2,6,3,7]=>[4,3,1]=>3360
[6,3,5,8,2,1,4,7]=>[3,3,2]=>1120
[2,3,4,1,8,6,5,7]=>[4,3,1]=>3360
[8,3,5,6,2,1,4,7]=>[5,3]=>2688
[2,3,8,5,1,4,7,6]=>[7,1]=>5760
[2,3,8,6,1,5,7,4]=>[7,1]=>5760
[2,8,6,7,1,3,5,4]=>[6,2]=>3360
[8,3,5,7,2,1,6,4]=>[5,3]=>2688
[2,3,8,5,6,1,7,4]=>[7,1]=>5760
[7,4,5,6,3,1,8,2]=>[6,2]=>3360
[8,4,5,6,3,1,7,2]=>[5,2,1]=>4032
[7,3,5,6,2,8,1,4]=>[3,3,2]=>1120
[7,3,5,8,2,1,6,4]=>[3,3,2]=>1120
[7,3,5,6,2,1,4,8]=>[4,3,1]=>3360
[2,7,6,5,1,3,4,8]=>[5,2,1]=>4032
[2,7,6,8,1,3,5,4]=>[4,2,2]=>1260
[2,7,6,5,8,3,1,4]=>[3,3,2]=>1120
[8,7,5,6,1,4,2,3]=>[4,2,2]=>1260
[2,6,4,1,8,5,7,3]=>[7,1]=>5760
[2,6,1,3,8,5,7,4]=>[7,1]=>5760
[2,7,1,3,6,5,8,4]=>[6,2]=>3360
[2,7,6,8,4,3,1,5]=>[3,3,2]=>1120
[2,7,6,1,8,3,4,5]=>[4,2,2]=>1260
[2,7,6,1,4,3,5,8]=>[5,2,1]=>4032
[7,3,5,1,2,8,4,6]=>[3,3,2]=>1120
[8,4,1,5,2,3,7,6]=>[4,3,1]=>3360
[7,8,1,6,3,4,2,5]=>[6,2]=>3360
[6,4,1,8,3,2,7,5]=>[7,1]=>5760
[2,3,8,6,4,1,7,5]=>[7,1]=>5760
[2,8,6,7,4,3,1,5]=>[6,2]=>3360
[8,3,5,7,2,4,1,6]=>[5,3]=>2688
[2,3,4,1,8,7,5,6]=>[4,4]=>1260
[2,8,6,1,7,3,4,5]=>[6,2]=>3360
[2,3,8,1,6,4,7,5]=>[7,1]=>5760
[2,3,8,1,4,5,7,6]=>[7,1]=>5760
[2,8,6,1,4,3,5,7]=>[6,2]=>3360
[1,2,3,4,5,6,7,9,8]=>[2,1,1,1,1,1,1,1]=>36
[2,1,3,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]=>36
[1,2,3,4,5,6,7,8,10,9]=>[2,1,1,1,1,1,1,1,1]=>45
[2,1,3,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]=>45
[1,2,3,4,5,6,7,8,9,11,10]=>[2,1,1,1,1,1,1,1,1,1]=>55
[9,1,2,3,4,5,6,7,10,8]=>[10]=>362880
[1,8,2,3,4,5,6,9,7]=>[8,1]=>45360
[7,1,2,3,4,5,6,9,8]=>[7,2]=>25920
[2,1,9,3,4,5,6,7,8]=>[7,2]=>25920
[2,8,1,3,4,5,6,7,9]=>[8,1]=>45360
[2,10,1,3,4,5,6,7,8,9]=>[10]=>362880
[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,1,1,1,1,1,1,1,1]=>55
[8,4,3,6,5,1,7,2]=>[5,1,1,1]=>1344
[8,5,6,3,4,1,7,2]=>[7,1]=>5760
[8,6,5,4,3,1,7,2]=>[4,2,1,1]=>2520
[1,7,6,5,4,2,3,8]=>[4,2,1,1]=>2520
[1,8,6,5,2,7,3,4]=>[4,3,1]=>3360
[8,7,5,4,1,6,3,2]=>[6,1,1]=>3360
[7,8,5,4,1,3,6,2]=>[5,2,1]=>4032
[6,8,5,4,2,1,7,3]=>[4,2,1,1]=>2520
[5,8,6,2,4,1,7,3]=>[7,1]=>5760
[4,8,2,6,5,1,7,3]=>[3,3,1,1]=>1120
[3,2,8,6,5,1,7,4]=>[5,1,1,1]=>1344
[3,2,1,7,6,4,5,8]=>[4,2,1,1]=>2520
[4,1,3,7,6,2,5,8]=>[6,1,1]=>3360
[5,1,7,3,6,2,4,8]=>[4,3,1]=>3360
[6,1,7,5,3,2,4,8]=>[4,3,1]=>3360
[7,1,6,5,2,4,3,8]=>[7,1]=>5760
[8,1,6,5,2,3,7,4]=>[5,2,1]=>4032
[1,2,7,6,3,4,5,8]=>[3,2,1,1,1]=>1120
[1,2,8,3,7,4,5,6]=>[4,2,1,1]=>2520
[8,1,7,2,6,3,5,4]=>[4,4]=>1260
[7,1,8,2,6,4,3,5]=>[8]=>5040
[6,1,8,2,4,7,3,5]=>[8]=>5040
[5,1,8,3,2,7,4,6]=>[5,3]=>2688
[4,1,3,8,2,7,5,6]=>[7,1]=>5760
[3,2,1,8,4,7,5,6]=>[5,2,1]=>4032
[3,2,8,7,1,6,5,4]=>[6,1,1]=>3360
[4,8,2,7,1,6,5,3]=>[4,3,1]=>3360
[5,8,7,2,1,6,4,3]=>[5,2,1]=>4032
[6,8,7,1,3,5,4,2]=>[6,2]=>3360
[7,8,6,1,5,3,4,2]=>[3,2,2,1]=>1680
[8,7,6,1,5,4,3,2]=>[7,1]=>5760
[1,8,7,2,6,5,3,4]=>[3,2,2,1]=>1680
[1,7,8,2,5,6,3,4]=>[5,1,1,1]=>1344
[8,6,7,1,4,5,3,2]=>[6,2]=>3360
[7,6,8,1,4,3,5,2]=>[4,4]=>1260
[6,5,8,3,2,1,7,4]=>[3,2,2,1]=>1680
[7,5,8,3,1,4,6,2]=>[8]=>5040
[8,5,7,3,1,6,4,2]=>[4,3,1]=>3360
[1,6,8,4,2,7,3,5]=>[6,1,1]=>3360
[1,5,4,8,2,7,3,6]=>[5,2,1]=>4032
[8,4,3,7,1,6,5,2]=>[6,1,1]=>3360
[7,4,3,8,1,5,6,2]=>[4,3,1]=>3360
[6,4,3,1,5,2,7,8]=>[4,1,1,1,1]=>420
[7,4,3,1,2,6,5,8]=>[5,1,1,1]=>1344
[8,4,3,1,2,5,7,6]=>[6,1,1]=>3360
[1,5,4,2,3,6,7,8]=>[4,1,1,1,1]=>420
[8,5,1,4,2,3,7,6]=>[4,2,1,1]=>2520
[7,5,1,4,2,6,3,8]=>[3,2,1,1,1]=>1120
[6,5,1,4,3,2,7,8]=>[5,1,1,1]=>1344
[5,6,1,3,4,2,7,8]=>[4,2,1,1]=>2520
[4,6,2,1,5,3,7,8]=>[3,2,1,1,1]=>1120
[3,2,6,1,5,4,7,8]=>[4,1,1,1,1]=>420
[3,2,7,1,4,6,5,8]=>[5,1,1,1]=>1344
[4,7,2,1,3,6,5,8]=>[4,2,1,1]=>2520
[5,7,1,3,2,6,4,8]=>[6,1,1]=>3360
[6,7,1,2,4,5,3,8]=>[7,1]=>5760
[7,6,1,2,5,4,3,8]=>[3,3,1,1]=>1120
[8,6,1,2,5,3,7,4]=>[6,1,1]=>3360
[1,7,2,3,6,4,5,8]=>[6,1,1]=>3360
[8,7,1,2,3,6,5,4]=>[7,1]=>5760
[7,8,1,2,3,5,6,4]=>[5,3]=>2688
[6,8,1,2,4,3,7,5]=>[4,3,1]=>3360
[5,8,1,3,2,4,7,6]=>[7,1]=>5760
[4,8,2,1,3,5,7,6]=>[5,2,1]=>4032
[3,2,8,1,4,5,7,6]=>[6,1,1]=>3360
[4,1,3,2,5,6,7,8]=>[3,1,1,1,1,1]=>112
[5,1,2,4,3,6,7,8]=>[4,1,1,1,1]=>420
[6,1,2,3,5,4,7,8]=>[5,1,1,1]=>1344
[7,1,2,3,4,6,5,8]=>[6,1,1]=>3360
[8,1,2,3,4,5,7,6]=>[7,1]=>5760
[6,7,3,8,5,1,2,4]=>[2,2,2,1,1]=>420
[6,7,4,5,1,8,3,2]=>[8]=>5040
[4,5,6,7,1,8,3,2]=>[8]=>5040
[3,5,6,2,7,4,8,1]=>[8]=>5040
[2,5,6,8,1,7,3,4]=>[3,3,2]=>1120
[8,2,4,5,1,6,3,7]=>[6,1,1]=>3360
[1,4,8,6,2,3,7,5]=>[6,1,1]=>3360
[1,5,6,8,2,3,7,4]=>[2,2,2,1,1]=>420
[8,1,3,2,5,4,6,7]=>[6,1,1]=>3360
[8,2,3,1,5,6,4,7]=>[4,1,1,1,1]=>420
[4,3,1,7,6,8,5,2]=>[8]=>5040
[5,2,7,8,1,6,3,4]=>[2,2,2,1,1]=>420
[5,3,7,2,6,4,8,1]=>[8]=>5040
[6,7,3,1,5,8,4,2]=>[6,1,1]=>3360
[6,7,2,8,1,5,3,4]=>[3,3,2]=>1120
[6,7,8,2,1,4,3,5]=>[8]=>5040
[5,1,7,3,4,8,6,2]=>[8]=>5040
[4,1,8,7,2,3,6,5]=>[8]=>5040
[3,8,1,2,7,4,5,6]=>[4,2,2]=>1260
[3,1,4,5,7,8,6,2]=>[8]=>5040
[2,1,8,3,4,7,6,5]=>[4,2,2]=>1260
[8,2,1,3,4,6,5,7]=>[6,1,1]=>3360
[1,8,2,3,4,5,7,6]=>[6,1,1]=>3360
[1,2,8,3,4,6,7,5]=>[4,1,1,1,1]=>420
[4,2,1,6,5,8,7,3]=>[5,1,1,1]=>1344
[5,2,6,1,4,8,7,3]=>[3,3,1,1]=>1120
[5,2,7,4,8,1,6,3]=>[6,1,1]=>3360
[5,2,7,4,8,6,1,3]=>[5,1,1,1]=>1344
[5,7,2,3,8,1,6,4]=>[8]=>5040
[5,6,2,1,3,8,7,4]=>[7,1]=>5760
[5,1,6,4,2,8,7,3]=>[3,3,1,1]=>1120
[5,6,1,3,2,8,7,4]=>[7,1]=>5760
[5,7,3,2,8,1,6,4]=>[7,1]=>5760
[5,7,3,1,8,2,6,4]=>[4,3,1]=>3360
[5,7,1,3,8,2,6,4]=>[5,3]=>2688
[1,5,7,4,8,3,6,2]=>[3,3,1,1]=>1120
[1,5,7,4,8,6,3,2]=>[3,2,1,1,1]=>1120
[5,1,7,4,8,6,2,3]=>[6,1,1]=>3360
[5,7,1,3,8,6,2,4]=>[5,2,1]=>4032
[5,7,3,1,8,6,2,4]=>[4,2,1,1]=>2520
[6,7,3,8,1,5,2,4]=>[3,2,2,1]=>1680
[6,7,3,8,5,2,1,4]=>[4,2,1,1]=>2520
[6,7,8,3,1,4,2,5]=>[6,2]=>3360
[1,6,7,8,4,5,3,2]=>[5,2,1]=>4032
[1,6,7,8,4,3,5,2]=>[7,1]=>5760
[6,7,1,8,3,2,5,4]=>[6,2]=>3360
[5,7,2,1,8,3,6,4]=>[4,4]=>1260
[6,7,2,8,3,1,5,4]=>[4,2,2]=>1260
[6,2,7,8,4,5,1,3]=>[7,1]=>5760
[6,2,7,8,4,1,5,3]=>[5,2,1]=>4032
[5,2,7,1,8,4,6,3]=>[7,1]=>5760
[4,2,1,7,8,5,6,3]=>[7,1]=>5760
[4,1,2,7,8,6,5,3]=>[7,1]=>5760
[6,2,7,8,1,5,4,3]=>[4,3,1]=>3360
[6,2,7,8,5,4,1,3]=>[6,1,1]=>3360
[6,7,2,8,5,3,1,4]=>[5,2,1]=>4032
[5,7,2,1,8,6,3,4]=>[4,3,1]=>3360
[5,7,1,2,8,6,3,4]=>[7,1]=>5760
[5,1,7,2,8,6,4,3]=>[7,1]=>5760
[1,5,7,3,8,6,4,2]=>[3,3,1,1]=>1120
[6,7,1,8,2,5,3,4]=>[6,2]=>3360
[6,7,8,2,4,1,3,5]=>[6,2]=>3360
[6,7,1,8,5,2,3,4]=>[5,2,1]=>4032
[1,6,7,8,5,3,4,2]=>[6,1,1]=>3360
[6,3,8,5,2,7,4,1]=>[8]=>5040
[6,5,2,8,4,7,3,1]=>[8]=>5040
[6,3,4,5,8,7,2,1]=>[8]=>5040
[5,6,1,4,8,7,3,2]=>[7,1]=>5760
[5,1,4,8,6,3,7,2]=>[7,1]=>5760
[3,4,7,1,8,6,5,2]=>[7,1]=>5760
[6,3,8,4,2,7,1,5]=>[4,3,1]=>3360
[3,6,8,7,1,4,2,5]=>[4,4]=>1260
[4,3,8,5,6,7,2,1]=>[8]=>5040
[4,6,1,2,7,8,5,3]=>[6,2]=>3360
[3,6,4,2,8,7,5,1]=>[8]=>5040
[6,3,7,5,2,8,1,4]=>[8]=>5040
[6,5,2,7,4,8,1,3]=>[8]=>5040
[5,7,1,4,8,3,2,6]=>[5,2,1]=>4032
[7,8,3,5,1,4,6,2]=>[5,2,1]=>4032
[5,8,1,4,6,7,2,3]=>[7,1]=>5760
[6,5,8,4,3,7,2,1]=>[7,1]=>5760
[6,3,7,4,2,8,5,1]=>[4,3,1]=>3360
[8,7,1,6,2,4,5,3]=>[3,3,2]=>1120
[3,8,6,7,1,4,5,2]=>[6,2]=>3360
[5,3,8,7,4,1,2,6]=>[8]=>5040
[4,3,8,7,1,5,6,2]=>[5,3]=>2688
[8,3,6,1,2,5,7,4]=>[4,3,1]=>3360
[5,6,1,8,7,3,2,4]=>[6,2]=>3360
[5,4,2,7,3,6,8,1]=>[7,1]=>5760
[7,5,3,6,4,2,8,1]=>[4,3,1]=>3360
[6,4,1,5,3,8,2,7]=>[8]=>5040
[8,2,6,3,4,7,5,1]=>[5,2,1]=>4032
[7,2,6,3,5,4,8,1]=>[3,3,1,1]=>1120
[6,2,7,4,3,5,8,1]=>[6,1,1]=>3360
[3,7,6,4,5,2,8,1]=>[6,1,1]=>3360
[2,7,6,5,3,4,8,1]=>[4,4]=>1260
[6,5,4,3,1,8,2,7]=>[6,2]=>3360
[8,6,5,4,2,7,3,1]=>[5,2,1]=>4032
[8,5,4,1,7,2,6,3]=>[4,4]=>1260
[7,5,4,1,8,3,2,6]=>[8]=>5040
[1,6,5,2,8,3,4,7]=>[7,1]=>5760
[1,6,5,3,4,8,2,7]=>[4,3,1]=>3360
[5,4,6,3,1,8,2,7]=>[6,2]=>3360
[6,5,8,4,2,7,3,1]=>[5,2,1]=>4032
[5,8,2,6,4,7,3,1]=>[8]=>5040
[7,8,5,3,2,6,4,1]=>[7,1]=>5760
[6,8,3,1,7,2,5,4]=>[5,2,1]=>4032
[1,8,6,3,7,5,2,4]=>[7,1]=>5760
[8,7,5,2,6,4,3,1]=>[6,2]=>3360
[8,7,1,6,2,5,4,3]=>[5,3]=>2688
[2,8,1,7,3,5,6,4]=>[8]=>5040
[4,8,1,3,7,2,6,5]=>[5,3]=>2688
[4,2,8,5,7,3,6,1]=>[7,1]=>5760
[5,1,7,6,8,3,2,4]=>[8]=>5040
[6,7,3,1,8,4,2,5]=>[3,2,2,1]=>1680
[1,7,3,8,4,5,2,6]=>[4,2,1,1]=>2520
[1,7,2,8,5,3,4,6]=>[6,1,1]=>3360
[7,6,1,8,4,3,2,5]=>[5,3]=>2688
[8,6,1,7,4,2,5,3]=>[3,3,2]=>1120
[8,1,2,7,3,4,6,5]=>[5,3]=>2688
[7,1,2,8,3,5,4,6]=>[8]=>5040
[8,2,6,1,7,3,5,4]=>[3,2,2,1]=>1680
[4,2,1,5,8,3,6,7]=>[7,1]=>5760
[5,4,3,1,6,8,2,7]=>[7,1]=>5760
[4,7,5,6,8,3,2,1]=>[6,2]=>3360
[6,5,4,8,2,7,3,1]=>[6,2]=>3360
[6,5,1,8,7,4,2,3]=>[5,3]=>2688
[8,6,4,7,5,3,2,1]=>[5,2,1]=>4032
[5,1,8,3,7,6,2,4]=>[4,3,1]=>3360
[5,4,8,1,7,2,6,3]=>[6,2]=>3360
[3,6,8,2,4,7,5,1]=>[5,3]=>2688
[5,7,3,8,2,6,4,1]=>[6,1,1]=>3360
[4,7,2,8,6,3,5,1]=>[5,3]=>2688
[2,3,8,7,4,5,6,1]=>[4,4]=>1260
[7,2,8,6,4,3,5,1]=>[7,1]=>5760
[2,1,8,7,5,6,3,4]=>[4,2,1,1]=>2520
[8,2,7,6,3,5,4,1]=>[5,2,1]=>4032
[8,1,7,6,5,2,4,3]=>[7,1]=>5760
[7,1,8,6,5,3,2,4]=>[4,3,1]=>3360
[1,2,8,7,6,3,4,5]=>[4,2,1,1]=>2520
[1,3,8,7,4,6,2,5]=>[6,1,1]=>3360
[5,1,6,8,7,4,2,3]=>[4,4]=>1260
[6,8,7,2,5,4,3,1]=>[5,2,1]=>4032
[3,8,7,6,4,5,2,1]=>[5,3]=>2688
[2,8,7,6,5,3,4,1]=>[4,3,1]=>3360
[1,8,7,6,5,4,2,3]=>[4,2,1,1]=>2520
[5,8,6,7,3,4,1,2]=>[6,2]=>3360
[4,8,6,7,3,5,1,2]=>[3,3,2]=>1120
[3,8,6,7,4,5,1,2]=>[6,2]=>3360
[2,8,6,7,4,5,1,3]=>[8]=>5040
[1,8,6,7,4,5,2,3]=>[7,1]=>5760
[1,8,5,7,4,6,2,3]=>[6,1,1]=>3360
[3,8,5,7,4,6,1,2]=>[5,2,1]=>4032
[4,8,5,7,3,6,1,2]=>[3,2,2,1]=>1680
[7,8,3,6,4,5,1,2]=>[3,2,2,1]=>1680
[6,8,3,7,4,5,1,2]=>[5,2,1]=>4032
[5,8,3,7,4,6,1,2]=>[4,2,1,1]=>2520
[4,7,3,8,5,6,1,2]=>[5,1,1,1]=>1344
[4,7,1,8,5,6,2,3]=>[4,2,1,1]=>2520
[3,7,1,8,5,6,2,4]=>[2,2,2,1,1]=>420
[3,7,2,8,5,6,1,4]=>[4,2,1,1]=>2520
[2,7,3,8,5,6,1,4]=>[3,2,1,1,1]=>1120
[2,7,4,8,5,6,1,3]=>[3,3,1,1]=>1120
[5,8,2,7,4,6,1,3]=>[4,3,1]=>3360
[6,8,2,7,4,5,1,3]=>[5,3]=>2688
[7,8,2,6,4,5,1,3]=>[3,3,2]=>1120
[7,8,1,6,4,5,2,3]=>[5,3]=>2688
[6,8,1,7,4,5,2,3]=>[8]=>5040
[5,8,1,7,4,6,2,3]=>[7,1]=>5760
[1,7,4,8,5,6,2,3]=>[3,2,1,1,1]=>1120
[1,7,3,8,5,6,2,4]=>[2,2,1,1,1,1]=>210
[1,8,5,6,2,7,3,4]=>[7,1]=>5760
[1,7,3,8,4,6,2,5]=>[3,2,1,1,1]=>1120
[4,8,1,7,3,6,2,5]=>[7,1]=>5760
[5,8,1,7,3,6,2,4]=>[4,3,1]=>3360
[6,8,1,7,3,5,2,4]=>[4,4]=>1260
[7,8,2,6,3,5,1,4]=>[6,2]=>3360
[6,8,2,7,3,5,1,4]=>[8]=>5040
[5,8,2,7,3,6,1,4]=>[7,1]=>5760
[4,8,2,7,3,6,1,5]=>[4,3,1]=>3360
[2,7,3,8,4,6,1,5]=>[3,3,1,1]=>1120
[1,8,4,7,3,6,2,5]=>[6,1,1]=>3360
[2,8,4,7,3,6,1,5]=>[7,1]=>5760
[3,8,4,7,2,6,1,5]=>[4,3,1]=>3360
[4,8,5,7,2,6,1,3]=>[4,3,1]=>3360
[3,8,5,7,2,6,1,4]=>[7,1]=>5760
[2,8,5,7,3,6,1,4]=>[5,2,1]=>4032
[1,8,5,7,3,6,2,4]=>[4,2,1,1]=>2520
[1,8,6,7,3,5,2,4]=>[4,3,1]=>3360
[2,8,6,7,3,5,1,4]=>[5,3]=>2688
[3,8,6,7,2,5,1,4]=>[8]=>5040
[4,8,6,7,2,5,1,3]=>[5,3]=>2688
[5,8,6,7,2,4,1,3]=>[8]=>5040
[6,8,5,7,1,4,2,3]=>[8]=>5040
[5,8,6,7,1,4,2,3]=>[6,2]=>3360
[4,8,6,7,1,5,2,3]=>[8]=>5040
[3,8,6,7,1,5,2,4]=>[4,4]=>1260
[1,5,2,8,6,7,3,4]=>[5,2,1]=>4032
[2,5,1,8,6,7,3,4]=>[6,2]=>3360
[2,6,1,8,5,7,3,4]=>[5,2,1]=>4032
[1,6,2,8,5,7,3,4]=>[4,2,1,1]=>2520
[3,8,5,7,1,6,2,4]=>[4,3,1]=>3360
[6,8,4,7,1,5,2,3]=>[5,3]=>2688
[7,8,4,6,1,5,2,3]=>[8]=>5040
[7,8,3,6,1,5,2,4]=>[7,1]=>5760
[6,8,3,7,1,5,2,4]=>[4,3,1]=>3360
[4,8,3,7,1,6,2,5]=>[6,1,1]=>3360
[3,8,4,7,1,6,2,5]=>[7,1]=>5760
[1,6,2,8,4,7,3,5]=>[4,3,1]=>3360
[2,6,1,8,4,7,3,5]=>[5,3]=>2688
[3,7,1,6,2,8,4,5]=>[6,2]=>3360
[4,8,1,6,2,7,3,5]=>[5,3]=>2688
[5,8,1,6,2,7,3,4]=>[8]=>5040
[7,8,1,5,2,6,3,4]=>[4,3,1]=>3360
[7,8,2,5,1,6,3,4]=>[7,1]=>5760
[6,8,2,5,1,7,3,4]=>[8]=>5040
[5,8,2,6,1,7,3,4]=>[6,2]=>3360
[4,8,2,6,1,7,3,5]=>[8]=>5040
[1,7,3,6,2,8,4,5]=>[6,1,1]=>3360
[1,2,3,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,2,3,4,5,6,8,9,7]=>[3,1,1,1,1,1,1]=>168
[1,2,3,4,5,7,8,9,6]=>[4,1,1,1,1,1]=>756
[1,2,3,4,6,7,8,9,5]=>[5,1,1,1,1]=>3024
[1,2,3,5,6,7,8,9,4]=>[6,1,1,1]=>10080
[1,2,4,5,6,7,8,9,3]=>[7,1,1]=>25920
[1,3,4,5,6,7,8,9,2]=>[8,1]=>45360
[1,2,3,4,5,6,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,2,3,4,5,6,9,8,7]=>[2,1,1,1,1,1,1,1]=>36
[1,2,3,4,5,6,7,9,10,8]=>[3,1,1,1,1,1,1,1]=>240
[1,2,3,4,5,8,7,9,6]=>[3,1,1,1,1,1,1]=>168
[1,2,3,4,5,6,8,9,10,7]=>[4,1,1,1,1,1,1]=>1260
[1,2,3,4,7,6,8,9,5]=>[4,1,1,1,1,1]=>756
[1,2,3,4,5,7,8,9,10,6]=>[5,1,1,1,1,1]=>6048
[1,2,3,6,5,7,8,9,4]=>[5,1,1,1,1]=>3024
[1,2,3,4,6,7,8,9,10,5]=>[6,1,1,1,1]=>25200
[1,2,5,4,6,7,8,9,3]=>[6,1,1,1]=>10080
[1,2,3,5,6,7,8,9,10,4]=>[7,1,1,1]=>86400
[1,4,3,5,6,7,8,9,2]=>[7,1,1]=>25920
[1,2,4,5,6,7,8,9,10,3]=>[8,1,1]=>226800
[3,2,4,5,6,7,8,9,1]=>[8,1]=>45360
[1,3,4,5,6,7,8,9,10,2]=>[9,1]=>403200
[6,7,4,8,3,5,1,2]=>[8]=>5040
[6,7,4,5,2,8,1,3]=>[8]=>5040
[5,7,4,6,2,3,1,8]=>[4,3,1]=>3360
[5,7,4,6,3,8,1,2]=>[8]=>5040
[5,7,4,8,3,6,1,2]=>[7,1]=>5760
[6,8,4,5,3,7,1,2]=>[3,3,2]=>1120
[5,8,4,6,3,7,1,2]=>[6,2]=>3360
[5,6,4,8,3,7,1,2]=>[8]=>5040
[5,6,3,7,2,4,1,8]=>[6,1,1]=>3360
[5,6,3,7,2,8,1,4]=>[7,1]=>5760
[5,6,3,8,2,7,1,4]=>[5,2,1]=>4032
[5,6,4,8,2,7,1,3]=>[5,3]=>2688
[5,8,4,6,2,7,1,3]=>[8]=>5040
[6,8,4,5,2,7,1,3]=>[5,3]=>2688
[7,8,4,5,2,6,1,3]=>[5,2,1]=>4032
[6,8,4,5,2,3,1,7]=>[8]=>5040
[5,8,4,6,2,3,1,7]=>[5,3]=>2688
[5,6,4,8,2,3,1,7]=>[8]=>5040
[5,6,3,8,2,4,1,7]=>[7,1]=>5760
[5,6,3,4,2,8,1,7]=>[6,1,1]=>3360
[4,6,3,5,2,7,1,8]=>[6,1,1]=>3360
[4,6,3,5,2,8,1,7]=>[7,1]=>5760
[4,6,3,8,2,5,1,7]=>[4,3,1]=>3360
[4,8,3,6,2,5,1,7]=>[7,1]=>5760
[5,8,3,6,2,4,1,7]=>[5,2,1]=>4032
[6,8,3,5,2,4,1,7]=>[7,1]=>5760
[7,8,3,5,2,4,1,6]=>[5,2,1]=>4032
[7,8,3,5,2,6,1,4]=>[4,2,1,1]=>2520
[5,8,3,6,2,7,1,4]=>[7,1]=>5760
[4,8,3,6,2,7,1,5]=>[4,3,1]=>3360
[4,6,3,8,2,7,1,5]=>[7,1]=>5760
[4,6,3,7,2,8,1,5]=>[4,3,1]=>3360
[4,7,3,6,2,5,1,8]=>[6,1,1]=>3360
[4,7,3,6,2,8,1,5]=>[7,1]=>5760
[4,7,3,8,2,6,1,5]=>[6,1,1]=>3360
[5,7,4,8,2,6,1,3]=>[4,3,1]=>3360
[5,7,3,6,2,8,1,4]=>[4,3,1]=>3360
[5,7,3,6,2,4,1,8]=>[4,2,1,1]=>2520
[6,7,3,5,2,4,1,8]=>[6,1,1]=>3360
[6,7,3,5,2,8,1,4]=>[7,1]=>5760
[6,7,4,8,2,5,1,3]=>[5,3]=>2688
[6,7,5,8,2,4,1,3]=>[8]=>5040
[6,8,5,7,2,3,1,4]=>[8]=>5040
[6,7,4,8,2,3,1,5]=>[8]=>5040
[6,7,3,8,2,4,1,5]=>[7,1]=>5760
[6,7,3,4,2,8,1,5]=>[6,1,1]=>3360
[5,7,3,4,2,6,1,8]=>[4,1,1,1,1]=>420
[5,7,3,4,2,8,1,6]=>[4,2,1,1]=>2520
[5,7,4,8,2,3,1,6]=>[4,4]=>1260
[5,8,4,7,2,3,1,6]=>[8]=>5040
[6,8,4,7,2,3,1,5]=>[5,3]=>2688
[7,8,4,6,2,3,1,5]=>[3,3,2]=>1120
[7,8,3,6,2,4,1,5]=>[3,2,2,1]=>1680
[6,8,3,7,2,4,1,5]=>[4,3,1]=>3360
[5,8,3,7,2,4,1,6]=>[7,1]=>5760
[4,8,3,7,2,5,1,6]=>[4,3,1]=>3360
[4,7,3,8,2,5,1,6]=>[7,1]=>5760
[4,7,3,5,2,8,1,6]=>[5,2,1]=>4032
[4,7,3,5,2,6,1,8]=>[5,1,1,1]=>1344
[4,5,3,7,2,6,1,8]=>[3,2,1,1,1]=>1120
[4,5,3,7,2,8,1,6]=>[3,2,2,1]=>1680
[4,5,3,8,2,7,1,6]=>[5,2,1]=>4032
[4,8,3,5,2,7,1,6]=>[7,1]=>5760
[5,8,3,4,2,7,1,6]=>[6,1,1]=>3360
[6,8,3,4,2,7,1,5]=>[3,3,1,1]=>1120
[7,8,3,4,2,6,1,5]=>[3,2,1,1,1]=>1120
[6,8,3,4,2,5,1,7]=>[6,1,1]=>3360
[5,8,3,4,2,6,1,7]=>[5,1,1,1]=>1344
[4,8,3,5,2,6,1,7]=>[6,1,1]=>3360
[4,5,3,8,2,6,1,7]=>[4,2,1,1]=>2520
[4,5,3,6,2,8,1,7]=>[5,2,1]=>4032
[4,7,5,2,1,8,3,6]=>[6,2]=>3360
[4,8,5,2,1,7,6,3]=>[6,2]=>3360
[4,6,5,2,1,3,8,7]=>[6,2]=>3360
[5,6,4,2,3,1,8,7]=>[6,2]=>3360
[6,4,5,3,1,2,8,7]=>[6,2]=>3360
[5,4,6,1,3,2,8,7]=>[6,2]=>3360
[4,6,8,1,7,3,2,5]=>[6,2]=>3360
[4,7,8,1,6,3,5,2]=>[6,2]=>3360
[7,4,8,1,6,5,3,2]=>[6,2]=>3360
[5,4,8,1,3,7,6,2]=>[6,2]=>3360
[8,4,5,3,1,7,6,2]=>[6,2]=>3360
[5,4,7,1,3,8,2,6]=>[6,2]=>3360
[6,4,8,1,7,5,2,3]=>[6,2]=>3360
[5,6,8,7,2,1,3,4]=>[4,4]=>1260
[8,5,7,6,4,2,1,3]=>[4,4]=>1260
[8,4,6,3,7,2,1,5]=>[4,4]=>1260
[6,3,2,8,7,4,1,5]=>[6,2]=>3360
[2,1,6,8,7,4,3,5]=>[6,2]=>3360
[2,1,7,8,6,4,5,3]=>[6,2]=>3360
[7,3,2,8,6,4,5,1]=>[6,2]=>3360
[7,6,8,5,2,4,3,1]=>[4,4]=>1260
[5,7,8,6,2,3,1,4]=>[4,4]=>1260
[5,8,7,6,3,2,1,4]=>[4,4]=>1260
[6,8,7,5,3,2,4,1]=>[4,4]=>1260
[5,8,4,2,3,7,6,1]=>[6,2]=>3360
[7,8,4,2,6,5,3,1]=>[6,2]=>3360
[4,8,7,2,6,3,5,1]=>[4,4]=>1260
[4,8,6,2,7,3,1,5]=>[6,2]=>3360
[3,6,1,8,7,4,2,5]=>[6,2]=>3360
[3,7,1,8,6,4,5,2]=>[6,2]=>3360
[3,8,1,6,7,5,2,4]=>[6,2]=>3360
[3,7,1,6,8,2,5,4]=>[6,2]=>3360
[4,7,6,2,8,1,3,5]=>[6,2]=>3360
[6,7,4,2,8,1,5,3]=>[6,2]=>3360
[6,8,4,2,7,5,1,3]=>[4,4]=>1260
[2,1,8,6,7,5,3,4]=>[6,2]=>3360
[8,3,2,6,7,5,1,4]=>[6,2]=>3360
[8,6,4,3,7,5,1,2]=>[6,2]=>3360
[5,8,6,7,3,1,2,4]=>[4,4]=>1260
[6,7,5,8,1,3,4,2]=>[4,4]=>1260
[7,6,5,8,1,4,3,2]=>[4,4]=>1260
[8,6,5,7,4,1,3,2]=>[4,4]=>1260
[7,6,4,3,8,1,5,2]=>[6,2]=>3360
[7,3,2,6,8,1,5,4]=>[6,2]=>3360
[2,1,7,6,8,3,5,4]=>[6,2]=>3360
[7,5,6,8,1,4,2,3]=>[4,4]=>1260
[6,5,7,8,1,2,4,3]=>[4,4]=>1260
[8,1,3,7,4,6,5,2]=>[3,3,1,1]=>1120
[5,2,8,7,4,6,1,3]=>[4,2,1,1]=>2520
[1,6,2,5,4,7,3,8]=>[4,2,1,1]=>2520
[6,2,7,5,4,8,3,1]=>[3,2,2,1]=>1680
[8,1,3,5,4,7,6,2]=>[3,2,2,1]=>1680
[6,1,5,4,3,8,7,2]=>[4,2,1,1]=>2520
[6,1,8,3,4,5,7,2]=>[7,1]=>5760
[7,1,5,3,4,8,6,2]=>[5,3]=>2688
[7,1,4,3,5,6,8,2]=>[4,2,1,1]=>2520
[8,1,3,4,5,6,7,2]=>[3,1,1,1,1,1]=>112
[1,7,2,4,5,6,3,8]=>[3,1,1,1,1,1]=>112
[6,3,2,7,5,1,8,4]=>[3,2,2,1]=>1680
[8,4,7,2,5,6,1,3]=>[4,2,1,1]=>2520
[6,5,8,2,4,7,3,1]=>[5,3]=>2688
[8,5,2,1,4,3,7,6]=>[7,1]=>5760
[6,5,2,8,4,1,3,7]=>[6,2]=>3360
[5,6,2,1,4,8,3,7]=>[5,3]=>2688
[3,6,1,8,5,2,4,7]=>[3,2,2,1]=>1680
[1,2,6,3,5,4,7,8]=>[3,1,1,1,1,1]=>112
[3,4,1,2,8,6,5,7]=>[3,2,2,1]=>1680
[4,3,1,2,6,8,5,7]=>[4,4]=>1260
[5,8,1,6,3,2,4,7]=>[5,3]=>2688
[6,3,8,5,2,1,4,7]=>[6,2]=>3360
[8,3,1,5,2,4,7,6]=>[7,1]=>5760
[3,8,2,6,1,5,7,4]=>[7,1]=>5760
[3,8,6,7,2,1,5,4]=>[5,3]=>2688
[8,5,6,4,2,1,7,3]=>[4,2,1,1]=>2520
[7,2,5,8,3,1,6,4]=>[3,2,2,1]=>1680
[1,7,5,6,3,2,4,8]=>[4,2,1,1]=>2520
[6,1,2,3,8,5,7,4]=>[7,1]=>5760
[7,1,2,3,6,5,8,4]=>[6,2]=>3360
[7,2,1,3,8,6,4,5]=>[4,2,1,1]=>2520
[1,5,7,3,2,4,6,8]=>[4,2,1,1]=>2520
[5,2,7,3,1,8,4,6]=>[3,2,2,1]=>1680
[5,8,2,4,1,3,7,6]=>[4,2,1,1]=>2520
[8,7,2,6,3,4,1,5]=>[6,2]=>3360
[4,8,1,6,3,2,7,5]=>[7,1]=>5760
[3,1,8,6,4,2,7,5]=>[7,1]=>5760
[8,1,6,7,4,3,2,5]=>[6,2]=>3360
[3,5,8,7,2,4,1,6]=>[6,2]=>3360
[4,2,1,3,7,8,5,6]=>[3,2,2,1]=>1680
[2,4,1,3,8,7,5,6]=>[4,4]=>1260
[2,5,8,3,1,7,4,6]=>[5,3]=>2688
[8,6,1,3,7,2,4,5]=>[6,2]=>3360
[2,8,1,3,6,4,7,5]=>[7,1]=>5760
[6,8,2,3,4,1,5,7]=>[6,2]=>3360
[5,1,8,3,2,4,6,7]=>[5,3]=>2688
[9,8,7,6,5,4,3,2,1]=>[2,2,2,2,1]=>945
[8,9,7,6,5,4,3,2,1]=>[4,2,2,1]=>11340
[8,7,9,6,5,4,3,2,1]=>[6,2,1]=>30240
[8,7,6,9,5,4,3,2,1]=>[8,1]=>45360
[8,7,6,5,9,4,3,2,1]=>[9]=>40320
[8,7,6,5,4,9,3,2,1]=>[7,2]=>25920
[8,7,6,5,4,3,9,2,1]=>[5,2,2]=>9072
[8,7,6,5,4,3,2,9,1]=>[3,2,2,2]=>2520
[8,7,6,5,4,3,2,1,9]=>[2,2,2,2,1]=>945
[9,10,8,7,6,5,4,3,2,1]=>[4,2,2,2]=>18900
[7,8,9,6,5,4,3,2,1]=>[4,2,2,1]=>11340
[9,8,10,7,6,5,4,3,2,1]=>[6,2,2]=>75600
[8,6,7,9,5,4,3,2,1]=>[6,2,1]=>30240
[9,8,7,10,6,5,4,3,2,1]=>[8,2]=>226800
[8,7,5,6,9,4,3,2,1]=>[7,2]=>25920
[9,8,7,6,10,5,4,3,2,1]=>[10]=>362880
[8,7,6,4,5,9,3,2,1]=>[7,1,1]=>25920
[9,8,7,6,5,10,4,3,2,1]=>[9,1]=>403200
[8,7,6,5,3,4,9,2,1]=>[5,4]=>18144
[9,8,7,6,5,4,10,3,2,1]=>[7,2,1]=>259200
[8,7,6,5,4,2,3,9,1]=>[4,3,2]=>15120
[9,8,7,6,5,4,3,10,2,1]=>[5,2,2,1]=>90720
[8,7,6,5,4,3,1,2,9]=>[4,2,2,1]=>11340
[9,8,7,6,5,4,3,2,10,1]=>[3,2,2,2,1]=>25200
[9,8,7,6,5,4,3,2,1,10]=>[2,2,2,2,1,1]=>4725
[1,4,2,7,8,6,3,5]=>[4,2,1,1]=>2520
[1,6,2,4,8,5,3,7]=>[6,1,1]=>3360
[1,6,2,4,7,5,3,8]=>[5,1,1,1]=>1344
[1,7,3,8,5,2,4,6]=>[5,1,1,1]=>1344
[1,7,3,2,8,6,4,5]=>[3,2,1,1,1]=>1120
[4,2,5,7,8,6,1,3]=>[3,3,1,1]=>1120
[7,2,3,1,8,5,6,4]=>[6,1,1]=>3360
[8,2,5,1,7,3,4,6]=>[7,1]=>5760
[6,2,1,8,3,4,7,5]=>[6,1,1]=>3360
[6,2,8,3,5,1,7,4]=>[3,2,1,1,1]=>1120
[6,2,4,8,5,7,1,3]=>[3,3,1,1]=>1120
[1,3,6,4,8,5,7,2]=>[5,1,1,1]=>1344
[1,3,6,4,7,5,8,2]=>[6,1,1]=>3360
[6,2,4,7,5,8,1,3]=>[6,1,1]=>3360
[6,2,1,3,7,8,4,5]=>[7,1]=>5760
[7,8,2,1,4,3,5,6]=>[4,4]=>1260
[7,6,4,2,3,1,8,5]=>[8]=>5040
[5,7,2,3,1,6,8,4]=>[5,2,1]=>4032
[7,5,4,2,6,8,1,3]=>[6,2]=>3360
[1,7,5,3,4,6,8,2]=>[3,3,1,1]=>1120
[8,2,5,4,6,7,1,3]=>[6,1,1]=>3360
[5,2,6,3,1,8,7,4]=>[4,2,1,1]=>2520
[8,2,6,4,3,1,7,5]=>[5,1,1,1]=>1344
[8,2,7,4,1,3,5,6]=>[6,1,1]=>3360
[1,2,8,4,3,5,6,7]=>[5,1,1,1]=>1344
[1,7,4,2,3,5,6,8]=>[6,1,1]=>3360
[6,8,4,1,3,2,5,7]=>[8]=>5040
[1,8,7,4,3,2,5,6]=>[3,3,1,1]=>1120
[1,6,3,8,2,4,7,5]=>[5,1,1,1]=>1344
[5,3,8,1,2,7,4,6]=>[8]=>5040
[5,1,8,3,2,6,4,7]=>[4,3,1]=>3360
[5,7,3,1,2,6,4,8]=>[5,1,1,1]=>1344
[1,7,5,4,2,6,3,8]=>[4,1,1,1,1]=>420
[1,5,8,2,4,6,3,7]=>[3,3,1,1]=>1120
[1,5,8,4,2,7,3,6]=>[4,2,1,1]=>2520
[1,4,6,2,8,3,7,5]=>[2,2,2,1,1]=>420
[5,3,1,6,7,2,4,8]=>[7,1]=>5760
[5,3,6,1,2,8,4,7]=>[8]=>5040
[1,6,3,2,7,8,4,5]=>[6,1,1]=>3360
[1,7,4,5,3,8,6,2]=>[4,3,1]=>3360
[6,3,4,1,2,5,8,7]=>[6,2]=>3360
[6,3,1,4,2,7,5,8]=>[6,1,1]=>3360
[1,8,3,2,4,5,6,7]=>[6,1,1]=>3360
[8,6,3,2,4,1,7,5]=>[6,1,1]=>3360
[8,5,3,2,6,7,1,4]=>[7,1]=>5760
[4,5,2,6,8,1,7,3]=>[4,3,1]=>3360
[4,2,5,6,7,8,1,3]=>[7,1]=>5760
[5,2,3,6,7,1,8,4]=>[6,1,1]=>3360
[6,2,3,4,1,7,8,5]=>[5,1,1,1]=>1344
[7,2,3,1,4,5,8,6]=>[6,1,1]=>3360
[8,6,1,4,3,2,5,7]=>[5,2,1]=>4032
[8,3,1,6,5,2,4,7]=>[7,1]=>5760
[3,7,5,1,8,2,4,6]=>[8]=>5040
[4,1,5,2,8,7,3,6]=>[5,3]=>2688
[8,1,2,4,6,5,3,7]=>[5,2,1]=>4032
[8,1,2,5,4,6,3,7]=>[5,2,1]=>4032
[8,2,6,5,1,3,4,7]=>[5,2,1]=>4032
[8,3,1,6,2,5,4,7]=>[8]=>5040
[8,1,2,6,4,5,3,7]=>[5,3]=>2688
[8,1,2,5,6,4,3,7]=>[5,3]=>2688
[8,1,2,6,5,4,3,7]=>[5,2,1]=>4032
[1,7,5,4,2,8,3,6]=>[4,2,1,1]=>2520
[5,1,4,8,2,7,3,6]=>[5,3]=>2688
[1,4,6,8,2,7,3,5]=>[4,3,1]=>3360
[1,4,7,6,2,8,3,5]=>[5,2,1]=>4032
[5,1,4,7,2,8,3,6]=>[3,3,2]=>1120
[1,7,4,5,2,8,3,6]=>[5,2,1]=>4032
[3,7,5,1,2,8,4,6]=>[6,2]=>3360
[5,7,2,8,1,3,4,6]=>[6,2]=>3360
[5,2,8,7,1,3,4,6]=>[3,2,2,1]=>1680
[4,1,5,8,2,7,3,6]=>[8]=>5040
[1,4,6,2,8,7,3,5]=>[3,2,2,1]=>1680
[1,4,2,8,6,7,3,5]=>[7,1]=>5760
[3,1,2,6,4,8,7,5]=>[4,3,1]=>3360
[2,1,7,6,3,4,8,5]=>[4,2,2]=>1260
[3,1,2,7,4,6,8,5]=>[4,3,1]=>3360
[1,4,7,2,6,8,3,5]=>[3,2,2,1]=>1680
[1,2,3,6,8,5,7,4]=>[4,1,1,1,1]=>420
[5,1,4,2,7,8,3,6]=>[6,2]=>3360
[1,4,2,7,6,8,3,5]=>[4,3,1]=>3360
[1,4,2,6,8,7,3,5]=>[5,2,1]=>4032
[3,1,2,8,4,6,7,5]=>[3,3,1,1]=>1120
[3,1,2,7,6,4,8,5]=>[5,3]=>2688
[5,3,7,1,8,2,4,6]=>[8]=>5040
[1,7,4,3,2,5,8,6]=>[5,2,1]=>4032
[4,8,7,2,1,3,5,6]=>[8]=>5040
[1,8,7,3,4,2,5,6]=>[4,3,1]=>3360
[3,1,7,8,2,6,4,5]=>[7,1]=>5760
[1,4,2,7,8,3,6,5]=>[5,2,1]=>4032
[5,2,8,1,3,4,7,6]=>[6,1,1]=>3360
[2,1,8,6,3,4,7,5]=>[3,2,2,1]=>1680
[1,4,2,6,8,3,7,5]=>[4,2,1,1]=>2520
[1,2,3,7,8,5,6,4]=>[5,1,1,1]=>1344
[1,2,3,7,5,8,6,4]=>[4,1,1,1,1]=>420
[1,4,2,7,3,8,6,5]=>[7,1]=>5760
[3,1,7,2,8,6,4,5]=>[5,2,1]=>4032
[2,1,7,8,3,4,6,5]=>[6,2]=>3360
[1,2,3,8,7,5,6,4]=>[3,2,1,1,1]=>1120
[10,1,2,3,4,5,6,7,8,9]=>[10]=>362880
[10,1,2,3,4,5,6,9,7,8]=>[10]=>362880
[10,1,2,3,4,5,9,6,7,8]=>[8,2]=>226800
[9,1,2,3,4,10,5,6,7,8]=>[7,3]=>172800
[10,1,2,3,9,4,5,6,7,8]=>[7,3]=>172800
[10,1,2,9,3,4,5,6,7,8]=>[10]=>362880
[9,1,10,2,3,4,5,6,7,8]=>[10]=>362880
[10,9,1,2,3,4,5,6,7,8]=>[10]=>362880
[11,1,2,3,4,5,6,7,8,9,10]=>[11]=>3628800
[10,1,2,3,4,5,6,7,8,11,9]=>[11]=>3628800
[8,1,2,3,4,5,6,9,10,7]=>[10]=>362880
[11,1,2,3,4,5,6,7,10,8,9]=>[11]=>3628800
[7,1,2,3,4,5,10,9,6,8]=>[10]=>362880
[6,1,2,3,4,10,9,5,7,8]=>[8,2]=>226800
[10,1,2,3,4,5,11,6,7,8,9]=>[8,3]=>1663200
[5,1,2,3,9,10,4,6,7,8]=>[7,3]=>172800
[11,1,2,3,4,10,5,6,7,8,9]=>[8,3]=>1663200
[4,1,2,10,9,3,5,6,7,8]=>[7,3]=>172800
[11,1,2,3,10,4,5,6,7,8,9]=>[11]=>3628800
[3,1,10,9,2,4,5,6,7,8]=>[10]=>362880
[10,1,2,11,3,4,5,6,7,8,9]=>[11]=>3628800
[2,9,10,1,3,4,5,6,7,8]=>[10]=>362880
[11,1,10,2,3,4,5,6,7,8,9]=>[11]=>3628800
[11,10,1,2,3,4,5,6,7,8,9]=>[6,5]=>1330560
[4,7,8,5,6,2,1,3]=>[6,2]=>3360
[5,7,8,4,2,6,1,3]=>[4,2,1,1]=>2520
[8,6,3,7,2,1,5,4]=>[7,1]=>5760
[7,6,3,8,2,1,5,4]=>[5,2,1]=>4032
[4,7,8,3,2,1,5,6]=>[5,3]=>2688
[5,7,8,3,2,1,4,6]=>[8]=>5040
[8,6,3,7,2,1,4,5]=>[5,2,1]=>4032
[5,6,3,8,2,1,4,7]=>[4,3,1]=>3360
[2,6,4,7,3,5,8,1]=>[8]=>5040
[8,4,3,2,1,6,5,7]=>[4,2,1,1]=>2520
[6,4,3,2,1,7,5,8]=>[4,2,1,1]=>2520
[8,4,3,2,1,7,6,5]=>[3,2,2,1]=>1680
[7,4,3,2,1,8,6,5]=>[5,2,1]=>4032
[6,5,4,2,8,7,1,3]=>[5,3]=>2688
[2,6,5,7,8,3,4,1]=>[6,2]=>3360
[8,5,4,2,6,7,1,3]=>[8]=>5040
[8,5,3,2,6,1,7,4]=>[6,1,1]=>3360
[7,5,3,2,6,1,8,4]=>[7,1]=>5760
[2,6,4,7,3,8,5,1]=>[4,4]=>1260
[3,5,4,2,7,8,1,6]=>[6,2]=>3360
[4,5,3,2,7,1,8,6]=>[7,1]=>5760
[5,6,3,4,1,2,8,7]=>[2,2,2,1,1]=>420
[8,5,3,7,2,6,4,1]=>[2,2,2,1,1]=>420
[8,5,7,4,2,6,3,1]=>[2,2,2,1,1]=>420
[7,5,8,4,2,6,1,3]=>[2,2,2,1,1]=>420
[2,1,7,8,5,6,3,4]=>[2,2,2,1,1]=>420
[6,8,3,7,5,1,4,2]=>[2,2,2,1,1]=>420
[5,7,3,8,1,6,2,4]=>[2,2,2,1,1]=>420
[3,2,6,4,8,5,1,7]=>[6,1,1]=>3360
[3,2,5,8,4,6,1,7]=>[6,1,1]=>3360
[3,5,2,4,1,7,6,8]=>[4,2,1,1]=>2520
[4,2,1,5,7,3,6,8]=>[6,1,1]=>3360
[4,5,2,3,7,1,6,8]=>[7,1]=>5760
[4,2,5,3,8,1,6,7]=>[7,1]=>5760
[4,2,5,8,3,1,6,7]=>[5,2,1]=>4032
[3,1,5,4,2,8,6,7]=>[4,3,1]=>3360
[4,1,5,3,8,2,6,7]=>[8]=>5040
[4,1,5,8,3,2,6,7]=>[6,2]=>3360
[4,3,8,5,2,1,6,7]=>[8]=>5040
[4,7,3,5,2,1,6,8]=>[6,1,1]=>3360
[4,3,2,7,5,1,6,8]=>[4,2,1,1]=>2520
[4,3,6,2,5,1,7,8]=>[5,1,1,1]=>1344
[4,6,3,2,5,1,7,8]=>[4,1,1,1,1]=>420
[4,6,7,1,3,2,5,8]=>[3,2,2,1]=>1680
[4,5,1,7,3,2,6,8]=>[7,1]=>5760
[4,5,1,3,7,2,6,8]=>[4,3,1]=>3360
[3,5,1,4,2,7,6,8]=>[2,2,2,1,1]=>420
[2,5,1,4,3,7,8,6]=>[4,3,1]=>3360
[5,2,1,4,3,7,8,6]=>[3,3,1,1]=>1120
[5,3,1,4,2,7,6,8]=>[4,2,1,1]=>2520
[4,3,1,5,7,2,6,8]=>[7,1]=>5760
[4,3,1,7,5,2,6,8]=>[6,1,1]=>3360
[4,3,6,1,5,2,7,8]=>[3,2,1,1,1]=>1120
[4,6,3,1,5,2,7,8]=>[2,2,1,1,1,1]=>210
[5,3,6,4,1,2,7,8]=>[3,2,1,1,1]=>1120
[4,3,6,1,7,2,5,8]=>[3,2,2,1]=>1680
[6,3,4,1,2,7,5,8]=>[7,1]=>5760
[6,2,4,1,3,7,8,5]=>[7,1]=>5760
[3,6,4,1,2,7,5,8]=>[4,3,1]=>3360
[4,6,3,1,7,2,5,8]=>[2,2,2,1,1]=>420
[5,3,6,2,1,4,7,8]=>[4,2,1,1]=>2520
[5,6,2,7,1,3,4,8]=>[3,2,2,1]=>1680
[4,5,2,7,3,1,6,8]=>[4,3,1]=>3360
[4,6,7,2,3,1,5,8]=>[4,3,1]=>3360
[4,6,2,1,7,3,5,8]=>[3,2,2,1]=>1680
[3,2,6,1,4,7,5,8]=>[6,1,1]=>3360
[3,6,2,1,4,7,5,8]=>[7,1]=>5760
[3,6,7,2,4,5,1,8]=>[4,3,1]=>3360
[3,5,2,7,4,6,1,8]=>[6,1,1]=>3360
[3,7,2,4,8,5,1,6]=>[4,3,1]=>3360
[7,2,1,4,6,3,8,5]=>[6,1,1]=>3360
[7,3,1,4,6,8,2,5]=>[4,3,1]=>3360
[3,2,6,1,5,7,4,8]=>[5,1,1,1]=>1344
[3,6,2,1,5,7,4,8]=>[6,1,1]=>3360
[6,3,2,1,5,7,4,8]=>[4,2,1,1]=>2520
[6,4,2,1,5,3,7,8]=>[5,1,1,1]=>1344
[4,2,6,1,5,3,7,8]=>[2,2,1,1,1,1]=>210
[4,2,1,7,5,3,6,8]=>[5,1,1,1]=>1344
[7,4,1,5,6,2,3,8]=>[4,3,1]=>3360
[7,3,1,5,2,6,4,8]=>[6,1,1]=>3360
[7,2,1,5,3,6,8,4]=>[6,1,1]=>3360
[6,2,5,1,3,7,8,4]=>[5,2,1]=>4032
[6,3,5,1,2,7,4,8]=>[4,3,1]=>3360
[6,4,5,1,7,2,3,8]=>[4,3,1]=>3360
[5,2,6,4,1,3,7,8]=>[2,2,1,1,1,1]=>210
[4,6,5,1,7,2,3,8]=>[3,2,2,1]=>1680
[3,6,5,1,2,7,4,8]=>[7,1]=>5760
[6,5,2,1,4,7,8,3]=>[8]=>5040
[6,5,3,1,4,7,2,8]=>[6,1,1]=>3360
[2,3,1,8,5,4,7,6]=>[3,3,1,1]=>1120
[2,4,1,5,8,3,7,6]=>[7,1]=>5760
[3,4,5,1,2,8,7,6]=>[5,2,1]=>4032
[3,4,5,1,8,2,7,6]=>[7,1]=>5760
[3,4,5,8,2,1,7,6]=>[7,1]=>5760
[3,4,5,2,8,1,7,6]=>[5,2,1]=>4032
[3,5,6,2,7,1,4,8]=>[4,3,1]=>3360
[3,5,6,2,7,1,8,4]=>[5,3]=>2688
[2,4,8,6,3,7,1,5]=>[5,3]=>2688
[1,8,4,6,3,7,2,5]=>[7,1]=>5760
[3,4,6,8,2,7,5,1]=>[8]=>5040
[3,4,6,2,8,7,5,1]=>[6,2]=>3360
[3,5,6,2,7,8,4,1]=>[4,4]=>1260
[3,5,6,2,7,4,1,8]=>[7,1]=>5760
[4,5,6,7,2,8,3,1]=>[6,2]=>3360
[3,5,6,8,7,2,4,1]=>[8]=>5040
[2,5,8,6,7,3,4,1]=>[8]=>5040
[2,5,8,6,7,3,1,4]=>[4,4]=>1260
[3,5,6,8,7,2,1,4]=>[6,2]=>3360
[4,5,6,7,2,1,8,3]=>[6,2]=>3360
[2,3,1,8,6,7,4,5]=>[5,3]=>2688
[1,8,3,2,6,7,5,4]=>[3,3,1,1]=>1120
[2,5,1,6,7,8,4,3]=>[8]=>5040
[3,5,6,1,7,4,2,8]=>[4,3,1]=>3360
[3,5,6,1,7,4,8,2]=>[4,4]=>1260
[3,5,6,8,7,1,4,2]=>[5,3]=>2688
[4,5,6,7,8,1,3,2]=>[5,3]=>2688
[4,5,6,7,1,3,2,8]=>[5,2,1]=>4032
[4,5,6,7,3,1,8,2]=>[8]=>5040
[3,5,6,8,7,4,1,2]=>[8]=>5040
[2,5,8,6,7,4,1,3]=>[4,2,2]=>1260
[2,5,8,6,7,4,3,1]=>[6,2]=>3360
[8,2,5,3,7,1,6,4]=>[7,1]=>5760
[8,2,4,3,7,1,6,5]=>[5,2,1]=>4032
[5,8,2,4,3,7,1,6]=>[7,1]=>5760
[4,2,5,6,1,8,3,7]=>[7,1]=>5760
[4,2,5,6,1,7,3,8]=>[6,1,1]=>3360
[6,1,5,7,3,2,4,8]=>[3,2,2,1]=>1680
[6,1,5,8,3,2,4,7]=>[3,3,2]=>1120
[3,8,2,4,7,1,5,6]=>[5,2,1]=>4032
[3,6,8,2,4,7,1,5]=>[8]=>5040
[4,3,5,6,7,1,8,2]=>[5,3]=>2688
[3,7,1,5,6,8,2,4]=>[4,2,2]=>1260
[3,7,1,5,8,2,4,6]=>[6,2]=>3360
[8,3,2,4,6,1,5,7]=>[5,2,1]=>4032
[7,3,2,4,6,1,5,8]=>[4,2,1,1]=>2520
[3,2,5,1,7,4,6,8]=>[6,1,1]=>3360
[3,2,5,1,8,4,6,7]=>[7,1]=>5760
[3,2,5,1,7,8,4,6]=>[5,2,1]=>4032
[7,8,3,2,4,6,1,5]=>[4,2,1,1]=>2520
[6,1,5,7,8,3,2,4]=>[8]=>5040
[4,2,5,6,1,7,8,3]=>[7,1]=>5760
[5,7,6,1,8,3,4,2]=>[6,2]=>3360
[5,8,6,1,7,3,4,2]=>[4,2,2]=>1260
[6,1,5,8,7,3,2,4]=>[6,2]=>3360
[8,7,3,2,4,6,1,5]=>[6,1,1]=>3360
[3,2,5,1,8,7,4,6]=>[7,1]=>5760
[3,2,5,1,6,4,7,8]=>[5,1,1,1]=>1344
[3,2,4,1,8,7,5,6]=>[4,3,1]=>3360
[3,2,5,1,6,8,7,4]=>[6,1,1]=>3360
[3,8,6,5,1,7,4,2]=>[6,2]=>3360
[3,7,6,5,1,8,4,2]=>[8]=>5040
[6,5,1,7,8,4,2,3]=>[8]=>5040
[3,2,5,1,6,7,8,4]=>[7,1]=>5760
[3,2,4,1,8,5,6,7]=>[4,3,1]=>3360
[3,2,4,1,7,5,6,8]=>[3,3,1,1]=>1120
[3,2,4,1,6,8,5,7]=>[4,3,1]=>3360
[3,2,4,1,8,5,7,6]=>[3,3,1,1]=>1120
[8,3,2,4,7,6,1,5]=>[4,2,1,1]=>2520
[3,2,5,1,8,4,7,6]=>[6,1,1]=>3360
[3,2,5,1,6,7,4,8]=>[6,1,1]=>3360
[6,5,1,7,4,2,3,8]=>[7,1]=>5760
[6,5,1,8,4,2,3,7]=>[8]=>5040
[8,4,2,3,7,5,1,6]=>[5,3]=>2688
[4,2,6,1,8,3,7,5]=>[2,2,2,1,1]=>420
[5,2,6,1,8,3,7,4]=>[4,2,1,1]=>2520
[8,4,6,1,7,3,5,2]=>[4,2,2]=>1260
[5,2,6,1,8,4,7,3]=>[6,1,1]=>3360
[7,4,2,3,8,5,1,6]=>[3,3,2]=>1120
[8,5,1,6,4,2,3,7]=>[4,4]=>1260
[7,5,1,6,4,2,3,8]=>[4,3,1]=>3360
[3,2,5,1,7,6,4,8]=>[5,1,1,1]=>1344
[3,2,5,1,8,6,4,7]=>[6,1,1]=>3360
[7,3,2,4,8,6,1,5]=>[2,2,2,1,1]=>420
[8,6,1,5,7,3,2,4]=>[8]=>5040
[4,2,6,1,8,5,7,3]=>[4,2,1,1]=>2520
[8,5,6,1,7,3,4,2]=>[6,2]=>3360
[3,6,8,5,1,7,4,2]=>[8]=>5040
[8,5,1,6,7,4,2,3]=>[3,3,2]=>1120
[3,2,5,1,8,6,7,4]=>[5,1,1,1]=>1344
[3,2,4,1,8,6,5,7]=>[3,3,1,1]=>1120
[3,2,4,1,5,8,6,7]=>[3,3,1,1]=>1120
[3,2,5,1,7,8,6,4]=>[7,1]=>5760
[7,8,5,1,6,4,2,3]=>[8]=>5040
[3,8,5,1,7,6,4,2]=>[5,2,1]=>4032
[3,7,5,1,8,6,4,2]=>[7,1]=>5760
[8,7,5,1,6,4,2,3]=>[6,2]=>3360
[3,2,5,1,8,7,6,4]=>[5,2,1]=>4032
[6,5,7,3,1,8,4,2]=>[5,3]=>2688
[4,6,3,7,1,8,5,2]=>[4,3,1]=>3360
[4,6,3,7,5,1,8,2]=>[6,1,1]=>3360
[4,2,6,1,7,5,3,8]=>[4,2,1,1]=>2520
[2,5,7,4,1,6,3,8]=>[3,2,1,1,1]=>1120
[2,5,7,4,1,6,8,3]=>[3,3,1,1]=>1120
[5,4,7,3,6,1,8,2]=>[5,3]=>2688
[5,4,7,8,3,1,6,2]=>[5,3]=>2688
[4,3,7,5,1,8,6,2]=>[5,3]=>2688
[6,4,3,8,5,1,7,2]=>[3,2,1,1,1]=>1120
[5,8,4,3,6,1,7,2]=>[3,2,2,1]=>1680
[5,4,8,3,6,1,7,2]=>[4,3,1]=>3360
[5,4,3,6,7,1,8,2]=>[7,1]=>5760
[2,5,4,6,1,7,3,8]=>[4,3,1]=>3360
[3,2,5,8,1,6,7,4]=>[3,2,1,1,1]=>1120
[2,5,4,6,8,1,7,3]=>[7,1]=>5760
[5,2,8,4,1,6,7,3]=>[2,2,1,1,1,1]=>210
[4,6,2,1,8,5,7,3]=>[5,2,1]=>4032
[2,4,1,7,5,8,6,3]=>[7,1]=>5760
[2,4,1,7,5,3,8,6]=>[7,1]=>5760
[2,6,4,1,8,5,3,7]=>[8]=>5040
[5,4,8,2,1,6,3,7]=>[3,2,2,1]=>1680
[2,5,8,4,1,6,3,7]=>[3,3,1,1]=>1120
[3,2,5,6,1,8,4,7]=>[4,3,1]=>3360
[4,8,3,2,6,1,5,7]=>[7,1]=>5760
[3,5,2,8,1,6,4,7]=>[4,3,1]=>3360
[3,2,1,6,8,5,4,7]=>[5,2,1]=>4032
[3,2,7,1,5,4,8,6]=>[6,1,1]=>3360
[3,2,7,1,5,8,6,4]=>[6,1,1]=>3360
[3,8,2,5,1,6,7,4]=>[6,1,1]=>3360
[4,8,3,2,6,7,1,5]=>[7,1]=>5760
[4,3,8,2,6,7,1,5]=>[8]=>5040
[4,3,2,6,7,8,1,5]=>[6,2]=>3360
[4,3,2,6,7,1,5,8]=>[3,2,2,1]=>1680
[4,3,7,2,6,8,1,5]=>[5,3]=>2688
[4,3,7,8,2,6,1,5]=>[7,1]=>5760
[2,5,7,4,8,1,6,3]=>[7,1]=>5760
[3,2,5,7,8,1,6,4]=>[7,1]=>5760
[3,2,5,7,1,6,8,4]=>[3,3,1,1]=>1120
[3,2,5,7,1,6,4,8]=>[3,2,1,1,1]=>1120
[6,3,2,7,1,5,4,8]=>[3,2,2,1]=>1680
[6,3,2,7,1,5,8,4]=>[3,3,2]=>1120
[6,3,2,7,8,1,5,4]=>[4,2,2]=>1260
[4,2,6,1,7,8,5,3]=>[3,2,2,1]=>1680
[6,5,2,1,7,8,4,3]=>[8]=>5040
[2,1,7,5,3,8,6,4]=>[6,2]=>3360
[6,2,1,8,5,3,7,4]=>[3,2,1,1,1]=>1120
[6,3,2,7,1,4,8,5]=>[6,2]=>3360
[6,3,2,1,4,7,8,5]=>[6,2]=>3360
[6,3,2,1,4,7,5,8]=>[5,2,1]=>4032
[3,5,2,1,7,4,6,8]=>[7,1]=>5760
[3,5,2,1,7,8,4,6]=>[6,2]=>3360
[5,8,4,2,1,7,3,6]=>[6,2]=>3360
[4,6,2,1,8,3,7,5]=>[3,2,2,1]=>1680
[2,4,1,7,3,8,6,5]=>[8]=>5040
[3,2,7,1,4,8,6,5]=>[7,1]=>5760
[3,5,8,2,1,7,4,6]=>[8]=>5040
[4,8,3,7,2,1,5,6]=>[7,1]=>5760
[4,3,7,2,8,1,5,6]=>[8]=>5040
[4,3,7,2,1,5,6,8]=>[7,1]=>5760
[4,8,3,2,7,1,5,6]=>[5,2,1]=>4032
[3,5,2,8,1,7,4,6]=>[4,4]=>1260
[6,3,2,8,1,4,7,5]=>[5,2,1]=>4032
[3,2,1,4,7,5,8,6]=>[4,2,1,1]=>2520
[5,3,2,1,8,4,6,7]=>[6,2]=>3360
[4,8,3,2,1,5,6,7]=>[7,1]=>5760
[4,3,8,2,1,5,6,7]=>[8]=>5040
[1,9,8,7,6,5,4,3,2]=>[2,2,2,2,1]=>945
[8,7,6,4,5,3,2,1,9]=>[2,2,2,1,1,1]=>1260
[1,9,8,7,5,6,4,3,2]=>[2,2,2,1,1,1]=>1260
[1,10,9,8,7,6,5,4,3,2]=>[2,2,2,2,1,1]=>4725
[10,9,8,7,6,5,4,3,2,1,11]=>[2,2,2,2,2,1]=>10395
[9,8,7,5,6,4,3,2,1,10]=>[3,2,2,2,1]=>25200
[8,7,5,4,6,3,2,1,9]=>[3,2,2,1,1]=>7560
[8,7,4,6,5,3,2,1,9]=>[3,2,2,1,1]=>7560
[1,9,8,6,5,7,4,3,2]=>[3,2,2,1,1]=>7560
[1,9,8,5,7,6,4,3,2]=>[3,2,2,1,1]=>7560
[1,10,9,8,6,7,5,4,3,2]=>[3,2,2,2,1]=>25200
[1,11,10,9,8,7,6,5,4,3,2]=>[2,2,2,2,2,1]=>10395
[6,2,3,1,5,4,8,7]=>[3,2,1,1,1]=>1120
[8,4,5,2,3,1,7,6]=>[3,2,2,1]=>1680
[8,6,7,2,5,3,4,1]=>[5,2,1]=>4032
[8,2,5,3,4,1,7,6]=>[3,3,1,1]=>1120
[6,2,5,3,4,1,8,7]=>[3,2,2,1]=>1680
[6,1,5,2,4,3,8,7]=>[6,2]=>3360
[6,4,5,1,3,2,8,7]=>[4,2,2]=>1260
[6,1,5,3,4,2,8,7]=>[3,3,2]=>1120
[6,3,5,1,4,2,8,7]=>[6,2]=>3360
[8,3,5,2,4,1,7,6]=>[4,3,1]=>3360
[8,3,7,5,6,2,4,1]=>[6,2]=>3360
[8,3,7,2,4,1,6,5]=>[8]=>5040
[8,3,5,1,4,2,7,6]=>[7,1]=>5760
[8,1,5,3,4,2,7,6]=>[4,3,1]=>3360
[8,4,5,1,3,2,7,6]=>[5,2,1]=>4032
[2,1,8,4,5,3,7,6]=>[3,2,1,1,1]=>1120
[8,6,7,4,5,1,3,2]=>[4,2,1,1]=>2520
[8,6,7,1,5,3,4,2]=>[7,1]=>5760
[8,6,7,3,5,1,4,2]=>[4,3,1]=>3360
[8,3,7,5,6,1,4,2]=>[8]=>5040
[8,5,7,3,6,1,4,2]=>[5,3]=>2688
[8,3,7,4,6,2,5,1]=>[5,2,1]=>4032
[8,3,7,4,6,1,5,2]=>[7,1]=>5760
[8,3,7,1,6,4,5,2]=>[8]=>5040
[8,1,7,3,6,4,5,2]=>[5,3]=>2688
[8,1,7,5,6,3,4,2]=>[5,3]=>2688
[8,4,7,5,6,1,3,2]=>[6,2]=>3360
[2,1,8,4,7,5,6,3]=>[3,2,2,1]=>1680
[8,1,7,3,4,2,6,5]=>[8]=>5040
[8,1,7,3,6,2,5,4]=>[8]=>5040
[8,3,7,1,6,2,5,4]=>[5,3]=>2688
[8,3,7,2,6,4,5,1]=>[6,2]=>3360
[8,2,7,3,6,4,5,1]=>[5,2,1]=>4032
[8,2,7,3,6,1,5,4]=>[7,1]=>5760
[8,2,7,1,6,3,5,4]=>[4,3,1]=>3360
[8,1,7,2,4,3,6,5]=>[5,3]=>2688
[8,1,3,2,7,4,6,5]=>[7,1]=>5760
[2,1,8,3,7,4,6,5]=>[6,2]=>3360
[8,1,5,2,4,3,7,6]=>[7,1]=>5760
[8,2,7,1,4,3,6,5]=>[4,3,1]=>3360
[8,2,7,3,4,1,6,5]=>[7,1]=>5760
[8,2,7,5,6,3,4,1]=>[5,2,1]=>4032
[8,4,7,5,6,2,3,1]=>[4,2,2]=>1260
[8,4,7,2,3,1,6,5]=>[6,2]=>3360
[8,2,3,1,7,4,6,5]=>[6,1,1]=>3360
[8,2,3,1,5,4,7,6]=>[4,1,1,1,1]=>420
[4,2,3,1,8,5,7,6]=>[3,2,1,1,1]=>1120
[4,1,3,2,8,6,7,5]=>[3,2,1,1,1]=>1120
[8,6,7,2,3,1,5,4]=>[5,3]=>2688
[8,2,3,1,7,5,6,4]=>[3,3,1,1]=>1120
[8,5,7,2,6,3,4,1]=>[6,2]=>3360
[8,5,7,2,6,1,4,3]=>[8]=>5040
[8,2,7,5,6,1,4,3]=>[7,1]=>5760
[8,6,7,2,5,1,4,3]=>[7,1]=>5760
[8,6,7,1,5,2,4,3]=>[5,2,1]=>4032
[8,6,7,1,3,2,5,4]=>[3,3,2]=>1120
[2,1,8,6,7,3,5,4]=>[4,2,2]=>1260
[2,1,8,3,7,5,6,4]=>[3,3,2]=>1120
[8,1,3,2,7,5,6,4]=>[4,3,1]=>3360
[8,1,7,5,6,2,4,3]=>[8]=>5040
[8,1,7,2,6,4,5,3]=>[8]=>5040
[8,2,7,1,6,4,5,3]=>[7,1]=>5760
[8,2,7,4,6,1,5,3]=>[6,1,1]=>3360
[8,2,7,4,6,3,5,1]=>[4,2,1,1]=>2520
[8,4,7,2,6,3,5,1]=>[4,2,2]=>1260
[8,4,7,2,6,1,5,3]=>[6,2]=>3360
[8,4,7,1,6,2,5,3]=>[8]=>5040
[8,1,7,4,6,2,5,3]=>[7,1]=>5760
[8,5,7,1,6,2,4,3]=>[5,3]=>2688
[2,1,8,5,7,3,6,4]=>[6,2]=>3360
[8,5,7,4,6,1,3,2]=>[5,2,1]=>4032
[8,5,7,1,6,3,4,2]=>[8]=>5040
[8,1,7,4,6,3,5,2]=>[4,3,1]=>3360
[8,4,7,1,6,3,5,2]=>[4,4]=>1260
[8,4,7,3,6,1,5,2]=>[8]=>5040
[2,4,8,3,6,1,7,5]=>[7,1]=>5760
[6,5,8,1,3,2,7,4]=>[7,1]=>5760
[4,5,8,6,3,2,7,1]=>[7,1]=>5760
[6,5,8,7,3,1,2,4]=>[6,2]=>3360
[1,5,8,7,3,6,2,4]=>[6,1,1]=>3360
[1,7,2,8,4,6,5,3]=>[6,1,1]=>3360
[6,7,2,8,4,1,5,3]=>[6,2]=>3360
[3,6,2,8,4,5,7,1]=>[7,1]=>5760
[2,6,1,8,4,5,7,3]=>[7,1]=>5760
[2,8,4,6,1,5,7,3]=>[7,1]=>5760
[6,3,1,8,4,5,7,2]=>[7,1]=>5760
[3,1,6,8,4,5,7,2]=>[7,1]=>5760
[2,3,6,8,4,5,7,1]=>[7,1]=>5760
[6,3,7,8,4,1,5,2]=>[6,2]=>3360
[1,3,7,8,4,6,5,2]=>[6,1,1]=>3360
[1,5,7,8,2,4,6,3]=>[5,2,1]=>4032
[5,1,7,8,2,4,6,3]=>[5,3]=>2688
[3,6,7,8,4,2,5,1]=>[6,2]=>3360
[7,6,1,8,4,2,5,3]=>[6,2]=>3360
[5,6,8,7,3,2,1,4]=>[6,2]=>3360
[2,8,3,7,1,6,5,4]=>[6,1,1]=>3360
[5,2,8,7,3,6,1,4]=>[6,1,1]=>3360
[7,2,1,8,4,6,5,3]=>[6,1,1]=>3360
[3,2,7,8,4,6,5,1]=>[6,1,1]=>3360
[5,2,7,8,1,4,6,3]=>[5,2,1]=>4032
[1,2,7,8,5,4,6,3]=>[5,1,1,1]=>1344
[4,2,1,3,8,5,6,7]=>[4,3,1]=>3360
[7,2,5,8,3,4,6,1]=>[5,2,1]=>4032
[6,2,8,5,4,3,1,7]=>[5,2,1]=>4032
[2,8,3,5,4,1,6,7]=>[5,2,1]=>4032
[2,8,4,5,3,1,6,7]=>[5,3]=>2688
[6,4,8,5,2,3,1,7]=>[5,3]=>2688
[7,3,5,8,2,4,6,1]=>[5,3]=>2688
[4,3,1,2,8,5,6,7]=>[4,4]=>1260
[3,4,2,1,8,5,6,7]=>[4,4]=>1260
[2,7,6,8,4,3,5,1]=>[6,2]=>3360
[5,7,1,8,3,4,6,2]=>[5,3]=>2688
[3,7,5,8,1,4,6,2]=>[5,3]=>2688
[1,7,5,8,3,4,6,2]=>[5,2,1]=>4032
[1,6,8,5,4,3,2,7]=>[5,2,1]=>4032
[4,6,8,5,1,3,2,7]=>[5,3]=>2688
[5,6,8,1,4,3,2,7]=>[5,3]=>2688
[7,5,8,6,3,4,2,1]=>[6,2]=>3360
[2,4,8,3,6,5,1,7]=>[6,2]=>3360
[2,8,4,1,5,6,3,7]=>[6,1,1]=>3360
[4,1,8,3,5,6,2,7]=>[6,1,1]=>3360
[5,6,8,4,1,3,2,7]=>[5,2,1]=>4032
[4,6,8,1,5,3,2,7]=>[5,2,1]=>4032
[1,6,8,4,5,3,2,7]=>[5,1,1,1]=>1344
[1,7,3,8,5,4,6,2]=>[5,1,1,1]=>1344
[3,7,1,8,5,4,6,2]=>[5,2,1]=>4032
[2,7,3,8,4,6,5,1]=>[6,1,1]=>3360
[7,1,3,8,4,6,5,2]=>[6,1,1]=>3360
[5,7,8,4,3,6,1,2]=>[6,1,1]=>3360
[2,8,7,4,1,6,5,3]=>[6,1,1]=>3360
[2,8,5,4,3,1,6,7]=>[5,2,1]=>4032
[6,5,8,4,2,3,1,7]=>[5,2,1]=>4032
[4,1,3,2,8,5,6,7]=>[4,3,1]=>3360
[1,4,3,2,8,5,6,7]=>[4,2,1,1]=>2520
[7,3,2,8,5,4,6,1]=>[5,2,1]=>4032
[6,4,8,2,5,3,1,7]=>[5,2,1]=>4032
[2,8,4,3,5,1,6,7]=>[5,2,1]=>4032
[2,8,3,4,5,1,6,7]=>[5,1,1,1]=>1344
[6,2,8,4,5,3,1,7]=>[5,1,1,1]=>1344
[7,2,3,8,5,4,6,1]=>[5,1,1,1]=>1344
[4,2,3,1,8,5,6,7]=>[4,2,1,1]=>2520
[3,2,1,4,8,5,6,7]=>[4,2,1,1]=>2520
[5,1,3,2,4,8,6,7]=>[4,3,1]=>3360
[2,8,1,5,3,4,7,6]=>[7,1]=>5760
[1,2,8,4,5,3,7,6]=>[3,1,1,1,1,1]=>112
[1,4,2,8,5,3,6,7]=>[6,1,1]=>3360
[1,8,4,2,5,3,6,7]=>[6,1,1]=>3360
[8,1,5,3,2,4,6,7]=>[8]=>5040
[3,8,1,5,2,4,6,7]=>[6,2]=>3360
[3,5,1,4,8,2,6,7]=>[5,2,1]=>4032
[1,5,2,8,4,3,6,7]=>[7,1]=>5760
[1,2,8,5,4,3,6,7]=>[4,2,1,1]=>2520
[1,2,5,4,3,8,6,7]=>[3,2,1,1,1]=>1120
[1,2,4,8,5,3,7,6]=>[4,1,1,1,1]=>420
[1,2,7,4,8,5,3,6]=>[3,2,1,1,1]=>1120
[1,5,2,7,8,4,3,6]=>[7,1]=>5760
[5,1,2,7,4,8,3,6]=>[6,2]=>3360
[8,3,5,1,4,7,2,6]=>[8]=>5040
[2,8,1,5,4,7,3,6]=>[6,2]=>3360
[1,2,8,5,7,4,3,6]=>[6,1,1]=>3360
[1,2,4,8,7,5,3,6]=>[6,1,1]=>3360
[2,8,1,4,3,7,6,5]=>[5,2,1]=>4032
[6,1,2,8,7,4,3,5]=>[8]=>5040
[6,4,1,2,8,7,3,5]=>[4,2,2]=>1260
[3,6,4,8,1,7,2,5]=>[5,3]=>2688
[7,6,1,4,2,8,3,5]=>[4,3,1]=>3360
[7,1,6,2,8,4,3,5]=>[6,2]=>3360
[1,6,7,2,8,4,3,5]=>[3,2,2,1]=>1680
[6,7,1,4,2,8,3,5]=>[7,1]=>5760
[6,3,7,1,4,8,2,5]=>[5,3]=>2688
[3,7,8,1,5,2,4,6]=>[7,1]=>5760
[7,1,2,8,5,3,4,6]=>[7,1]=>5760
[1,7,2,8,4,5,3,6]=>[4,3,1]=>3360
[1,4,2,7,8,5,3,6]=>[4,3,1]=>3360
[6,1,2,8,4,3,7,5]=>[4,3,1]=>3360
[6,4,1,2,8,3,7,5]=>[3,2,2,1]=>1680
[7,6,1,3,2,4,8,5]=>[8]=>5040
[6,7,1,3,2,4,8,5]=>[4,4]=>1260
[1,2,7,3,5,8,4,6]=>[3,2,1,1,1]=>1120
[1,2,7,5,8,3,4,6]=>[6,1,1]=>3360
[5,8,1,3,7,2,4,6]=>[5,3]=>2688
[1,2,5,8,7,3,4,6]=>[6,1,1]=>3360
[1,2,5,8,3,7,4,6]=>[4,2,1,1]=>2520
[2,8,1,7,3,5,4,6]=>[6,2]=>3360
[8,6,1,3,2,4,7,5]=>[7,1]=>5760
[4,2,8,1,7,3,6,5]=>[5,2,1]=>4032
[2,8,1,7,4,3,6,5]=>[8]=>5040
[7,1,2,8,4,3,6,5]=>[5,3]=>2688
[1,2,8,4,7,5,3,6]=>[5,1,1,1]=>1344
[1,2,8,7,4,5,3,6]=>[6,1,1]=>3360
[2,8,1,7,5,3,4,6]=>[5,2,1]=>4032
[8,3,7,1,5,2,4,6]=>[7,1]=>5760
[3,8,6,1,4,7,2,5]=>[8]=>5040
[8,6,1,4,2,7,3,5]=>[7,1]=>5760
[8,1,6,2,7,4,3,5]=>[8]=>5040
[7,1,2,8,6,4,3,5]=>[4,4]=>1260
[7,4,1,2,8,6,3,5]=>[3,2,2,1]=>1680
[3,7,4,8,1,6,2,5]=>[5,2,1]=>4032
[3,4,8,7,1,6,2,5]=>[4,3,1]=>3360
[4,2,8,1,7,6,3,5]=>[4,2,1,1]=>2520
[2,8,1,7,6,4,3,5]=>[8]=>5040
[7,8,3,4,1,5,2,6]=>[6,1,1]=>3360
[7,8,3,4,1,6,2,5]=>[5,1,1,1]=>1344
[6,8,3,4,1,7,2,5]=>[6,1,1]=>3360
[6,7,3,4,1,8,2,5]=>[4,2,1,1]=>2520
[5,7,3,4,1,8,2,6]=>[2,2,2,1,1]=>420
[5,8,3,4,1,7,2,6]=>[4,2,1,1]=>2520
[5,8,3,4,1,6,2,7]=>[3,2,1,1,1]=>1120
[6,8,3,4,1,5,2,7]=>[3,3,1,1]=>1120
[6,7,3,4,1,5,2,8]=>[3,2,1,1,1]=>1120
[5,7,3,4,1,6,2,8]=>[2,2,1,1,1,1]=>210
[5,6,2,8,3,4,1,7]=>[8]=>5040
[5,6,2,7,3,4,1,8]=>[7,1]=>5760
[4,6,2,8,3,5,1,7]=>[4,4]=>1260
[4,7,3,5,1,6,2,8]=>[3,2,1,1,1]=>1120
[4,8,3,5,1,6,2,7]=>[3,3,1,1]=>1120
[4,8,3,5,1,7,2,6]=>[4,3,1]=>3360
[4,7,3,5,1,8,2,6]=>[3,2,2,1]=>1680
[5,6,2,3,1,7,4,8]=>[5,2,1]=>4032
[5,6,2,4,1,8,3,7]=>[5,2,1]=>4032
[5,6,2,4,1,7,3,8]=>[4,2,1,1]=>2520
[4,6,2,5,1,7,3,8]=>[4,3,1]=>3360
[4,6,2,5,1,8,3,7]=>[5,3]=>2688
[4,5,1,8,3,7,2,6]=>[8]=>5040
[4,5,1,7,3,8,2,6]=>[6,2]=>3360
[4,6,2,7,3,8,1,5]=>[5,3]=>2688
[5,6,2,7,3,8,1,4]=>[8]=>5040
[5,6,2,7,4,8,1,3]=>[4,4]=>1260
[5,6,3,8,4,7,1,2]=>[7,1]=>5760
[5,6,2,8,4,7,1,3]=>[8]=>5040
[5,6,2,8,3,7,1,4]=>[6,2]=>3360
[4,6,2,8,3,7,1,5]=>[8]=>5040
[4,5,1,7,3,6,2,8]=>[6,1,1]=>3360
[4,5,1,8,3,6,2,7]=>[7,1]=>5760
[9,2,1,3,4,5,6,7,8]=>[8,1]=>45360
[10,2,1,3,4,5,6,7,8,9]=>[9,1]=>403200
[9,2,3,1,4,5,6,7,8]=>[7,1,1]=>25920
[4,2,3,5,6,7,8,9,1]=>[7,1,1]=>25920
[3,4,2,5,6,7,8,9,1]=>[9]=>40320
[3,2,4,5,6,7,8,9,10,1]=>[9,1]=>403200
[2,3,4,5,6,7,8,9,10,11,1]=>[11]=>3628800
[6,5,3,2,1,4,8,7]=>[5,2,1]=>4032
[4,6,3,5,2,1,8,7]=>[5,2,1]=>4032
[8,7,3,5,2,4,1,6]=>[7,1]=>5760
[6,8,2,4,5,7,3,1]=>[6,1,1]=>3360
[8,7,2,4,5,3,1,6]=>[6,1,1]=>3360
[3,6,1,4,5,2,8,7]=>[2,2,2,1,1]=>420
[8,3,7,4,5,2,1,6]=>[6,1,1]=>3360
[6,3,8,4,5,7,2,1]=>[6,1,1]=>3360
[5,8,7,4,3,6,2,1]=>[6,1,1]=>3360
[2,8,7,4,3,6,1,5]=>[6,1,1]=>3360
[8,1,7,4,3,6,2,5]=>[6,1,1]=>3360
[8,7,3,5,1,4,2,6]=>[5,2,1]=>4032
[2,1,6,8,5,7,4,3]=>[5,2,1]=>4032
[6,8,3,5,1,7,4,2]=>[5,2,1]=>4032
[5,1,8,4,7,6,3,2]=>[6,1,1]=>3360
[2,5,8,4,7,6,3,1]=>[6,1,1]=>3360
[4,3,8,1,5,6,7,2]=>[3,2,1,1,1]=>1120
[4,8,1,3,5,6,7,2]=>[3,2,1,1,1]=>1120
[5,8,7,4,1,6,3,2]=>[2,2,2,1,1]=>420
[5,8,3,6,1,4,7,2]=>[2,2,2,1,1]=>420
[4,8,3,6,1,2,7,5]=>[6,1,1]=>3360
[3,8,7,4,1,6,2,5]=>[6,1,1]=>3360
[3,8,1,2,5,6,7,4]=>[3,2,1,1,1]=>1120
[8,7,1,4,2,6,3,5]=>[6,1,1]=>3360
[8,6,3,1,2,4,7,5]=>[6,1,1]=>3360
[8,1,7,4,5,2,3,6]=>[4,2,1,1]=>2520
[2,8,7,4,5,1,3,6]=>[4,2,1,1]=>2520
[8,7,2,4,1,6,3,5]=>[3,3,1,1]=>1120
[5,8,3,6,2,4,7,1]=>[4,2,1,1]=>2520
[8,6,3,2,1,4,7,5]=>[3,3,1,1]=>1120
[8,7,3,5,2,1,4,6]=>[4,3,1]=>3360
[5,8,3,6,2,1,7,4]=>[6,1,1]=>3360
[5,8,7,4,2,6,1,3]=>[6,1,1]=>3360
[2,6,8,4,5,7,1,3]=>[4,2,1,1]=>2520
[6,1,8,4,5,7,2,3]=>[4,2,1,1]=>2520
[6,8,3,5,1,7,2,4]=>[7,1]=>5760
[2,1,5,8,3,6,7,4]=>[2,2,2,1,1]=>420
[5,8,3,6,1,2,7,4]=>[4,2,1,1]=>2520
[4,1,8,2,5,6,7,3]=>[3,2,1,1,1]=>1120
[2,4,8,1,5,6,7,3]=>[3,2,1,1,1]=>1120
[4,8,2,1,5,6,7,3]=>[3,2,1,1,1]=>1120
[3,4,8,2,5,6,7,1]=>[3,2,1,1,1]=>1120
[5,8,1,4,7,6,2,3]=>[6,1,1]=>3360
[5,8,3,1,6,2,7,4]=>[6,1,1]=>3360
[4,5,3,8,6,1,7,2]=>[6,1,1]=>3360
[3,4,1,8,5,6,7,2]=>[3,2,1,1,1]=>1120
[2,4,6,8,10,1,3,5,7,9]=>[10]=>362880
[2,4,6,9,10,1,3,5,7,8]=>[7,3]=>172800
[2,4,7,8,10,1,3,5,6,9]=>[8,2]=>226800
[2,4,7,9,10,1,3,5,6,8]=>[5,3,2]=>120960
[2,4,8,9,10,1,3,5,6,7]=>[5,5]=>72576
[2,5,6,8,10,1,3,4,7,9]=>[8,2]=>226800
[2,5,6,9,10,1,3,4,7,8]=>[10]=>362880
[2,5,7,8,10,1,3,4,6,9]=>[6,2,2]=>75600
[2,5,7,9,10,1,3,4,6,8]=>[8,2]=>226800
[2,5,8,9,10,1,3,4,6,7]=>[10]=>362880
[2,6,7,8,10,1,3,4,5,9]=>[3,3,2,2]=>25200
[2,6,7,9,10,1,3,4,5,8]=>[5,3,2]=>120960
[2,6,8,9,10,1,3,4,5,7]=>[7,3]=>172800
[2,7,8,9,10,1,3,4,5,6]=>[10]=>362880
[3,4,6,8,10,1,2,5,7,9]=>[7,3]=>172800
[3,4,6,9,10,1,2,5,7,8]=>[4,3,3]=>50400
[3,4,7,8,10,1,2,5,6,9]=>[10]=>362880
[3,4,7,9,10,1,2,5,6,8]=>[7,3]=>172800
[3,4,8,9,10,1,2,5,6,7]=>[10]=>362880
[3,5,6,8,10,1,2,4,7,9]=>[5,3,2]=>120960
[3,5,6,9,10,1,2,4,7,8]=>[7,3]=>172800
[3,5,7,8,10,1,2,4,6,9]=>[8,2]=>226800
[3,5,7,9,10,1,2,4,6,8]=>[10]=>362880
[3,5,8,9,10,1,2,4,6,7]=>[6,4]=>151200
[3,6,7,8,10,1,2,4,5,9]=>[5,3,2]=>120960
[3,6,7,9,10,1,2,4,5,8]=>[5,5]=>72576
[3,6,8,9,10,1,2,4,5,7]=>[10]=>362880
[3,7,8,9,10,1,2,4,5,6]=>[8,2]=>226800
[4,5,6,8,10,1,2,3,7,9]=>[5,5]=>72576
[4,5,6,9,10,1,2,3,7,8]=>[10]=>362880
[4,5,7,8,10,1,2,3,6,9]=>[10]=>362880
[4,5,7,9,10,1,2,3,6,8]=>[6,4]=>151200
[4,5,8,9,10,1,2,3,6,7]=>[4,4,2]=>56700
[4,6,7,8,10,1,2,3,5,9]=>[7,3]=>172800
[4,6,7,9,10,1,2,3,5,8]=>[10]=>362880
[4,6,8,9,10,1,2,3,5,7]=>[8,2]=>226800
[4,7,8,9,10,1,2,3,5,6]=>[6,2,2]=>75600
[5,6,7,8,10,1,2,3,4,9]=>[10]=>362880
[5,6,7,9,10,1,2,3,4,8]=>[8,2]=>226800
[5,6,8,9,10,1,2,3,4,7]=>[6,2,2]=>75600
[5,7,8,9,10,1,2,3,4,6]=>[4,2,2,2]=>18900
[2,4,6,8,10,12,1,3,5,7,9,11]=>[12]=>39916800
[2,4,6,8,11,12,1,3,5,7,9,10]=>[9,3]=>17740800
[2,4,6,9,10,12,1,3,5,7,8,11]=>[7,5]=>13685760
[2,4,6,9,11,12,1,3,5,7,8,10]=>[12]=>39916800
[2,4,6,10,11,12,1,3,5,7,8,9]=>[7,5]=>13685760
[2,4,7,8,10,12,1,3,5,6,9,11]=>[6,6]=>6652800
[2,4,7,9,10,12,1,3,5,6,8,11]=>[12]=>39916800
[2,4,7,9,11,12,1,3,5,6,8,10]=>[9,3]=>17740800
[2,4,7,10,11,12,1,3,5,6,8,9]=>[12]=>39916800
[2,4,9,10,11,12,1,3,5,6,7,8]=>[12]=>39916800
[2,5,6,8,10,12,1,3,4,7,9,11]=>[7,5]=>13685760
[2,5,6,8,11,12,1,3,4,7,9,10]=>[12]=>39916800
[2,5,6,9,10,12,1,3,4,7,8,11]=>[5,5,2]=>4790016
[2,5,6,10,11,12,1,3,4,7,8,9]=>[12]=>39916800
[2,5,7,8,10,12,1,3,4,6,9,11]=>[12]=>39916800
[2,5,7,8,11,12,1,3,4,6,9,10]=>[9,3]=>17740800
[2,5,7,10,11,12,1,3,4,6,8,9]=>[7,5]=>13685760
[2,5,8,9,11,12,1,3,4,6,7,10]=>[5,3,2,2]=>3991680
[2,5,8,10,11,12,1,3,4,6,7,9]=>[5,5,2]=>4790016
[2,5,9,10,11,12,1,3,4,6,7,8]=>[7,5]=>13685760
[2,6,7,8,11,12,1,3,4,5,9,10]=>[12]=>39916800
[2,6,7,10,11,12,1,3,4,5,8,9]=>[12]=>39916800
[2,6,9,10,11,12,1,3,4,5,7,8]=>[12]=>39916800
[2,7,8,9,10,12,1,3,4,5,6,11]=>[3,3,2,2,2]=>554400
[2,7,8,9,11,12,1,3,4,5,6,10]=>[5,3,2,2]=>3991680
[2,7,9,10,11,12,1,3,4,5,6,8]=>[9,3]=>17740800
[2,8,9,10,11,12,1,3,4,5,6,7]=>[12]=>39916800
[3,4,6,8,10,12,1,2,5,7,9,11]=>[9,3]=>17740800
[3,4,6,9,10,12,1,2,5,7,8,11]=>[12]=>39916800
[3,4,6,9,11,12,1,2,5,7,8,10]=>[6,6]=>6652800
[3,4,6,10,11,12,1,2,5,7,8,9]=>[12]=>39916800
[3,4,7,8,11,12,1,2,5,6,9,10]=>[3,3,3,3]=>246400
[3,4,7,9,10,12,1,2,5,6,8,11]=>[9,3]=>17740800
[3,4,7,10,11,12,1,2,5,6,8,9]=>[9,3]=>17740800
[3,4,8,9,10,12,1,2,5,6,7,11]=>[12]=>39916800
[3,4,8,9,11,12,1,2,5,6,7,10]=>[9,3]=>17740800
[3,4,8,10,11,12,1,2,5,6,7,9]=>[12]=>39916800
[3,4,9,10,11,12,1,2,5,6,7,8]=>[6,6]=>6652800
[3,5,6,8,10,12,1,2,4,7,9,11]=>[12]=>39916800
[3,5,6,8,11,12,1,2,4,7,9,10]=>[6,6]=>6652800
[3,5,6,9,11,12,1,2,4,7,8,10]=>[6,4,2]=>9979200
[3,5,7,8,10,12,1,2,4,6,9,11]=>[9,3]=>17740800
[3,5,7,9,11,12,1,2,4,6,8,10]=>[4,3,3,2]=>3326400
[3,5,7,10,11,12,1,2,4,6,8,9]=>[5,4,3]=>7983360
[3,5,8,10,11,12,1,2,4,6,7,9]=>[7,5]=>13685760
[3,5,9,10,11,12,1,2,4,6,7,8]=>[12]=>39916800
[3,6,7,8,11,12,1,2,4,5,9,10]=>[9,3]=>17740800
[3,6,7,9,10,12,1,2,4,5,8,11]=>[5,3,2,2]=>3991680
[3,6,7,10,11,12,1,2,4,5,8,9]=>[9,3]=>17740800
[3,6,8,10,11,12,1,2,4,5,7,9]=>[12]=>39916800
[3,7,8,9,10,12,1,2,4,5,6,11]=>[5,3,2,2]=>3991680
[3,7,8,9,11,12,1,2,4,5,6,10]=>[5,5,2]=>4790016
[3,7,8,10,11,12,1,2,4,5,6,9]=>[7,5]=>13685760
[3,7,9,10,11,12,1,2,4,5,6,8]=>[12]=>39916800
[4,5,6,8,10,12,1,2,3,7,9,11]=>[7,5]=>13685760
[4,5,6,8,11,12,1,2,3,7,9,10]=>[12]=>39916800
[4,5,6,9,10,12,1,2,3,7,8,11]=>[12]=>39916800
[4,5,6,10,11,12,1,2,3,7,8,9]=>[4,4,4]=>1247400
[4,5,7,8,10,12,1,2,3,6,9,11]=>[12]=>39916800
[4,5,7,8,11,12,1,2,3,6,9,10]=>[9,3]=>17740800
[4,5,7,9,10,12,1,2,3,6,8,11]=>[7,5]=>13685760
[4,5,7,9,11,12,1,2,3,6,8,10]=>[5,4,3]=>7983360
[4,5,8,9,10,12,1,2,3,6,7,11]=>[12]=>39916800
[4,5,8,9,11,12,1,2,3,6,7,10]=>[9,3]=>17740800
[4,5,8,10,11,12,1,2,3,6,7,9]=>[12]=>39916800
[4,6,7,8,11,12,1,2,3,5,9,10]=>[12]=>39916800
[4,6,7,9,10,12,1,2,3,5,8,11]=>[5,5,2]=>4790016
[4,6,7,9,11,12,1,2,3,5,8,10]=>[7,5]=>13685760
[4,6,7,10,11,12,1,2,3,5,8,9]=>[12]=>39916800
[4,6,8,9,11,12,1,2,3,5,7,10]=>[12]=>39916800
[4,6,8,10,11,12,1,2,3,5,7,9]=>[6,6]=>6652800
[4,6,9,10,11,12,1,2,3,5,7,8]=>[6,4,2]=>9979200
[4,7,8,9,11,12,1,2,3,5,6,10]=>[7,5]=>13685760
[4,7,8,10,11,12,1,2,3,5,6,9]=>[12]=>39916800
[5,6,7,8,10,12,1,2,3,4,9,11]=>[12]=>39916800
[5,6,7,8,11,12,1,2,3,4,9,10]=>[6,6]=>6652800
[5,6,7,9,10,12,1,2,3,4,8,11]=>[7,5]=>13685760
[5,6,7,9,11,12,1,2,3,4,8,10]=>[12]=>39916800
[5,6,8,9,10,12,1,2,3,4,7,11]=>[12]=>39916800
[5,6,8,10,11,12,1,2,3,4,7,9]=>[6,4,2]=>9979200
[5,6,9,10,11,12,1,2,3,4,7,8]=>[4,4,2,2]=>1871100
[5,7,8,9,10,12,1,2,3,4,6,11]=>[9,3]=>17740800
[5,7,8,9,11,12,1,2,3,4,6,10]=>[12]=>39916800
[6,7,8,9,10,12,1,2,3,4,5,11]=>[12]=>39916800
[7,8,9,10,11,12,1,2,3,4,5,6]=>[2,2,2,2,2,2]=>10395
[4,5,7,6,2,3,8,1]=>[6,2]=>3360
[3,5,7,2,6,4,8,1]=>[4,4]=>1260
[8,4,3,7,6,1,5,2]=>[7,1]=>5760
[8,2,4,7,1,6,5,3]=>[6,1,1]=>3360
[6,7,1,3,5,8,4,2]=>[7,1]=>5760
[5,8,7,3,6,1,4,2]=>[3,3,2]=>1120
[4,8,3,7,6,1,5,2]=>[5,2,1]=>4032
[3,8,4,7,6,1,5,2]=>[6,2]=>3360
[2,8,4,7,1,6,5,3]=>[7,1]=>5760
[8,1,4,7,2,6,5,3]=>[7,1]=>5760
[8,1,3,2,7,6,5,4]=>[4,2,1,1]=>2520
[3,8,2,1,7,6,5,4]=>[5,2,1]=>4032
[6,7,1,2,8,5,4,3]=>[5,3]=>2688
[8,3,2,1,7,6,5,4]=>[3,2,2,1]=>1680
[1,4,2,7,8,6,5,3]=>[6,1,1]=>3360
[8,4,2,7,1,6,5,3]=>[7,1]=>5760
[8,5,7,2,1,6,4,3]=>[7,1]=>5760
[1,5,7,2,8,6,4,3]=>[6,1,1]=>3360
[5,4,7,6,8,1,3,2]=>[6,2]=>3360
[1,4,8,7,2,6,5,3]=>[4,2,1,1]=>2520
[4,3,8,7,6,1,5,2]=>[5,3]=>2688
[6,7,2,8,1,5,4,3]=>[5,3]=>2688
[5,2,7,8,1,6,4,3]=>[4,2,1,1]=>2520
[4,2,8,7,1,6,5,3]=>[4,2,1,1]=>2520
[3,2,8,1,7,6,5,4]=>[4,2,1,1]=>2520
[1,3,8,2,7,6,5,4]=>[4,2,1,1]=>2520
[2,1,8,3,7,6,5,4]=>[3,2,2,1]=>1680
[5,1,7,8,2,6,4,3]=>[4,3,1]=>3360
[4,8,1,7,2,6,5,3]=>[7,1]=>5760
[3,8,1,2,7,6,5,4]=>[3,2,2,1]=>1680
[8,1,2,3,7,6,5,4]=>[5,2,1]=>4032
[3,1,4,5,6,7,8,9,10,2]=>[10]=>362880
[2,3,4,5,6,7,8,9,11,1,10]=>[11]=>3628800
[10,3,4,5,6,7,8,1,2,9]=>[10]=>362880
[10,1,4,5,6,7,8,9,2,3]=>[10]=>362880
[3,1,4,5,6,7,8,9,10,11,2]=>[11]=>3628800
[2,3,4,5,6,7,8,9,10,12,1,11]=>[12]=>39916800
[11,3,4,5,6,7,8,9,1,2,10]=>[11]=>3628800
[2,10,4,5,6,7,8,1,3,9]=>[10]=>362880
[8,3,4,5,6,7,1,10,2,9]=>[10]=>362880
[3,1,10,5,6,7,8,9,2,4]=>[10]=>362880
[9,1,4,5,6,7,8,2,10,3]=>[10]=>362880
[11,1,4,5,6,7,8,9,10,2,3]=>[11]=>3628800
[3,1,4,5,6,7,8,9,10,11,12,2]=>[12]=>39916800
[6,7,1,8,4,5,2,3]=>[6,2]=>3360
[3,7,1,5,8,2,6,4]=>[3,3,2]=>1120
[2,7,1,5,8,3,6,4]=>[5,3]=>2688
[2,6,5,1,8,3,7,4]=>[7,1]=>5760
[3,6,5,1,8,2,7,4]=>[5,2,1]=>4032
[4,6,5,1,8,7,2,3]=>[3,3,2]=>1120
[5,6,4,1,8,7,2,3]=>[5,3]=>2688
[8,1,4,5,7,6,2,3]=>[7,1]=>5760
[6,4,5,1,8,7,2,3]=>[5,3]=>2688
[5,4,6,1,8,7,2,3]=>[8]=>5040
[4,5,6,1,8,7,2,3]=>[6,2]=>3360
[3,5,6,1,8,2,7,4]=>[7,1]=>5760
[2,5,6,1,8,3,7,4]=>[5,2,1]=>4032
[2,4,6,1,3,8,7,5]=>[4,3,1]=>3360
[3,4,6,1,2,8,7,5]=>[7,1]=>5760
[4,3,6,1,2,8,7,5]=>[5,2,1]=>4032
[5,3,6,1,8,2,7,4]=>[4,3,1]=>3360
[7,3,1,5,8,2,6,4]=>[5,3]=>2688
[8,1,3,5,7,2,6,4]=>[7,1]=>5760
[8,1,2,5,7,3,6,4]=>[8]=>5040
[7,2,1,5,8,3,6,4]=>[4,3,1]=>3360
[6,2,5,1,8,3,7,4]=>[6,1,1]=>3360
[4,2,6,1,3,8,7,5]=>[4,2,1,1]=>2520
[2,3,6,1,4,8,7,5]=>[7,1]=>5760
[4,2,5,3,1,8,7,6]=>[4,2,1,1]=>2520
[6,2,4,1,3,8,7,5]=>[6,1,1]=>3360
[7,2,1,4,3,8,6,5]=>[6,1,1]=>3360
[8,1,2,4,3,7,6,5]=>[5,2,1]=>4032
[8,1,3,4,2,7,6,5]=>[4,2,1,1]=>2520
[7,3,1,4,2,8,6,5]=>[7,1]=>5760
[6,3,4,1,2,8,7,5]=>[7,1]=>5760
[4,6,3,1,2,8,7,5]=>[4,2,1,1]=>2520
[3,6,4,1,2,8,7,5]=>[4,3,1]=>3360
[2,6,4,1,3,8,7,5]=>[7,1]=>5760
[2,7,1,4,3,8,6,5]=>[7,1]=>5760
[3,7,1,4,2,8,6,5]=>[5,2,1]=>4032
[4,7,1,3,2,8,6,5]=>[5,3]=>2688
[8,1,6,7,2,3,5,4]=>[6,2]=>3360
[4,7,1,2,3,8,6,5]=>[8]=>5040
[3,7,1,2,4,8,6,5]=>[6,2]=>3360
[2,7,1,3,4,8,6,5]=>[8]=>5040
[2,6,3,1,4,8,7,5]=>[6,1,1]=>3360
[3,6,2,1,4,8,7,5]=>[7,1]=>5760
[5,6,2,1,8,3,7,4]=>[4,3,1]=>3360
[6,5,2,1,8,3,7,4]=>[7,1]=>5760
[8,1,5,2,7,3,6,4]=>[4,4]=>1260
[8,1,4,2,3,7,6,5]=>[6,2]=>3360
[7,4,1,2,3,8,6,5]=>[6,2]=>3360
[6,4,2,1,3,8,7,5]=>[7,1]=>5760
[5,4,2,3,1,8,7,6]=>[3,2,2,1]=>1680
[3,5,2,4,1,8,7,6]=>[4,2,1,1]=>2520
[6,3,2,1,4,8,7,5]=>[5,2,1]=>4032
[7,3,1,2,4,8,6,5]=>[8]=>5040
[8,1,3,2,4,7,6,5]=>[5,2,1]=>4032
[8,1,2,3,4,7,6,5]=>[6,2]=>3360
[7,2,1,3,4,8,6,5]=>[7,1]=>5760
[6,2,3,1,4,8,7,5]=>[5,1,1,1]=>1344
[2,4,3,6,1,5,8,7]=>[5,2,1]=>4032
[2,4,3,6,5,8,1,7]=>[6,1,1]=>3360
[2,4,6,3,5,8,7,1]=>[6,1,1]=>3360
[2,4,6,3,5,8,1,7]=>[7,1]=>5760
[4,2,6,5,3,1,8,7]=>[5,2,1]=>4032
[4,2,6,5,1,8,7,3]=>[3,3,1,1]=>1120
[4,2,6,5,8,1,7,3]=>[6,1,1]=>3360
[4,2,6,5,8,3,1,7]=>[5,2,1]=>4032
[2,4,6,1,5,8,3,7]=>[4,3,1]=>3360
[2,1,4,6,5,8,3,7]=>[5,2,1]=>4032
[2,4,1,6,5,8,7,3]=>[6,1,1]=>3360
[4,2,6,5,8,3,7,1]=>[4,2,1,1]=>2520
[2,6,4,3,8,7,5,1]=>[6,2]=>3360
[4,2,6,8,5,3,7,1]=>[3,2,1,1,1]=>1120
[2,4,6,8,1,5,7,3]=>[7,1]=>5760
[2,4,6,1,8,5,7,3]=>[4,3,1]=>3360
[2,4,1,6,8,5,7,3]=>[7,1]=>5760
[2,1,4,6,8,5,7,3]=>[5,2,1]=>4032
[2,1,4,6,8,5,3,7]=>[6,2]=>3360
[2,4,6,1,8,5,3,7]=>[5,3]=>2688
[2,4,6,8,1,5,3,7]=>[8]=>5040
[4,2,6,8,5,1,3,7]=>[6,1,1]=>3360
[2,4,6,8,3,5,7,1]=>[4,3,1]=>3360
[2,4,6,8,3,5,1,7]=>[5,3]=>2688
[2,4,6,8,3,1,5,7]=>[8]=>5040
[2,4,6,3,1,8,5,7]=>[8]=>5040
[2,4,6,3,8,1,5,7]=>[5,3]=>2688
[2,4,6,3,8,5,1,7]=>[8]=>5040
[2,4,6,3,8,5,7,1]=>[7,1]=>5760
[2,4,3,6,8,5,7,1]=>[6,1,1]=>3360
[2,4,3,6,8,5,1,7]=>[7,1]=>5760
[2,4,3,6,8,1,5,7]=>[4,3,1]=>3360
[2,4,3,1,6,8,5,7]=>[4,3,1]=>3360
[2,4,1,3,6,8,7,5]=>[4,3,1]=>3360
[2,4,3,6,1,8,7,5]=>[6,1,1]=>3360
[2,4,3,6,8,1,7,5]=>[4,2,1,1]=>2520
[2,4,6,3,8,1,7,5]=>[5,2,1]=>4032
[2,1,4,6,8,3,7,5]=>[3,2,2,1]=>1680
[2,4,1,6,8,3,7,5]=>[5,2,1]=>4032
[2,4,6,8,1,3,7,5]=>[5,2,1]=>4032
[2,4,6,8,3,1,7,5]=>[7,1]=>5760
[4,6,2,8,5,7,1,3]=>[7,1]=>5760
[6,2,4,8,7,1,3,5]=>[5,2,1]=>4032
[6,4,2,8,7,5,3,1]=>[8]=>5040
[2,6,4,8,1,7,5,3]=>[5,3]=>2688
[2,1,6,4,8,7,5,3]=>[5,2,1]=>4032
[2,6,1,4,8,7,3,5]=>[5,2,1]=>4032
[6,4,2,8,7,5,1,3]=>[4,4]=>1260
[1,6,4,7,3,8,2,5]=>[7,1]=>5760
[1,3,7,4,5,8,2,6]=>[3,2,1,1,1]=>1120
[5,2,4,7,3,6,8,1]=>[6,1,1]=>3360
[1,7,6,3,4,8,2,5]=>[5,2,1]=>4032
[8,1,6,3,7,2,4,5]=>[8]=>5040
[7,1,6,3,8,2,4,5]=>[6,2]=>3360
[1,2,7,4,8,3,5,6]=>[5,1,1,1]=>1344
[6,1,7,3,4,8,2,5]=>[8]=>5040
[2,1,7,4,5,8,3,6]=>[2,2,2,1,1]=>420
[5,1,4,7,3,8,2,6]=>[6,2]=>3360
[4,3,1,7,5,8,2,6]=>[5,2,1]=>4032
[2,8,6,3,7,1,4,5]=>[8]=>5040
[6,8,1,3,7,2,4,5]=>[8]=>5040
[5,8,2,1,7,3,4,6]=>[4,4]=>1260
[5,7,2,1,8,3,4,6]=>[8]=>5040
[6,7,1,3,8,2,4,5]=>[6,2]=>3360
[5,1,2,4,8,3,6,7]=>[7,1]=>5760
[4,3,6,1,5,8,2,7]=>[5,2,1]=>4032
[2,6,1,4,5,8,3,7]=>[6,1,1]=>3360
[6,5,1,3,4,8,2,7]=>[8]=>5040
[1,6,2,4,8,3,5,7]=>[3,3,1,1]=>1120
[8,5,1,3,7,2,4,6]=>[8]=>5040
[1,5,3,2,8,4,6,7]=>[6,1,1]=>3360
[6,4,2,1,5,8,3,7]=>[7,1]=>5760
[2,5,3,4,1,8,6,7]=>[3,3,1,1]=>1120
[4,3,5,2,1,8,6,7]=>[5,3]=>2688
[2,6,4,8,7,1,3,5]=>[5,3]=>2688
[1,6,4,8,7,2,3,5]=>[5,2,1]=>4032
[2,7,8,3,6,1,4,5]=>[8]=>5040
[4,3,2,8,7,1,5,6]=>[4,2,2]=>1260
[5,2,4,8,7,1,3,6]=>[7,1]=>5760
[6,2,8,3,7,1,4,5]=>[5,2,1]=>4032
[5,1,4,8,7,2,3,6]=>[8]=>5040
[3,8,2,1,5,4,7,6]=>[6,1,1]=>3360
[8,3,2,1,6,4,5,7]=>[6,2]=>3360
[8,4,2,5,1,6,3,7]=>[7,1]=>5760
[3,8,2,1,4,5,7,6]=>[7,1]=>5760
[3,2,7,1,4,6,8,5]=>[6,1,1]=>3360
[3,2,8,1,4,6,7,5]=>[5,1,1,1]=>1344
[3,2,8,1,4,7,6,5]=>[5,2,1]=>4032
[3,7,2,1,5,8,4,6]=>[5,2,1]=>4032
[3,2,1,7,5,8,6,4]=>[4,2,1,1]=>2520
[4,3,7,6,8,1,2,5]=>[3,3,2]=>1120
[3,2,8,1,6,7,4,5]=>[7,1]=>5760
[3,2,1,8,7,5,6,4]=>[3,2,2,1]=>1680
[3,8,2,1,7,4,5,6]=>[6,2]=>3360
[3,2,8,1,7,4,6,5]=>[7,1]=>5760
[3,2,8,1,6,4,7,5]=>[6,1,1]=>3360
[4,2,7,6,1,3,8,5]=>[7,1]=>5760
[4,2,8,7,1,3,6,5]=>[7,1]=>5760
[4,2,7,8,1,3,6,5]=>[4,3,1]=>3360
[3,2,6,1,8,4,7,5]=>[4,2,1,1]=>2520
[3,7,2,1,8,4,5,6]=>[8]=>5040
[4,7,3,8,5,1,2,6]=>[4,2,1,1]=>2520
[3,2,7,1,8,6,4,5]=>[4,2,1,1]=>2520
[4,3,6,8,7,1,2,5]=>[8]=>5040
[3,2,6,1,7,8,4,5]=>[7,1]=>5760
[5,3,6,4,8,7,1,2]=>[7,1]=>5760
[1,4,6,2,7,8,5,3]=>[3,2,2,1]=>1680
[1,2,7,5,4,8,6,3]=>[4,2,1,1]=>2520
[7,3,8,5,4,6,1,2]=>[3,2,2,1]=>1680
[3,8,7,5,4,6,1,2]=>[3,2,2,1]=>1680
[4,5,6,3,8,7,1,2]=>[5,3]=>2688
[6,8,3,5,4,7,1,2]=>[3,2,2,1]=>1680
[1,6,2,5,4,8,7,3]=>[4,2,1,1]=>2520
[6,2,1,5,4,8,7,3]=>[4,2,1,1]=>2520
[4,1,6,2,8,7,5,3]=>[5,3]=>2688
[7,8,1,2,4,6,5,3]=>[7,1]=>5760
[4,3,6,1,8,2,7,5]=>[3,2,2,1]=>1680
[2,3,8,5,4,1,6,7]=>[6,2]=>3360
[4,8,1,5,2,3,7,6]=>[7,1]=>5760
[3,4,6,1,5,8,2,7]=>[7,1]=>5760
[7,8,4,1,5,3,2,6]=>[7,1]=>5760
[7,8,5,1,6,3,2,4]=>[5,3]=>2688
[2,6,1,5,7,3,8,4]=>[4,4]=>1260
[5,1,7,6,4,3,2,8]=>[7,1]=>5760
[6,1,7,8,4,3,2,5]=>[5,3]=>2688
[7,1,8,6,4,3,2,5]=>[5,3]=>2688
[1,8,7,6,4,3,2,5]=>[7,1]=>5760
[3,1,6,7,5,8,2,4]=>[7,1]=>5760
[7,8,1,6,5,3,2,4]=>[7,1]=>5760
[7,8,2,1,4,5,6,3]=>[5,3]=>2688
[6,1,2,5,7,3,8,4]=>[4,4]=>1260
[4,2,1,5,6,3,7,8]=>[5,1,1,1]=>1344
[4,3,6,1,5,7,2,8]=>[4,2,1,1]=>2520
[1,3,6,8,5,7,2,4]=>[4,2,1,1]=>2520
[6,4,1,5,2,3,7,8]=>[3,3,1,1]=>1120
[4,1,7,5,2,3,8,6]=>[4,4]=>1260
[7,2,3,5,4,1,8,6]=>[4,2,1,1]=>2520
[2,8,3,5,4,1,7,6]=>[4,2,1,1]=>2520
[4,2,6,3,8,1,7,5]=>[4,2,1,1]=>2520
[7,8,2,3,4,1,6,5]=>[5,3]=>2688
[3,1,6,4,7,8,2,5]=>[7,1]=>5760
[1,8,5,7,4,3,2,6]=>[7,1]=>5760
[7,1,5,8,4,3,2,6]=>[5,3]=>2688
[5,1,8,7,4,3,2,6]=>[5,3]=>2688
[6,5,1,8,4,3,2,7]=>[5,3]=>2688
[7,5,8,1,4,3,2,6]=>[5,3]=>2688
[5,8,7,1,4,3,2,6]=>[5,3]=>2688
[7,8,4,6,1,3,2,5]=>[5,3]=>2688
[7,8,5,4,1,3,2,6]=>[7,1]=>5760
[3,5,6,4,1,8,2,7]=>[7,1]=>5760
[7,6,5,1,4,3,2,8]=>[7,1]=>5760
[1,2,3,4,5,6,9,7,8]=>[3,1,1,1,1,1,1]=>168
[1,2,3,4,5,8,6,9,7]=>[4,1,1,1,1,1]=>756
[1,2,3,4,7,5,8,9,6]=>[5,1,1,1,1]=>3024
[1,2,3,6,4,7,8,9,5]=>[6,1,1,1]=>10080
[1,2,5,3,6,7,8,9,4]=>[7,1,1]=>25920
[1,4,2,5,6,7,8,9,3]=>[8,1]=>45360
[9,8,1,2,3,4,5,6,7]=>[5,4]=>18144
[7,8,9,1,2,3,4,5,6]=>[3,3,3]=>2240
[9,8,7,1,2,3,4,5,6]=>[6,3]=>20160
[6,7,8,9,1,2,3,4,5]=>[9]=>40320
[9,6,7,8,1,2,3,4,5]=>[3,2,2,2]=>2520
[8,9,6,7,1,2,3,4,5]=>[9]=>40320
[9,8,6,7,1,2,3,4,5]=>[6,3]=>20160
[9,8,7,6,1,2,3,4,5]=>[4,3,2]=>15120
[9,5,6,7,8,1,2,3,4]=>[9]=>40320
[8,9,5,6,7,1,2,3,4]=>[9]=>40320
[9,8,5,6,7,1,2,3,4]=>[5,4]=>18144
[9,7,8,5,6,1,2,3,4]=>[5,2,2]=>9072
[9,8,7,5,6,1,2,3,4]=>[5,4]=>18144
[9,8,7,6,5,1,2,3,4]=>[4,4,1]=>11340
[7,8,9,4,5,6,1,2,3]=>[2,2,2,1,1,1]=>1260
[9,7,8,4,5,6,1,2,3]=>[6,1,1,1]=>10080
[9,8,7,4,5,6,1,2,3]=>[4,2,1,1,1]=>7560
[8,9,6,7,4,5,1,2,3]=>[9]=>40320
[9,8,6,7,4,5,1,2,3]=>[7,2]=>25920
[9,8,7,6,4,5,1,2,3]=>[4,3,2]=>15120
[9,8,7,6,5,4,1,2,3]=>[4,2,2,1]=>11340
[9,7,8,5,6,3,4,1,2]=>[9]=>40320
[9,8,7,5,6,3,4,1,2]=>[5,4]=>18144
[9,8,7,6,5,3,4,1,2]=>[4,4,1]=>11340
[9,8,7,6,5,4,3,1,2]=>[4,2,2,1]=>11340
[9,10,1,2,3,4,5,6,7,8]=>[5,5]=>72576
[8,9,10,1,2,3,4,5,6,7]=>[10]=>362880
[10,8,9,1,2,3,4,5,6,7]=>[4,3,3]=>50400
[10,9,8,1,2,3,4,5,6,7]=>[6,4]=>151200
[7,8,9,10,1,2,3,4,5,6]=>[5,5]=>72576
[10,7,8,9,1,2,3,4,5,6]=>[10]=>362880
[9,10,7,8,1,2,3,4,5,6]=>[3,3,2,2]=>25200
[10,9,7,8,1,2,3,4,5,6]=>[6,2,2]=>75600
[10,9,8,7,1,2,3,4,5,6]=>[6,4]=>151200
[10,6,7,8,9,1,2,3,4,5]=>[10]=>362880
[9,10,6,7,8,1,2,3,4,5]=>[10]=>362880
[10,9,6,7,8,1,2,3,4,5]=>[6,4]=>151200
[10,8,9,6,7,1,2,3,4,5]=>[10]=>362880
[10,9,8,6,7,1,2,3,4,5]=>[8,2]=>226800
[10,9,8,7,6,1,2,3,4,5]=>[4,4,2]=>56700
[9,10,5,6,7,8,1,2,3,4]=>[5,5]=>72576
[10,9,5,6,7,8,1,2,3,4]=>[10]=>362880
[8,9,10,5,6,7,1,2,3,4]=>[10]=>362880
[10,9,8,5,6,7,1,2,3,4]=>[6,4]=>151200
[9,10,7,8,5,6,1,2,3,4]=>[4,4,1,1]=>56700
[10,9,7,8,5,6,1,2,3,4]=>[8,1,1]=>226800
[10,9,8,7,5,6,1,2,3,4]=>[4,4,1,1]=>56700
[10,9,8,7,6,5,1,2,3,4]=>[4,4,2]=>56700
[10,7,8,9,4,5,6,1,2,3]=>[6,4]=>151200
[9,10,7,8,4,5,6,1,2,3]=>[10]=>362880
[10,9,7,8,4,5,6,1,2,3]=>[8,2]=>226800
[10,9,8,7,4,5,6,1,2,3]=>[4,4,2]=>56700
[10,8,9,6,7,4,5,1,2,3]=>[6,2,2]=>75600
[10,9,8,6,7,4,5,1,2,3]=>[4,2,2,2]=>18900
[10,9,8,7,6,4,5,1,2,3]=>[4,4,2]=>56700
[10,9,8,7,6,5,4,1,2,3]=>[4,2,2,2]=>18900
[9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,1,1]=>4725
[10,9,7,8,5,6,3,4,1,2]=>[4,2,2,1,1]=>56700
[10,9,8,7,5,6,3,4,1,2]=>[4,4,1,1]=>56700
[10,9,8,7,6,5,3,4,1,2]=>[4,4,2]=>56700
[10,9,8,7,6,5,4,3,1,2]=>[4,2,2,2]=>18900
[3,4,6,2,7,1,5,8]=>[3,2,2,1]=>1680
[3,2,7,5,4,1,6,8]=>[4,2,1,1]=>2520
[4,3,6,2,8,1,5,7]=>[5,3]=>2688
[6,1,2,5,4,7,8,3]=>[6,2]=>3360
[4,3,6,8,1,7,2,5]=>[4,4]=>1260
[1,4,6,3,7,5,8,2]=>[7,1]=>5760
[4,6,7,2,5,8,1,3]=>[7,1]=>5760
[2,4,6,1,7,5,3,8]=>[4,3,1]=>3360
[7,5,4,6,2,8,1,3]=>[4,2,2]=>1260
[5,6,3,2,7,1,4,8]=>[6,1,1]=>3360
[5,6,3,2,7,1,8,4]=>[7,1]=>5760
[2,4,1,7,8,5,3,6]=>[5,3]=>2688
[2,5,4,1,6,3,8,7]=>[6,2]=>3360
[3,5,2,1,6,4,7,8]=>[6,1,1]=>3360
[6,8,4,3,2,1,5,7]=>[4,2,2]=>1260
[3,7,5,8,2,1,4,6]=>[8]=>5040
[8,6,4,3,2,1,7,5]=>[5,2,1]=>4032
[6,3,7,2,5,1,8,4]=>[5,2,1]=>4032
[3,6,7,2,8,1,4,5]=>[6,2]=>3360
[6,3,7,2,8,1,4,5]=>[4,2,2]=>1260
[3,2,6,1,7,4,5,8]=>[4,2,1,1]=>2520
[3,5,2,1,4,7,6,8]=>[5,2,1]=>4032
[7,3,5,2,1,8,4,6]=>[6,2]=>3360
[2,5,4,1,3,7,8,6]=>[5,3]=>2688
[3,7,2,8,6,1,4,5]=>[8]=>5040
[5,3,8,2,1,4,7,6]=>[5,2,1]=>4032
[4,8,7,3,2,1,5,6]=>[8]=>5040
[8,4,7,3,2,1,5,6]=>[5,3]=>2688
[8,3,5,2,1,4,7,6]=>[7,1]=>5760
[7,3,2,8,6,1,4,5]=>[6,2]=>3360
[7,8,6,5,4,3,2,1,9]=>[4,2,2,1]=>11340
[1,8,9,7,6,5,4,3,2]=>[4,2,2,1]=>11340
[8,9,7,6,5,4,3,2,1,10]=>[4,2,2,1,1]=>56700
[7,6,8,5,4,3,2,1,9]=>[6,2,1]=>30240
[6,8,7,5,4,3,2,1,9]=>[6,2,1]=>30240
[1,8,7,9,6,5,4,3,2]=>[6,2,1]=>30240
[1,7,9,8,6,5,4,3,2]=>[6,2,1]=>30240
[1,9,10,8,7,6,5,4,3,2]=>[4,2,2,1,1]=>56700
[7,8,3,5,4,6,1,2]=>[2,2,2,1,1]=>420
[8,6,3,7,5,2,4,1]=>[2,2,2,1,1]=>420
[5,4,1,6,3,2,8,7]=>[3,3,2]=>1120
[5,4,1,6,2,3,8,7]=>[6,2]=>3360
[5,7,1,6,2,8,3,4]=>[5,3]=>2688
[5,7,1,6,2,8,4,3]=>[8]=>5040
[2,7,6,5,1,8,3,4]=>[8]=>5040
[2,7,6,5,1,8,4,3]=>[5,3]=>2688
[2,3,6,5,1,4,8,7]=>[6,2]=>3360
[2,3,6,4,1,5,8,7]=>[5,2,1]=>4032
[2,3,6,1,5,4,8,7]=>[5,2,1]=>4032
[2,7,6,1,4,8,5,3]=>[5,3]=>2688
[2,7,6,1,4,8,3,5]=>[8]=>5040
[7,3,5,1,8,4,2,6]=>[8]=>5040
[7,3,5,1,8,6,4,2]=>[4,3,1]=>3360
[2,7,6,1,5,8,4,3]=>[4,3,1]=>3360
[2,7,6,4,1,8,5,3]=>[4,3,1]=>3360
[2,1,7,6,3,8,5,4]=>[3,3,2]=>1120
[2,1,7,6,3,8,4,5]=>[6,2]=>3360
[5,7,3,6,2,8,4,1]=>[7,1]=>5760
[2,7,6,4,1,8,3,5]=>[7,1]=>5760
[7,3,5,1,8,6,2,4]=>[7,1]=>5760
[6,3,5,1,8,2,4,7]=>[8]=>5040
[2,3,4,8,7,6,1,5]=>[7,1]=>5760
[2,3,4,8,5,7,1,6]=>[7,1]=>5760
[7,3,5,4,8,1,2,6]=>[7,1]=>5760
[6,4,3,5,8,7,2,1]=>[7,1]=>5760
[2,1,4,5,8,7,3,6]=>[6,2]=>3360
[6,4,3,5,8,7,1,2]=>[4,3,1]=>3360
[7,3,5,4,8,1,6,2]=>[4,3,1]=>3360
[2,3,4,8,7,5,6,1]=>[5,3]=>2688
[2,3,4,8,7,5,1,6]=>[8]=>5040
[2,7,6,5,4,8,1,3]=>[3,3,2]=>1120
[7,3,5,6,8,4,1,2]=>[4,2,2]=>1260
[7,3,5,6,8,1,4,2]=>[4,4]=>1260
[7,3,5,6,8,1,2,4]=>[8]=>5040
[6,4,1,5,8,7,2,3]=>[8]=>5040
[6,4,1,5,8,7,3,2]=>[4,4]=>1260
[6,4,1,5,8,3,7,2]=>[4,3,1]=>3360
[5,7,1,6,3,8,2,4]=>[3,3,2]=>1120
[6,4,1,5,8,3,2,7]=>[5,3]=>2688
[7,4,1,5,8,2,3,6]=>[5,3]=>2688
[7,4,1,5,8,2,6,3]=>[8]=>5040
[6,3,5,7,8,2,1,4]=>[8]=>5040
[6,3,5,7,8,2,4,1]=>[6,2]=>3360
[2,7,6,4,5,8,3,1]=>[6,1,1]=>3360
[5,7,3,6,1,8,4,2]=>[5,2,1]=>4032
[2,1,4,5,8,6,3,7]=>[5,2,1]=>4032
[7,3,5,4,8,6,2,1]=>[6,1,1]=>3360
[2,3,4,8,5,6,1,7]=>[6,1,1]=>3360
[2,3,4,8,7,1,6,5]=>[8]=>5040
[2,3,4,8,1,7,6,5]=>[6,2]=>3360
[2,3,4,8,1,6,7,5]=>[6,1,1]=>3360
[2,3,4,8,5,1,7,6]=>[6,1,1]=>3360
[6,3,5,4,8,2,7,1]=>[6,1,1]=>3360
[7,4,3,5,8,2,1,6]=>[5,2,1]=>4032
[2,1,4,5,8,3,7,6]=>[5,2,1]=>4032
[7,4,3,5,8,2,6,1]=>[7,1]=>5760
[6,3,5,4,8,2,1,7]=>[7,1]=>5760
[2,3,4,8,5,1,6,7]=>[7,1]=>5760
[2,3,4,8,1,6,5,7]=>[7,1]=>5760
[2,3,4,8,1,5,7,6]=>[7,1]=>5760
[7,8,2,6,1,5,3,4]=>[8]=>5040
[7,8,1,6,2,5,3,4]=>[5,3]=>2688
[1,8,6,7,2,5,3,4]=>[7,1]=>5760
[1,8,5,7,2,6,3,4]=>[6,1,1]=>3360
[5,8,1,7,2,6,3,4]=>[7,1]=>5760
[5,8,2,7,1,6,3,4]=>[5,2,1]=>4032
[2,8,6,7,1,5,3,4]=>[8]=>5040
[2,8,5,7,1,6,3,4]=>[7,1]=>5760
[2,8,1,7,5,6,3,4]=>[6,1,1]=>3360
[1,8,2,7,5,6,3,4]=>[5,1,1,1]=>1344
[1,8,2,7,4,6,3,5]=>[6,1,1]=>3360
[2,8,1,7,4,6,3,5]=>[7,1]=>5760
[2,8,4,7,1,6,3,5]=>[4,3,1]=>3360
[4,8,2,7,1,6,3,5]=>[7,1]=>5760
[4,8,1,7,2,6,3,5]=>[4,3,1]=>3360
[1,8,4,7,2,6,3,5]=>[3,3,1,1]=>1120
[4,8,1,7,5,6,2,3]=>[6,1,1]=>3360
[1,8,4,7,5,6,2,3]=>[5,1,1,1]=>1344
[1,8,3,7,5,6,2,4]=>[4,1,1,1,1]=>420
[3,8,1,7,5,6,2,4]=>[4,2,1,1]=>2520
[3,8,1,7,4,6,2,5]=>[5,2,1]=>4032
[1,8,3,7,4,6,2,5]=>[5,1,1,1]=>1344
[1,8,3,7,2,6,4,5]=>[3,2,1,1,1]=>1120
[3,8,1,7,2,6,4,5]=>[3,2,2,1]=>1680
[3,8,2,7,1,6,4,5]=>[5,2,1]=>4032
[3,8,2,7,4,6,1,5]=>[7,1]=>5760
[3,8,2,7,5,6,1,4]=>[6,1,1]=>3360
[4,8,2,7,5,6,1,3]=>[3,3,1,1]=>1120
[4,8,3,7,5,6,1,2]=>[3,2,1,1,1]=>1120
[3,8,4,7,5,6,1,2]=>[4,2,1,1]=>2520
[2,8,4,7,5,6,1,3]=>[6,1,1]=>3360
[2,8,3,7,5,6,1,4]=>[5,1,1,1]=>1344
[2,8,3,7,4,6,1,5]=>[6,1,1]=>3360
[2,8,3,7,1,6,4,5]=>[4,2,1,1]=>2520
[2,8,1,7,3,6,4,5]=>[5,2,1]=>4032
[7,5,2,8,6,4,1,3]=>[6,2]=>3360
[7,5,1,8,6,2,3,4]=>[3,3,2]=>1120
[7,4,8,6,1,5,2,3]=>[6,2]=>3360
[1,6,7,4,2,8,5,3]=>[6,1,1]=>3360
[1,6,7,3,8,5,2,4]=>[7,1]=>5760
[7,1,8,3,5,6,2,4]=>[3,3,1,1]=>1120
[7,3,8,6,2,5,1,4]=>[6,2]=>3360
[7,4,2,8,6,1,3,5]=>[8]=>5040
[7,3,1,8,4,2,5,6]=>[8]=>5040
[1,5,7,8,2,6,3,4]=>[2,2,2,1,1]=>420
[2,6,3,7,8,5,4,1]=>[5,2,1]=>4032
[2,6,3,7,8,4,5,1]=>[7,1]=>5760
[2,4,7,3,5,6,8,1]=>[6,1,1]=>3360
[2,5,3,7,8,1,6,4]=>[7,1]=>5760
[3,1,5,4,7,8,2,6]=>[5,2,1]=>4032
[5,3,1,4,8,2,6,7]=>[7,1]=>5760
[5,2,4,8,6,1,3,7]=>[4,3,1]=>3360
[5,2,3,8,4,6,7,1]=>[4,1,1,1,1]=>420
[4,8,2,3,5,7,1,6]=>[7,1]=>5760
[1,4,7,8,3,6,2,5]=>[6,1,1]=>3360
[4,8,1,3,6,7,2,5]=>[5,3]=>2688
[6,4,2,8,1,3,7,5]=>[7,1]=>5760
[6,3,8,1,4,7,2,5]=>[8]=>5040
[5,8,1,3,6,2,7,4]=>[7,1]=>5760
[1,5,7,4,2,6,8,3]=>[3,2,1,1,1]=>1120
[5,8,1,4,2,6,3,7]=>[6,1,1]=>3360
[6,5,1,2,8,7,3,4]=>[4,4]=>1260
[6,5,3,1,4,2,8,7]=>[5,2,1]=>4032
[5,3,1,6,4,2,7,8]=>[6,1,1]=>3360
[3,5,6,1,2,8,7,4]=>[5,2,1]=>4032
[3,4,5,8,2,7,1,6]=>[8]=>5040
[3,4,6,2,8,1,5,7]=>[3,3,2]=>1120
[3,5,2,6,8,1,7,4]=>[7,1]=>5760
[4,2,5,6,1,3,8,7]=>[5,2,1]=>4032
[5,3,6,8,4,7,2,1]=>[4,4]=>1260
[3,7,2,5,4,8,6,1]=>[6,2]=>3360
[8,4,2,5,7,3,6,1]=>[6,2]=>3360
[4,7,2,5,8,3,6,1]=>[4,4]=>1260
[5,2,6,8,4,3,7,1]=>[4,2,1,1]=>2520
[3,1,6,5,4,8,2,7]=>[6,2]=>3360
[4,1,6,5,8,3,2,7]=>[6,2]=>3360
[5,1,6,8,4,3,2,7]=>[6,2]=>3360
[8,5,4,7,6,3,2,1]=>[6,2]=>3360
[5,7,1,8,4,3,2,6]=>[6,2]=>3360
[2,7,1,5,4,3,8,6]=>[6,2]=>3360
[8,2,1,5,4,3,7,6]=>[4,2,1,1]=>2520
[8,4,1,5,7,3,2,6]=>[4,4]=>1260
[8,5,6,7,1,3,2,4]=>[6,2]=>3360
[8,4,6,1,7,3,2,5]=>[6,2]=>3360
[8,3,6,1,4,7,2,5]=>[4,4]=>1260
[2,7,6,1,4,3,8,5]=>[6,2]=>3360
[6,7,8,5,1,3,2,4]=>[6,2]=>3360
[5,7,6,8,2,3,4,1]=>[6,2]=>3360
[5,7,2,8,4,3,6,1]=>[4,4]=>1260
[6,7,8,2,4,3,5,1]=>[4,4]=>1260
[4,7,6,2,8,3,5,1]=>[6,2]=>3360
[8,3,6,2,4,7,5,1]=>[6,2]=>3360
[3,7,6,2,4,8,5,1]=>[4,4]=>1260
[5,7,3,8,4,6,2,1]=>[4,2,1,1]=>2520
[4,7,3,5,8,6,2,1]=>[4,2,1,1]=>2520
[8,7,2,1,4,3,6,5]=>[4,4]=>1260
[8,7,3,1,4,6,2,5]=>[4,2,1,1]=>2520
[8,7,6,3,2,5,4,1]=>[6,2]=>3360
[8,7,3,5,1,6,2,4]=>[4,2,1,1]=>2520
[8,7,2,5,1,3,6,4]=>[4,4]=>1260
[8,2,6,5,1,3,7,4]=>[4,2,1,1]=>2520
[8,4,6,5,7,1,2,3]=>[4,4]=>1260
[5,7,6,8,4,1,2,3]=>[6,2]=>3360
[4,7,6,5,8,1,2,3]=>[6,2]=>3360
[3,7,6,5,1,8,2,4]=>[6,2]=>3360
[8,1,2,3,4,5,6,7,9]=>[8,1]=>45360
[1,9,2,3,4,5,6,7,8]=>[8,1]=>45360
[9,1,2,3,4,5,6,7,8,10]=>[9,1]=>403200
[7,8,1,2,3,4,5,6,9]=>[4,4,1]=>11340
[1,8,9,2,3,4,5,6,7]=>[4,4,1]=>11340
[1,10,2,3,4,5,6,7,8,9]=>[9,1]=>403200
[10,1,2,3,4,5,6,7,8,9,11]=>[10,1]=>3991680
[8,9,1,2,3,4,5,6,7,10]=>[9,1]=>403200
[7,1,8,2,3,4,5,6,9]=>[8,1]=>45360
[6,8,1,2,3,4,5,7,9]=>[8,1]=>45360
[1,8,2,9,3,4,5,6,7]=>[8,1]=>45360
[1,7,9,2,3,4,5,6,8]=>[8,1]=>45360
[1,9,10,2,3,4,5,6,7,8]=>[9,1]=>403200
[1,11,2,3,4,5,6,7,8,9,10]=>[10,1]=>3991680
[3,6,4,8,7,5,1,2]=>[8]=>5040
[5,6,4,3,8,7,1,2]=>[6,2]=>3360
[1,6,2,4,7,8,5,3]=>[4,2,1,1]=>2520
[3,4,7,2,8,1,6,5]=>[4,2,2]=>1260
[7,3,8,4,5,6,1,2]=>[3,2,1,1,1]=>1120
[3,5,6,4,8,7,1,2]=>[4,3,1]=>3360
[4,6,8,5,3,7,1,2]=>[8]=>5040
[1,8,5,2,7,3,6,4]=>[4,3,1]=>3360
[4,2,7,5,1,8,6,3]=>[4,3,1]=>3360
[7,8,1,4,2,6,5,3]=>[6,1,1]=>3360
[6,5,1,3,4,2,8,7]=>[6,2]=>3360
[1,6,8,7,4,2,3,5]=>[5,2,1]=>4032
[7,2,1,4,5,6,8,3]=>[4,1,1,1,1]=>420
[1,2,8,3,6,5,7,4]=>[3,2,1,1,1]=>1120
[6,1,3,2,7,5,8,4]=>[7,1]=>5760
[7,6,5,8,1,4,2,3]=>[8]=>5040
[5,8,6,7,3,2,1,4]=>[8]=>5040
[1,8,3,5,4,2,7,6]=>[3,2,1,1,1]=>1120
[2,8,5,7,4,3,1,6]=>[8]=>5040
[5,3,8,7,1,2,6,4]=>[6,2]=>3360
[6,5,3,8,2,1,7,4]=>[2,2,2,1,1]=>420
[7,8,4,6,3,1,2,5]=>[8]=>5040
[2,6,4,5,3,8,1,7]=>[5,3]=>2688
[6,8,5,4,3,1,2,7]=>[3,2,2,1]=>1680
[6,1,4,2,8,5,7,3]=>[7,1]=>5760
[4,8,6,5,3,2,7,1]=>[7,1]=>5760
[8,6,5,1,2,4,7,3]=>[7,1]=>5760
[6,7,5,8,2,1,4,3]=>[6,2]=>3360
[1,7,5,8,2,6,4,3]=>[6,1,1]=>3360
[1,3,8,5,7,6,2,4]=>[6,1,1]=>3360
[6,3,8,5,7,1,2,4]=>[6,2]=>3360
[8,3,1,5,6,2,7,4]=>[7,1]=>5760
[6,8,5,2,1,4,7,3]=>[7,1]=>5760
[3,8,2,5,6,1,7,4]=>[7,1]=>5760
[2,8,1,5,6,3,7,4]=>[7,1]=>5760
[8,1,2,5,6,3,7,4]=>[7,1]=>5760
[1,8,2,5,7,6,3,4]=>[6,1,1]=>3360
[5,1,8,6,2,7,3,4]=>[5,3]=>2688
[2,5,8,6,1,7,3,4]=>[5,3]=>2688
[8,6,1,5,7,2,3,4]=>[6,2]=>3360
[3,8,6,5,7,1,2,4]=>[5,3]=>2688
[7,6,5,8,1,2,4,3]=>[6,2]=>3360
[5,1,7,6,8,4,2,3]=>[6,2]=>3360
[5,1,3,7,8,6,2,4]=>[6,1,1]=>3360
[7,2,5,8,1,6,4,3]=>[6,1,1]=>3360
[3,2,8,5,7,6,1,4]=>[6,1,1]=>3360
[8,2,1,5,7,6,3,4]=>[6,1,1]=>3360
[5,2,8,6,1,7,3,4]=>[5,2,1]=>4032
[1,2,8,6,5,7,3,4]=>[5,1,1,1]=>1344
[4,2,1,3,6,7,8,5]=>[4,3,1]=>3360
[8,2,5,6,3,7,1,4]=>[5,2,1]=>4032
[7,2,6,5,4,1,8,3]=>[5,2,1]=>4032
[6,1,3,5,4,7,8,2]=>[5,2,1]=>4032
[6,1,5,3,4,7,8,2]=>[5,3]=>2688
[7,5,6,2,4,1,8,3]=>[5,3]=>2688
[8,5,2,6,3,7,1,4]=>[5,3]=>2688
[4,3,1,2,6,7,8,5]=>[4,4]=>1260
[8,1,6,5,7,3,2,4]=>[6,2]=>3360
[3,5,8,6,2,7,1,4]=>[6,2]=>3360
[5,8,1,6,3,7,2,4]=>[5,3]=>2688
[1,8,5,6,3,7,2,4]=>[5,2,1]=>4032
[1,7,6,5,4,2,8,3]=>[5,2,1]=>4032
[5,7,6,1,4,2,8,3]=>[5,3]=>2688
[7,1,4,2,6,5,8,3]=>[6,2]=>3360
[4,1,7,3,5,6,8,2]=>[6,1,1]=>3360
[2,7,4,1,5,6,8,3]=>[6,1,1]=>3360
[5,7,6,4,1,2,8,3]=>[5,2,1]=>4032
[4,7,6,1,5,2,8,3]=>[5,2,1]=>4032
[1,7,6,4,5,2,8,3]=>[5,1,1,1]=>1344
[1,8,3,6,5,7,2,4]=>[5,1,1,1]=>1344
[3,8,1,6,5,7,2,4]=>[5,2,1]=>4032
[8,1,3,5,7,6,2,4]=>[6,1,1]=>3360
[7,8,5,4,1,6,2,3]=>[6,1,1]=>3360
[6,1,5,4,3,7,8,2]=>[5,2,1]=>4032
[7,5,6,4,2,1,8,3]=>[5,2,1]=>4032
[8,3,2,6,5,7,1,4]=>[5,2,1]=>4032
[7,4,6,2,5,1,8,3]=>[5,2,1]=>4032
[6,1,4,3,5,7,8,2]=>[5,2,1]=>4032
[6,1,3,4,5,7,8,2]=>[5,1,1,1]=>1344
[7,2,6,4,5,1,8,3]=>[5,1,1,1]=>1344
[8,2,3,6,5,7,1,4]=>[5,1,1,1]=>1344
[3,4,7,2,5,1,6,8]=>[4,2,1,1]=>2520
[1,4,7,2,5,8,3,6]=>[2,2,2,1,1]=>420
[4,3,6,7,5,8,1,2]=>[4,3,1]=>3360
[6,3,7,5,8,4,1,2]=>[8]=>5040
[3,2,7,6,5,1,4,8]=>[5,1,1,1]=>1344
[1,2,7,6,5,8,3,4]=>[3,2,1,1,1]=>1120
[4,8,2,6,1,5,3,7]=>[4,4]=>1260
[4,3,6,2,5,1,8,7]=>[5,2,1]=>4032
[7,8,1,2,5,6,3,4]=>[3,3,1,1]=>1120
[4,1,6,2,5,7,3,8]=>[3,3,1,1]=>1120
[2,1,8,6,4,7,3,5]=>[6,2]=>3360
[1,8,3,6,7,4,5,2]=>[2,2,2,1,1]=>420
[3,1,6,4,7,2,5,8]=>[4,2,1,1]=>2520
[6,8,5,1,3,4,2,7]=>[3,3,2]=>1120
[2,8,3,4,5,1,7,6]=>[4,1,1,1,1]=>420
[1,3,7,4,8,2,5,6]=>[6,1,1]=>3360
[5,3,7,4,1,6,2,8]=>[3,2,1,1,1]=>1120
[5,8,7,6,3,1,2,4]=>[8]=>5040
[7,5,6,8,1,4,3,2]=>[8]=>5040
[1,2,7,8,5,4,3,6]=>[3,2,1,1,1]=>1120
[6,3,1,2,8,4,5,7]=>[5,3]=>2688
[4,2,1,3,6,5,8,7]=>[3,2,2,1]=>1680
[7,8,2,1,4,5,3,6]=>[8]=>5040
[7,8,4,1,5,3,6,2]=>[5,2,1]=>4032
[7,5,1,6,4,3,8,2]=>[8]=>5040
[6,5,1,8,2,7,4,3]=>[6,2]=>3360
[6,8,1,7,5,2,3,4]=>[7,1]=>5760
[5,6,1,7,4,8,2,3]=>[8]=>5040
[3,1,7,5,6,4,8,2]=>[5,3]=>2688
[7,1,8,6,5,4,2,3]=>[3,2,2,1]=>1680
[2,6,5,7,3,4,8,1]=>[6,2]=>3360
[1,6,4,7,5,8,2,3]=>[6,1,1]=>3360
[8,5,3,6,2,7,4,1]=>[3,2,2,1]=>1680
[1,3,7,4,6,8,2,5]=>[3,3,1,1]=>1120
[4,7,5,6,3,2,8,1]=>[6,2]=>3360
[1,7,6,5,4,8,2,3]=>[3,2,2,1]=>1680
[8,1,6,5,7,2,4,3]=>[5,3]=>2688
[1,2,7,6,8,3,4,5]=>[4,2,1,1]=>2520
[6,1,7,5,3,8,2,4]=>[8]=>5040
[2,1,7,5,6,8,3,4]=>[4,2,2]=>1260
[5,4,1,7,6,8,2,3]=>[5,3]=>2688
[4,8,5,6,2,7,3,1]=>[8]=>5040
[3,8,6,4,2,7,5,1]=>[7,1]=>5760
[7,8,5,2,4,6,3,1]=>[7,1]=>5760
[2,8,6,3,7,4,5,1]=>[3,3,2]=>1120
[7,8,1,6,2,4,5,3]=>[6,2]=>3360
[6,8,1,4,7,2,5,3]=>[5,2,1]=>4032
[3,8,4,1,7,2,6,5]=>[5,3]=>2688
[5,4,7,1,8,3,2,6]=>[8]=>5040
[3,7,4,1,8,5,2,6]=>[3,3,2]=>1120
[6,7,1,4,8,3,2,5]=>[3,2,2,1]=>1680
[2,7,1,8,4,5,3,6]=>[4,4]=>1260
[6,1,2,8,4,3,5,7]=>[4,4]=>1260
[6,5,1,4,3,8,2,7]=>[7,1]=>5760
[1,6,2,5,8,3,4,7]=>[4,3,1]=>3360
[8,5,1,3,7,2,6,4]=>[4,4]=>1260
[8,4,2,1,7,3,6,5]=>[8]=>5040
[7,4,2,1,8,5,3,6]=>[5,3]=>2688
[1,5,4,2,8,3,6,7]=>[7,1]=>5760
[6,4,3,1,5,8,2,7]=>[6,1,1]=>3360
[3,7,6,8,4,5,2,1]=>[6,2]=>3360
[2,7,6,8,5,3,4,1]=>[5,2,1]=>4032
[1,7,6,8,5,4,2,3]=>[4,2,1,1]=>2520
[1,4,8,6,7,5,2,3]=>[5,2,1]=>4032
[2,4,8,6,7,3,5,1]=>[6,2]=>3360
[7,3,8,5,4,6,2,1]=>[5,2,1]=>4032
[3,4,8,5,6,7,2,1]=>[5,3]=>2688
[6,3,5,8,4,7,2,1]=>[8]=>5040
[5,4,3,8,6,7,2,1]=>[7,1]=>5760
[5,4,2,8,7,3,6,1]=>[8]=>5040
[6,2,5,8,7,3,4,1]=>[7,1]=>5760
[3,2,8,5,7,4,6,1]=>[4,3,1]=>3360
[1,3,8,7,5,6,2,4]=>[5,1,1,1]=>1344
[2,1,8,7,4,6,3,5]=>[5,2,1]=>4032
[3,1,8,5,7,6,2,4]=>[7,1]=>5760
[6,1,5,8,7,4,2,3]=>[8]=>5040
[5,4,1,8,7,6,2,3]=>[7,1]=>5760
[5,8,6,7,4,3,2,1]=>[6,2]=>3360
[4,8,7,5,6,3,2,1]=>[8]=>5040
[4,2,1,6,3,5,8,7]=>[5,2,1]=>4032
[6,2,1,4,3,5,8,7]=>[4,2,1,1]=>2520
[6,2,1,4,3,8,5,7]=>[6,1,1]=>3360
[8,2,1,4,3,6,5,7]=>[5,1,1,1]=>1344
[6,2,4,1,3,8,5,7]=>[7,1]=>5760
[6,2,4,1,3,5,8,7]=>[5,2,1]=>4032
[2,1,6,4,3,5,8,7]=>[3,2,2,1]=>1680
[2,6,1,4,3,5,8,7]=>[5,2,1]=>4032
[2,6,4,1,3,5,8,7]=>[6,2]=>3360
[4,6,2,1,3,5,8,7]=>[4,2,2]=>1260
[6,4,2,1,3,5,8,7]=>[6,2]=>3360
[8,4,2,1,3,6,5,7]=>[7,1]=>5760
[8,4,2,1,6,3,5,7]=>[8]=>5040
[6,4,2,1,8,3,5,7]=>[5,3]=>2688
[2,6,1,4,3,8,5,7]=>[7,1]=>5760
[2,1,6,4,3,8,5,7]=>[5,2,1]=>4032
[2,1,8,4,3,6,5,7]=>[4,2,1,1]=>2520
[2,8,1,4,3,6,5,7]=>[6,1,1]=>3360
[2,8,4,1,3,6,5,7]=>[7,1]=>5760
[4,8,2,1,3,6,5,7]=>[5,2,1]=>4032
[6,8,2,1,4,3,5,7]=>[8]=>5040
[8,6,2,1,4,3,5,7]=>[5,3]=>2688
[2,8,1,4,6,3,5,7]=>[7,1]=>5760
[2,6,1,4,8,3,5,7]=>[4,3,1]=>3360
[2,6,4,1,8,3,5,7]=>[5,3]=>2688
[4,6,2,8,1,3,5,7]=>[5,3]=>2688
[4,2,6,1,8,3,5,7]=>[3,2,2,1]=>1680
[6,2,4,1,8,3,5,7]=>[4,3,1]=>3360
[4,2,1,6,8,3,5,7]=>[4,3,1]=>3360
[4,2,1,6,3,8,5,7]=>[7,1]=>5760
[4,2,1,3,6,8,5,7]=>[4,3,1]=>3360
[2,1,4,3,8,6,5,7]=>[3,2,2,1]=>1680
[2,4,1,3,8,6,5,7]=>[4,3,1]=>3360
[4,2,1,3,8,6,5,7]=>[3,3,1,1]=>1120
[4,2,1,8,3,6,5,7]=>[6,1,1]=>3360
[4,2,1,8,6,3,5,7]=>[7,1]=>5760
[8,2,1,6,4,3,5,7]=>[7,1]=>5760
[8,2,6,1,4,3,5,7]=>[5,2,1]=>4032
[2,4,8,1,3,6,5,7]=>[4,3,1]=>3360
[2,4,1,8,3,6,5,7]=>[7,1]=>5760
[2,1,4,8,3,6,5,7]=>[5,2,1]=>4032
[2,1,4,8,6,3,5,7]=>[6,2]=>3360
[2,4,8,1,6,3,5,7]=>[5,3]=>2688
[2,4,8,6,1,3,5,7]=>[8]=>5040
[4,2,8,6,1,3,5,7]=>[7,1]=>5760
[8,4,6,2,1,3,5,7]=>[4,2,2]=>1260
[4,6,8,2,1,3,5,7]=>[8]=>5040
[2,6,8,4,1,3,5,7]=>[7,1]=>5760
[2,6,8,1,4,3,5,7]=>[8]=>5040
[2,1,6,8,4,3,5,7]=>[4,2,2]=>1260
[2,1,8,6,4,3,5,7]=>[6,2]=>3360
[2,8,6,4,1,3,5,7]=>[5,2,1]=>4032
[4,8,6,2,1,3,5,7]=>[6,2]=>3360
[6,8,4,2,1,3,5,7]=>[8]=>5040
[3,2,6,1,5,4,8,7]=>[4,2,1,1]=>2520
[5,2,4,3,8,1,7,6]=>[4,2,1,1]=>2520
[6,2,4,1,5,3,8,7]=>[4,2,1,1]=>2520
[4,3,6,1,5,2,8,7]=>[3,2,2,1]=>1680
[4,3,5,2,8,1,7,6]=>[7,1]=>5760
[4,3,7,2,6,5,8,1]=>[6,2]=>3360
[4,3,8,2,6,1,7,5]=>[7,1]=>5760
[4,3,8,1,7,2,6,5]=>[6,2]=>3360
[4,3,8,1,5,2,7,6]=>[4,2,1,1]=>2520
[5,1,8,3,4,2,7,6]=>[7,1]=>5760
[5,4,8,1,3,2,7,6]=>[7,1]=>5760
[2,1,5,4,8,3,7,6]=>[4,2,1,1]=>2520
[5,1,7,6,8,3,4,2]=>[4,4]=>1260
[4,3,7,6,8,1,5,2]=>[5,3]=>2688
[4,3,7,1,8,5,6,2]=>[6,2]=>3360
[4,3,6,5,8,1,7,2]=>[7,1]=>5760
[6,3,5,4,7,2,8,1]=>[7,1]=>5760
[6,3,5,4,8,1,7,2]=>[4,2,1,1]=>2520
[7,1,6,3,8,4,5,2]=>[5,3]=>2688
[7,4,6,5,8,1,3,2]=>[4,4]=>1260
[2,1,8,4,6,3,7,5]=>[4,2,1,1]=>2520
[8,4,6,1,3,2,7,5]=>[7,1]=>5760
[8,1,6,3,4,2,7,5]=>[7,1]=>5760
[8,1,6,3,7,2,5,4]=>[6,2]=>3360
[8,3,5,1,7,2,6,4]=>[5,3]=>2688
[8,3,5,2,6,1,7,4]=>[7,1]=>5760
[7,3,5,2,6,4,8,1]=>[5,3]=>2688
[8,2,6,3,5,1,7,4]=>[5,1,1,1]=>1344
[8,2,7,1,5,3,6,4]=>[3,3,1,1]=>1120
[8,2,4,1,5,3,7,6]=>[5,1,1,1]=>1344
[8,2,4,1,7,3,6,5]=>[7,1]=>5760
[8,2,4,3,6,1,7,5]=>[4,2,1,1]=>2520
[3,2,8,4,6,1,7,5]=>[5,1,1,1]=>1344
[3,2,8,1,5,4,7,6]=>[5,1,1,1]=>1344
[3,2,7,6,8,1,5,4]=>[7,1]=>5760
[3,2,7,1,8,5,6,4]=>[7,1]=>5760
[3,2,6,5,8,1,7,4]=>[3,3,1,1]=>1120
[6,5,7,2,4,3,8,1]=>[5,3]=>2688
[6,5,8,2,4,1,7,3]=>[3,2,2,1]=>1680
[7,2,4,1,8,5,6,3]=>[7,1]=>5760
[7,6,8,2,4,1,5,3]=>[6,2]=>3360
[7,6,8,1,5,2,4,3]=>[3,2,2,1]=>1680
[2,1,7,3,8,5,6,4]=>[6,2]=>3360
[7,1,3,2,8,5,6,4]=>[7,1]=>5760
[7,1,8,5,6,2,4,3]=>[6,2]=>3360
[7,1,8,2,6,4,5,3]=>[6,2]=>3360
[7,2,8,1,5,4,6,3]=>[4,2,1,1]=>2520
[6,2,7,4,5,3,8,1]=>[5,1,1,1]=>1344
[5,4,7,2,6,3,8,1]=>[6,2]=>3360
[5,4,8,2,6,1,7,3]=>[3,2,2,1]=>1680
[6,5,8,1,7,2,4,3]=>[6,2]=>3360
[2,1,6,5,8,3,7,4]=>[3,2,2,1]=>1680
[6,5,7,4,8,1,3,2]=>[3,2,2,1]=>1680
[6,5,7,1,8,3,4,2]=>[5,3]=>2688
[6,1,7,4,8,3,5,2]=>[7,1]=>5760
[5,4,7,1,8,3,6,2]=>[5,3]=>2688
[5,4,6,3,8,1,7,2]=>[7,1]=>5760
[2,1,4,3,7,8,6,5,11,12,10,9]=>[4,4,2,2]=>1871100
[2,1,4,3,9,10,11,12,8,7,6,5]=>[4,4,2,2]=>1871100
[2,1,5,6,4,3,8,7,11,12,10,9]=>[4,4,2,2]=>1871100
[2,1,5,6,4,3,9,10,8,7,12,11]=>[4,4,2,2]=>1871100
[2,1,5,6,4,3,9,11,8,12,10,7]=>[6,4,2]=>9979200
[2,1,5,6,4,3,10,11,12,9,8,7]=>[4,4,2,2]=>1871100
[2,1,5,7,4,8,6,3,11,12,10,9]=>[6,4,2]=>9979200
[2,1,5,9,4,10,11,12,8,7,6,3]=>[6,4,2]=>9979200
[2,1,6,7,8,5,4,3,11,12,10,9]=>[4,4,2,2]=>1871100
[2,1,6,8,10,5,11,7,12,9,4,3]=>[6,4,2]=>9979200
[2,1,7,8,9,10,6,5,4,3,12,11]=>[4,4,2,2]=>1871100
[2,1,7,8,9,11,6,5,4,12,10,3]=>[6,4,2]=>9979200
[2,1,8,9,10,11,12,7,6,5,4,3]=>[4,4,2,2]=>1871100
[3,4,2,1,6,5,8,7,11,12,10,9]=>[4,4,2,2]=>1871100
[3,4,2,1,6,5,9,10,8,7,12,11]=>[4,4,2,2]=>1871100
[3,4,2,1,6,5,9,11,8,12,10,7]=>[6,4,2]=>9979200
[3,4,2,1,6,5,10,11,12,9,8,7]=>[4,4,2,2]=>1871100
[3,4,2,1,7,8,6,5,10,9,12,11]=>[4,4,2,2]=>1871100
[3,4,2,1,7,8,6,5,11,12,10,9]=>[4,4,4]=>1247400
[3,4,2,1,7,9,6,10,8,5,12,11]=>[6,4,2]=>9979200
[3,4,2,1,7,10,6,11,12,9,8,5]=>[6,4,2]=>9979200
[3,4,2,1,8,9,10,7,6,5,12,11]=>[4,4,2,2]=>1871100
[3,4,2,1,8,9,11,7,6,12,10,5]=>[6,4,2]=>9979200
[3,4,2,1,9,10,11,12,8,7,6,5]=>[4,4,4]=>1247400
[3,5,2,6,4,1,8,7,11,12,10,9]=>[6,4,2]=>9979200
[3,5,2,6,4,1,9,10,8,7,12,11]=>[6,4,2]=>9979200
[3,5,2,6,4,1,9,11,8,12,10,7]=>[6,6]=>6652800
[3,5,2,6,4,1,10,11,12,9,8,7]=>[6,4,2]=>9979200
[3,5,2,7,4,9,6,11,8,12,10,1]=>[12]=>39916800
[3,5,2,8,4,10,11,7,12,9,6,1]=>[12]=>39916800
[3,6,2,7,8,5,4,1,11,12,10,9]=>[6,4,2]=>9979200
[3,6,2,8,9,5,11,7,4,12,10,1]=>[12]=>39916800
[3,6,2,9,10,5,11,12,8,7,4,1]=>[12]=>39916800
[3,7,2,8,9,10,6,5,4,1,12,11]=>[6,4,2]=>9979200
[3,7,2,8,10,11,6,5,12,9,4,1]=>[12]=>39916800
[3,8,2,9,10,11,12,7,6,5,4,1]=>[6,4,2]=>9979200
[4,5,6,3,2,1,8,7,11,12,10,9]=>[4,4,2,2]=>1871100
[4,5,6,3,2,1,9,10,8,7,12,11]=>[4,4,2,2]=>1871100
[4,5,6,3,2,1,9,11,8,12,10,7]=>[6,4,2]=>9979200
[4,5,6,3,2,1,10,11,12,9,8,7]=>[4,4,2,2]=>1871100
[4,5,7,3,2,8,6,1,11,12,10,9]=>[6,4,2]=>9979200
[4,5,9,3,2,10,11,12,8,7,6,1]=>[6,4,2]=>9979200
[4,6,7,3,9,5,2,11,8,12,10,1]=>[12]=>39916800
[4,6,8,3,9,5,10,7,2,1,12,11]=>[6,4,2]=>9979200
[4,6,8,3,10,5,11,7,12,9,2,1]=>[12]=>39916800
[4,6,9,3,10,5,11,12,8,7,2,1]=>[6,6]=>6652800
[4,7,8,3,9,11,6,5,2,12,10,1]=>[12]=>39916800
[4,7,9,3,10,11,6,12,8,5,2,1]=>[6,4,2]=>9979200
[5,6,7,8,4,3,2,1,10,9,12,11]=>[4,4,2,2]=>1871100
[5,6,7,8,4,3,2,1,11,12,10,9]=>[4,4,4]=>1247400
[5,6,7,9,4,3,2,10,8,1,12,11]=>[6,4,2]=>9979200
[5,6,7,10,4,3,2,11,12,9,8,1]=>[6,4,2]=>9979200
[5,6,8,9,4,3,11,7,2,12,10,1]=>[12]=>39916800
[5,6,8,10,4,3,11,7,12,9,2,1]=>[6,6]=>6652800
[5,6,9,10,4,3,11,12,8,7,2,1]=>[12]=>39916800
[5,7,8,10,4,11,6,3,12,9,2,1]=>[6,4,2]=>9979200
[5,8,9,10,4,11,12,7,6,3,2,1]=>[12]=>39916800
[6,7,8,9,10,5,4,3,2,1,12,11]=>[4,4,2,2]=>1871100
[6,7,8,9,11,5,4,3,2,12,10,1]=>[6,4,2]=>9979200
[6,7,9,10,11,5,4,12,8,3,2,1]=>[12]=>39916800
[7,8,9,10,11,12,6,5,4,3,2,1]=>[4,4,4]=>1247400
[2,8,3,1,5,4,6,7]=>[6,1,1]=>3360
[2,5,3,4,7,1,8,6]=>[6,1,1]=>3360
[2,4,8,3,5,7,6,1]=>[5,2,1]=>4032
[4,2,5,3,1,8,6,7]=>[4,3,1]=>3360
[4,2,1,8,5,3,6,7]=>[6,1,1]=>3360
[5,4,1,3,8,2,6,7]=>[8]=>5040
[5,1,4,8,3,2,6,7]=>[8]=>5040
[1,5,8,4,3,2,6,7]=>[6,1,1]=>3360
[1,8,5,4,3,2,6,7]=>[4,2,1,1]=>2520
[1,7,4,3,8,5,2,6]=>[3,2,2,1]=>1680
[1,5,7,3,8,4,2,6]=>[7,1]=>5760
[5,1,4,7,8,3,2,6]=>[8]=>5040
[4,8,1,5,7,3,6,2]=>[6,2]=>3360
[8,1,5,3,7,4,6,2]=>[5,3]=>2688
[3,8,4,7,6,5,2,1]=>[6,2]=>3360
[1,6,8,5,3,7,4,2]=>[7,1]=>5760
[6,8,1,7,4,3,5,2]=>[3,3,2]=>1120
[6,4,8,1,7,3,5,2]=>[6,2]=>3360
[6,4,8,7,1,5,2,3]=>[3,3,2]=>1120
[7,6,4,1,3,8,2,5]=>[8]=>5040
[1,7,5,6,3,2,8,4]=>[5,2,1]=>4032
[4,2,1,7,8,5,3,6]=>[4,3,1]=>3360
[2,7,4,6,3,1,8,5]=>[8]=>5040
[2,6,8,4,3,7,5,1]=>[7,1]=>5760
[6,2,4,8,3,7,5,1]=>[7,1]=>5760
[7,2,6,3,4,1,8,5]=>[7,1]=>5760
[2,6,7,3,1,4,8,5]=>[8]=>5040
[2,7,1,8,3,5,4,6]=>[8]=>5040
[2,1,7,3,5,8,4,6]=>[3,2,2,1]=>1680
[8,7,1,3,6,2,4,5]=>[8]=>5040
[8,2,1,7,3,5,6,4]=>[7,1]=>5760
[7,8,2,6,3,1,5,4]=>[8]=>5040
[8,7,2,6,3,5,4,1]=>[6,2]=>3360
[1,2,8,7,4,5,6,3]=>[4,2,1,1]=>2520
[8,3,7,1,5,6,2,4]=>[3,3,1,1]=>1120
[8,6,1,2,7,5,3,4]=>[8]=>5040
[8,1,6,2,7,4,5,3]=>[6,2]=>3360
[1,8,5,2,6,7,4,3]=>[7,1]=>5760
[5,2,1,8,6,7,4,3]=>[7,1]=>5760
[2,8,5,7,6,4,3,1]=>[5,3]=>2688
[1,7,8,5,2,6,4,3]=>[4,2,1,1]=>2520
[7,8,1,6,4,2,5,3]=>[8]=>5040
[7,8,6,1,5,3,2,4]=>[5,2,1]=>4032
[7,3,8,6,1,5,2,4]=>[8]=>5040
[8,7,6,1,5,3,4,2]=>[5,2,1]=>4032
[8,7,1,6,4,5,3,2]=>[5,3]=>2688
[8,1,7,5,6,4,3,2]=>[3,3,2]=>1120
[1,8,6,7,5,4,3,2]=>[4,2,1,1]=>2520
[6,3,5,2,1,4,8,7]=>[6,2]=>3360
[6,3,5,7,2,8,4,1]=>[3,3,2]=>1120
[8,5,2,7,4,3,1,6]=>[8]=>5040
[4,5,3,6,1,2,8,7]=>[5,2,1]=>4032
[3,5,1,4,6,2,8,7]=>[3,2,2,1]=>1680
[8,3,4,5,7,2,1,6]=>[8]=>5040
[5,7,4,6,3,8,2,1]=>[6,2]=>3360
[2,8,4,6,3,7,1,5]=>[8]=>5040
[8,1,4,7,3,6,2,5]=>[7,1]=>5760
[8,3,4,7,5,1,2,6]=>[4,3,1]=>3360
[8,5,1,4,7,3,2,6]=>[4,3,1]=>3360
[8,5,3,7,1,4,2,6]=>[7,1]=>5760
[2,1,8,5,7,4,3,6]=>[6,2]=>3360
[6,5,3,7,1,8,4,2]=>[5,2,1]=>4032
[6,5,1,4,7,8,3,2]=>[7,1]=>5760
[6,3,4,7,5,8,1,2]=>[7,1]=>5760
[5,1,4,6,8,3,7,2]=>[4,3,1]=>3360
[4,7,1,3,5,8,6,2]=>[4,3,1]=>3360
[4,8,3,7,1,2,6,5]=>[7,1]=>5760
[3,8,6,4,1,7,2,5]=>[7,1]=>5760
[3,8,1,2,5,7,6,4]=>[3,2,2,1]=>1680
[2,8,7,5,4,1,3,6]=>[4,2,2]=>1260
[8,7,2,6,4,1,3,5]=>[5,3]=>2688
[3,8,6,7,4,2,1,5]=>[8]=>5040
[5,7,6,8,4,2,3,1]=>[4,4]=>1260
[5,3,7,8,2,4,6,1]=>[8]=>5040
[8,3,6,2,1,4,7,5]=>[4,3,1]=>3360
[5,3,7,6,2,1,8,4]=>[8]=>5040
[5,3,6,2,8,7,1,4]=>[8]=>5040
[5,7,8,6,4,2,1,3]=>[6,2]=>3360
[2,6,7,5,4,8,1,3]=>[6,2]=>3360
[6,1,7,4,5,8,2,3]=>[6,1,1]=>3360
[6,7,3,5,1,8,2,4]=>[5,2,1]=>4032
[2,1,6,7,5,8,3,4]=>[5,2,1]=>4032
[2,1,5,7,3,6,8,4]=>[3,2,2,1]=>1680
[5,7,3,6,1,2,8,4]=>[5,2,1]=>4032
[4,1,7,2,5,6,8,3]=>[3,3,1,1]=>1120
[2,4,7,1,6,5,8,3]=>[3,3,2]=>1120
[4,6,2,1,8,7,5,3]=>[6,2]=>3360
[3,4,6,2,7,8,5,1]=>[4,2,2]=>1260
[4,6,1,2,5,8,7,3]=>[6,1,1]=>3360
[5,6,1,4,8,2,7,3]=>[4,2,1,1]=>2520
[5,6,3,1,8,7,2,4]=>[4,3,1]=>3360
[3,5,6,4,7,1,8,2]=>[4,3,1]=>3360
[3,4,6,1,5,7,8,2]=>[7,1]=>5760
[3,4,1,5,7,6,8,2]=>[5,2,1]=>4032
[3,8,2,7,1,6,5,4]=>[7,1]=>5760
[3,8,2,7,6,1,5,4]=>[8]=>5040
[3,8,2,7,6,5,1,4]=>[6,2]=>3360
[3,8,2,7,6,5,4,1]=>[4,2,2]=>1260
[4,8,7,2,6,5,3,1]=>[4,2,2]=>1260
[4,8,7,2,6,5,1,3]=>[6,2]=>3360
[4,8,7,2,6,1,5,3]=>[8]=>5040
[4,8,7,2,1,6,5,3]=>[7,1]=>5760
[4,8,7,3,1,6,5,2]=>[5,2,1]=>4032
[4,8,7,3,2,1,6,5]=>[5,3]=>2688
[4,8,7,3,2,6,1,5]=>[4,3,1]=>3360
[4,8,7,3,2,6,5,1]=>[7,1]=>5760
[4,8,7,3,6,2,5,1]=>[8]=>5040
[4,8,7,3,6,2,1,5]=>[4,4]=>1260
[4,8,7,3,6,1,5,2]=>[6,2]=>3360
[4,8,7,3,6,5,1,2]=>[4,2,2]=>1260
[4,8,7,3,6,5,2,1]=>[6,2]=>3360
[5,8,7,6,3,4,2,1]=>[6,2]=>3360
[5,8,7,6,3,1,4,2]=>[6,2]=>3360
[5,8,7,6,3,2,4,1]=>[8]=>5040
[5,8,7,6,2,4,3,1]=>[4,2,2]=>1260
[5,8,7,6,2,1,4,3]=>[8]=>5040
[5,8,7,6,4,2,3,1]=>[6,2]=>3360
[5,8,7,6,4,2,1,3]=>[8]=>5040
[5,8,7,6,4,1,3,2]=>[4,2,2]=>1260
[5,8,7,6,4,3,1,2]=>[6,2]=>3360
[7,3,5,2,6,4,1,8]=>[5,2,1]=>4032
[7,2,1,5,6,4,3,8]=>[3,3,1,1]=>1120
[1,4,6,7,3,8,2,5]=>[4,3,1]=>3360
[6,4,5,7,1,3,8,2]=>[4,4]=>1260
[6,3,5,1,7,4,8,2]=>[5,3]=>2688
[2,4,6,7,3,8,1,5]=>[4,4]=>1260
[1,4,6,7,3,8,5,2]=>[7,1]=>5760
[1,5,6,7,8,3,4,2]=>[3,2,2,1]=>1680
[2,5,6,7,8,3,1,4]=>[6,2]=>3360
[3,2,1,6,7,8,4,5]=>[5,2,1]=>4032
[5,2,1,6,7,8,4,3]=>[7,1]=>5760
[5,3,6,1,7,8,4,2]=>[4,4]=>1260
[6,4,5,7,2,1,8,3]=>[6,2]=>3360
[5,4,6,7,2,8,3,1]=>[8]=>5040
[6,3,5,2,7,1,8,4]=>[6,2]=>3360
[6,3,4,2,1,7,8,5]=>[5,3]=>2688
[3,4,6,7,2,8,5,1]=>[4,4]=>1260
[4,2,1,5,7,3,8,6]=>[7,1]=>5760
[1,5,6,7,8,2,4,3]=>[5,2,1]=>4032
[1,5,6,7,8,4,2,3]=>[7,1]=>5760
[3,4,6,7,1,8,5,2]=>[8]=>5040
[4,3,6,1,7,8,5,2]=>[4,2,2]=>1260
[2,1,4,3,6,5,8,7,9]=>[2,2,2,2,1]=>945
[2,4,1,3,6,5,8,7,9]=>[4,2,2,1]=>11340
[2,4,1,6,3,5,8,7,9]=>[6,2,1]=>30240
[2,4,1,6,3,8,5,7,9]=>[8,1]=>45360
[2,4,1,6,3,7,5,9,8]=>[7,2]=>25920
[2,4,1,5,3,7,6,9,8]=>[5,2,2]=>9072
[2,3,1,5,4,7,6,9,8]=>[3,2,2,2]=>2520
[1,3,2,5,4,7,6,9,8]=>[2,2,2,2,1]=>945
[2,4,1,3,6,5,8,7,10,9]=>[4,2,2,2]=>18900
[2,4,6,1,3,5,8,7,9]=>[3,3,2,1]=>10080
[2,4,1,6,3,5,8,7,10,9]=>[6,2,2]=>75600
[2,4,1,6,8,3,5,7,9]=>[5,3,1]=>24192
[2,4,1,6,3,8,5,7,10,9]=>[8,2]=>226800
[2,4,1,6,3,8,9,5,7]=>[7,2]=>25920
[2,4,1,6,3,8,5,10,7,9]=>[10]=>362880
[2,4,1,6,3,7,5,8,9]=>[7,1,1]=>25920
[2,4,1,6,3,8,5,9,7,10]=>[9,1]=>403200
[2,4,1,5,3,8,6,9,7]=>[5,4]=>18144
[2,4,1,6,3,7,5,9,8,10]=>[7,2,1]=>259200
[2,3,1,6,4,7,5,9,8]=>[4,3,2]=>15120
[2,4,1,5,3,7,6,9,8,10]=>[5,2,2,1]=>90720
[1,4,2,5,3,7,6,9,8]=>[4,2,2,1]=>11340
[2,3,1,5,4,7,6,9,8,10]=>[3,2,2,2,1]=>25200
[1,3,2,5,4,7,6,9,8,10]=>[2,2,2,2,1,1]=>4725
[7,1,2,3,4,5,6,8,9]=>[7,1,1]=>25920
[1,4,3,6,2,5,7,8]=>[4,1,1,1,1]=>420
[1,4,3,7,2,5,6,8]=>[5,1,1,1]=>1344
[1,4,3,7,6,8,2,5]=>[3,3,1,1]=>1120
[1,4,3,7,5,8,2,6]=>[3,2,1,1,1]=>1120
[1,4,3,7,2,6,5,8]=>[4,1,1,1,1]=>420
[1,5,3,7,4,8,2,6]=>[4,2,1,1]=>2520
[1,3,2,6,5,8,4,7]=>[4,2,1,1]=>2520
[1,5,4,8,2,6,3,7]=>[4,2,1,1]=>2520
[1,5,4,8,3,7,2,6]=>[7,1]=>5760
[1,2,3,6,5,8,4,7]=>[4,1,1,1,1]=>420
[6,8,2,4,5,7,1,3]=>[3,3,1,1]=>1120
[3,7,8,4,5,2,6,1]=>[3,3,1,1]=>1120
[7,8,1,4,5,3,6,2]=>[4,2,1,1]=>2520
[3,8,7,4,1,6,5,2]=>[4,2,1,1]=>2520
[4,8,3,6,1,5,7,2]=>[4,2,1,1]=>2520
[5,8,3,1,6,4,7,2]=>[4,2,1,1]=>2520
[5,8,1,4,7,6,3,2]=>[4,2,1,1]=>2520
[7,5,1,8,6,2,4,3]=>[5,3]=>2688
[7,4,1,8,2,6,3,5]=>[4,3,1]=>3360
[7,1,8,4,2,6,3,5]=>[6,1,1]=>3360
[1,6,3,8,5,2,4,7]=>[3,2,1,1,1]=>1120
[6,1,3,8,5,2,4,7]=>[3,3,1,1]=>1120
[7,2,8,4,1,6,5,3]=>[3,2,1,1,1]=>1120
[7,2,8,3,6,5,1,4]=>[3,2,2,1]=>1680
[7,2,8,3,6,1,5,4]=>[4,3,1]=>3360
[7,1,8,2,3,6,5,4]=>[7,1]=>5760
[1,5,2,3,8,4,7,6]=>[6,1,1]=>3360
[5,1,2,3,8,4,7,6]=>[7,1]=>5760
[6,2,8,1,3,5,4,7]=>[7,1]=>5760
[6,3,1,4,2,8,5,7]=>[7,1]=>5760
[3,1,6,4,2,8,5,7]=>[7,1]=>5760
[2,6,3,8,7,1,5,4]=>[3,2,2,1]=>1680
[2,6,3,8,5,1,4,7]=>[3,3,1,1]=>1120
[2,5,1,3,8,4,7,6]=>[7,1]=>5760
[1,2,5,3,8,4,7,6]=>[5,1,1,1]=>1344
[1,2,4,8,3,7,6,5]=>[4,2,1,1]=>2520
[2,4,8,1,3,7,6,5]=>[3,3,2]=>1120
[2,4,8,3,7,1,6,5]=>[8]=>5040
[2,4,8,3,7,6,1,5]=>[7,1]=>5760
[2,5,4,1,3,8,7,6]=>[5,2,1]=>4032
[4,8,2,3,7,6,1,5]=>[7,1]=>5760
[4,8,2,3,7,1,6,5]=>[8]=>5040
[4,8,1,2,3,7,6,5]=>[6,2]=>3360
[1,4,8,2,3,7,6,5]=>[3,2,2,1]=>1680
[1,4,8,3,7,2,6,5]=>[7,1]=>5760
[6,3,8,1,5,2,4,7]=>[7,1]=>5760
[5,3,8,1,2,4,7,6]=>[7,1]=>5760
[6,5,1,2,8,7,4,3]=>[8]=>5040
[5,3,1,6,4,2,8,7]=>[6,2]=>3360
[5,1,6,2,8,7,4,3]=>[8]=>5040
[1,4,2,5,8,7,6,3]=>[5,2,1]=>4032
[4,3,1,5,8,2,7,6]=>[7,1]=>5760
[3,4,8,7,2,6,1,5]=>[7,1]=>5760
[3,4,8,7,1,2,6,5]=>[4,4]=>1260
[3,4,8,1,7,2,6,5]=>[8]=>5040
[1,3,4,8,7,2,6,5]=>[7,1]=>5760
[1,3,4,8,2,7,6,5]=>[5,2,1]=>4032
[3,4,8,1,2,7,6,5]=>[6,2]=>3360
[3,4,8,2,7,1,6,5]=>[6,2]=>3360
[3,4,8,2,7,6,1,5]=>[5,2,1]=>4032
[7,8,2,1,5,3,6,4]=>[7,1]=>5760
[6,4,1,2,7,3,5,8]=>[3,2,2,1]=>1680
[2,3,7,5,4,1,8,6]=>[6,2]=>3360
[6,3,1,5,4,2,7,8]=>[4,2,1,1]=>2520
[7,8,1,5,4,2,6,3]=>[6,2]=>3360
[7,8,3,5,4,1,6,2]=>[3,2,2,1]=>1680
[7,8,2,5,4,1,3,6]=>[6,2]=>3360
[7,8,2,5,4,6,1,3]=>[3,2,2,1]=>1680
[6,2,1,5,4,7,3,8]=>[4,2,1,1]=>2520
[5,3,6,1,4,7,8,2]=>[5,3]=>2688
[5,3,6,2,4,7,1,8]=>[7,1]=>5760
[6,4,2,1,7,3,8,5]=>[5,3]=>2688
[4,3,7,5,8,6,1,2]=>[7,1]=>5760
[4,2,7,1,8,3,6,5]=>[3,2,2,1]=>1680
[3,2,6,7,4,8,1,5]=>[7,1]=>5760
[3,1,6,7,4,8,5,2]=>[5,3]=>2688
[1,7,6,5,3,8,4,2]=>[7,1]=>5760
[2,7,6,5,3,8,1,4]=>[5,3]=>2688
[1,7,6,5,2,4,8,3]=>[7,1]=>5760
[2,7,6,5,3,1,4,8]=>[7,1]=>5760
[2,7,1,4,8,3,5,6]=>[7,1]=>5760
[3,7,6,4,8,5,1,2]=>[7,1]=>5760
[5,7,6,3,8,4,1,2]=>[5,3]=>2688
[5,1,6,2,4,8,3,7]=>[4,4]=>1260
[4,7,6,5,2,1,3,8]=>[7,1]=>5760
[4,7,6,5,2,8,1,3]=>[5,3]=>2688
[4,7,6,5,1,8,3,2]=>[5,3]=>2688
[1,7,6,5,2,8,3,4]=>[7,1]=>5760
[1,7,6,5,3,2,8,4]=>[7,1]=>5760
[4,7,6,5,1,2,8,3]=>[5,3]=>2688
[4,7,6,5,3,1,8,2]=>[5,3]=>2688
[6,1,3,5,4,8,7,2]=>[4,2,1,1]=>2520
[5,2,6,3,4,1,7,8]=>[5,1,1,1]=>1344
[5,1,6,2,4,7,8,3]=>[4,4]=>1260
[1,2,6,3,4,8,7,5]=>[5,1,1,1]=>1344
[1,7,2,4,8,3,6,5]=>[4,2,1,1]=>2520
[6,1,4,2,8,3,5,7]=>[5,3]=>2688
[4,1,8,2,6,3,5,7]=>[5,3]=>2688
[4,7,2,1,5,3,6,8]=>[4,2,1,1]=>2520
[4,7,1,6,2,3,8,5]=>[4,4]=>1260
[1,7,2,6,8,3,5,4]=>[7,1]=>5760
[1,2,6,7,4,8,5,3]=>[3,3,1,1]=>1120
[3,1,6,7,4,2,8,5]=>[4,4]=>1260
[3,2,8,5,4,6,1,7]=>[4,2,1,1]=>2520
[4,7,6,3,5,8,1,2]=>[7,1]=>5760
[4,7,1,2,5,3,8,6]=>[7,1]=>5760
[3,7,6,5,2,4,1,8]=>[7,1]=>5760
[3,7,6,5,1,4,8,2]=>[5,3]=>2688
[3,7,6,5,2,1,8,4]=>[5,3]=>2688
[1,7,6,5,8,2,4,3]=>[7,1]=>5760
[3,7,6,5,8,1,4,2]=>[5,3]=>2688
[3,7,6,5,1,2,4,8]=>[7,1]=>5760
[3,1,6,8,4,2,5,7]=>[4,4]=>1260
[4,7,6,8,3,5,1,2]=>[5,3]=>2688
[2,7,6,5,1,4,3,8]=>[7,1]=>5760
[2,7,6,5,8,1,3,4]=>[5,3]=>2688
[2,7,6,5,8,4,1,3]=>[5,3]=>2688
[6,3,2,1,7,4,8,5]=>[3,3,2]=>1120
[4,2,1,7,3,5,8,6]=>[7,1]=>5760
[8,4,1,5,2,7,6,3]=>[3,3,2]=>1120
[8,2,5,1,3,7,6,4]=>[3,2,2,1]=>1680
[4,3,7,2,1,5,8,6]=>[8]=>5040
[4,7,2,5,3,1,8,6]=>[8]=>5040
[2,7,5,4,1,3,8,6]=>[7,1]=>5760
[7,5,4,3,2,1,8,6]=>[4,2,2]=>1260
[6,5,2,1,8,4,3,7]=>[5,3]=>2688
[5,7,4,3,2,8,1,6]=>[4,2,2]=>1260
[1,7,6,2,4,8,3,5]=>[7,1]=>5760
[2,7,3,6,4,8,1,5]=>[4,3,1]=>3360
[6,2,7,5,3,8,1,4]=>[7,1]=>5760
[7,1,8,5,3,6,4,2]=>[7,1]=>5760
[5,8,3,2,7,1,6,4]=>[4,3,1]=>3360
[8,7,2,6,1,5,4,3]=>[8]=>5040
[1,8,5,7,4,3,6,2]=>[5,2,1]=>4032
[1,8,5,7,2,4,6,3]=>[4,3,1]=>3360
[3,8,6,1,7,2,5,4]=>[6,2]=>3360
[7,2,8,5,6,1,4,3]=>[5,2,1]=>4032
[6,3,7,5,8,2,1,4]=>[5,3]=>2688
[3,7,2,6,8,4,1,5]=>[4,2,2]=>1260
[3,6,5,8,1,4,2,7]=>[5,3]=>2688
[2,6,5,8,4,1,3,7]=>[5,3]=>2688
[6,3,5,1,8,4,2,7]=>[5,3]=>2688
[8,4,1,5,7,3,6,2]=>[8]=>5040
[5,4,1,6,8,2,3,7]=>[5,3]=>2688
[6,3,7,4,8,5,2,1]=>[4,3,1]=>3360
[4,7,2,5,8,6,3,1]=>[4,3,1]=>3360
[6,3,1,8,4,7,5,2]=>[8]=>5040
[6,5,3,8,7,4,1,2]=>[7,1]=>5760
[5,4,8,1,7,6,2,3]=>[5,2,1]=>4032
[5,2,8,1,7,3,6,4]=>[7,1]=>5760
[6,4,7,8,1,5,3,2]=>[3,3,2]=>1120
[5,3,8,7,2,1,6,4]=>[8]=>5040
[8,3,7,6,1,5,4,2]=>[8]=>5040
[8,2,7,6,5,1,4,3]=>[6,1,1]=>3360
[4,3,8,7,6,2,1,5]=>[5,3]=>2688
[2,4,8,7,6,1,3,5]=>[8]=>5040
[3,5,8,7,2,6,1,4]=>[5,2,1]=>4032
[4,7,3,8,6,5,1,2]=>[5,2,1]=>4032
[7,5,8,6,4,3,2,1]=>[8]=>5040
[5,8,7,3,6,4,2,1]=>[8]=>5040
[4,8,7,6,2,5,3,1]=>[6,2]=>3360
[3,8,7,6,5,1,4,2]=>[5,2,1]=>4032
[2,8,7,6,5,4,1,3]=>[5,2,1]=>4032
[3,4,1,2,5,6,7,8,9]=>[2,2,1,1,1,1,1]=>378
[3,2,1,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]=>36
[4,5,6,1,2,3,7,8,9]=>[2,2,2,1,1,1]=>1260
[4,2,5,1,3,6,7,8,9]=>[2,2,1,1,1,1,1]=>378
[4,3,2,1,5,6,7,8,9]=>[2,2,1,1,1,1,1]=>378
[5,6,7,8,1,2,3,4,9]=>[2,2,2,2,1]=>945
[5,2,6,7,1,3,4,8,9]=>[2,2,2,1,1,1]=>1260
[5,6,3,4,1,2,7,8,9]=>[2,2,1,1,1,1,1]=>378
[5,3,2,6,1,4,7,8,9]=>[2,2,2,1,1,1]=>1260
[5,4,3,2,1,6,7,8,9]=>[2,2,1,1,1,1,1]=>378
[6,2,7,8,9,1,3,4,5]=>[2,2,2,2,1]=>945
[6,7,3,4,8,1,2,5,9]=>[2,2,2,1,1,1]=>1260
[6,3,2,7,8,1,4,5,9]=>[2,2,2,2,1]=>945
[6,4,7,2,5,1,3,8,9]=>[2,2,2,1,1,1]=>1260
[6,4,3,2,7,1,5,8,9]=>[2,2,2,1,1,1]=>1260
[6,5,4,3,2,1,7,8,9]=>[2,2,2,1,1,1]=>1260
[7,4,8,2,5,9,1,3,6]=>[2,2,2,2,1]=>945
[7,4,3,2,8,9,1,5,6]=>[2,2,2,2,1]=>945
[7,8,5,6,3,4,1,2,9]=>[2,2,2,2,1]=>945
[7,5,3,8,2,6,1,4,9]=>[2,2,2,1,1,1]=>1260
[7,5,4,3,2,8,1,6,9]=>[2,2,2,2,1]=>945
[7,6,5,4,3,2,1,8,9]=>[2,2,2,1,1,1]=>1260
[8,6,9,4,7,2,5,1,3]=>[2,2,2,2,1]=>945
[8,6,4,3,9,2,7,1,5]=>[2,2,2,2,1]=>945
[8,6,5,4,3,2,9,1,7]=>[2,2,2,2,1]=>945
[3,4,1,2,5,6,7,8,9,10]=>[2,2,1,1,1,1,1,1]=>630
[3,2,1,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]=>45
[4,5,6,1,2,3,7,8,9,10]=>[2,2,2,1,1,1,1]=>3150
[4,2,5,1,3,6,7,8,9,10]=>[2,2,1,1,1,1,1,1]=>630
[4,3,2,1,5,6,7,8,9,10]=>[2,2,1,1,1,1,1,1]=>630
[5,6,7,8,1,2,3,4,9,10]=>[2,2,2,2,1,1]=>4725
[5,2,6,7,1,3,4,8,9,10]=>[2,2,2,1,1,1,1]=>3150
[5,6,3,4,1,2,7,8,9,10]=>[2,2,1,1,1,1,1,1]=>630
[5,3,2,6,1,4,7,8,9,10]=>[2,2,2,1,1,1,1]=>3150
[5,4,3,2,1,6,7,8,9,10]=>[2,2,1,1,1,1,1,1]=>630
[6,2,7,8,9,1,3,4,5,10]=>[2,2,2,2,1,1]=>4725
[6,7,3,4,8,1,2,5,9,10]=>[2,2,2,1,1,1,1]=>3150
[6,3,2,7,8,1,4,5,9,10]=>[2,2,2,2,1,1]=>4725
[6,4,7,2,5,1,3,8,9,10]=>[2,2,2,1,1,1,1]=>3150
[6,4,3,2,7,1,5,8,9,10]=>[2,2,2,1,1,1,1]=>3150
[6,5,4,3,2,1,7,8,9,10]=>[2,2,2,1,1,1,1]=>3150
[7,8,3,4,9,10,1,2,5,6]=>[2,2,2,2,1,1]=>4725
[7,8,9,4,5,6,1,2,3,10]=>[2,2,2,1,1,1,1]=>3150
[7,4,3,2,8,9,1,5,6,10]=>[2,2,2,2,1,1]=>4725
[7,8,5,6,3,4,1,2,9,10]=>[2,2,2,2,1,1]=>4725
[7,5,3,8,2,6,1,4,9,10]=>[2,2,2,1,1,1,1]=>3150
[7,5,4,3,2,8,1,6,9,10]=>[2,2,2,2,1,1]=>4725
[7,6,5,4,3,2,1,8,9,10]=>[2,2,2,1,1,1,1]=>3150
[8,5,9,10,2,6,7,1,3,4]=>[2,2,2,2,1,1]=>4725
[8,5,3,9,2,6,10,1,4,7]=>[2,2,2,2,1,1]=>4725
[8,6,9,4,7,2,5,1,3,10]=>[2,2,2,2,1,1]=>4725
[8,6,4,3,9,2,7,1,5,10]=>[2,2,2,2,1,1]=>4725
[8,6,5,4,3,2,9,1,7,10]=>[2,2,2,2,1,1]=>4725
[8,7,6,5,4,3,2,1,9,10]=>[2,2,2,2,1,1]=>4725
[9,7,5,4,3,10,2,8,1,6]=>[2,2,2,2,1,1]=>4725
[3,6,5,1,2,4,8,7]=>[6,2]=>3360
[3,7,5,8,2,4,1,6]=>[5,3]=>2688
[3,8,5,7,2,4,1,6]=>[8]=>5040
[5,1,7,8,4,3,2,6]=>[8]=>5040
[5,1,2,6,4,3,8,7]=>[6,2]=>3360
[6,1,2,5,4,3,8,7]=>[4,2,2]=>1260
[5,1,2,4,6,3,8,7]=>[5,2,1]=>4032
[4,1,2,6,5,3,8,7]=>[5,2,1]=>4032
[4,1,5,7,8,3,2,6]=>[4,4]=>1260
[4,1,5,8,7,3,2,6]=>[8]=>5040
[4,7,1,8,3,6,2,5]=>[5,2,1]=>4032
[4,1,7,8,5,2,3,6]=>[5,2,1]=>4032
[5,1,7,4,8,2,3,6]=>[5,2,1]=>4032
[7,5,3,8,1,4,2,6]=>[4,3,1]=>3360
[2,1,5,8,7,3,4,6]=>[6,2]=>3360
[5,1,8,4,7,2,3,6]=>[7,1]=>5760
[4,1,8,7,5,2,3,6]=>[7,1]=>5760
[4,7,1,6,3,2,8,5]=>[8]=>5040
[6,1,2,3,7,5,8,4]=>[8]=>5040
[7,1,2,3,8,6,5,4]=>[7,1]=>5760
[7,1,2,3,5,8,6,4]=>[7,1]=>5760
[6,8,1,4,3,7,2,5]=>[7,1]=>5760
[8,7,3,2,4,1,6,5]=>[7,1]=>5760
[2,1,7,3,4,8,6,5]=>[6,2]=>3360
[7,8,3,2,4,1,6,5]=>[4,3,1]=>3360
[6,7,1,4,3,8,2,5]=>[5,2,1]=>4032
[8,1,2,3,5,7,6,4]=>[5,2,1]=>4032
[8,1,2,3,6,7,5,4]=>[5,3]=>2688
[7,1,2,3,6,8,5,4]=>[8]=>5040
[7,1,2,3,8,5,6,4]=>[8]=>5040
[8,1,2,3,7,5,6,4]=>[5,3]=>2688
[8,1,2,3,6,5,7,4]=>[5,2,1]=>4032
[7,1,8,5,4,3,2,6]=>[3,3,2]=>1120
[7,8,2,6,3,4,1,5]=>[4,2,2]=>1260
[6,8,2,7,3,4,1,5]=>[4,4]=>1260
[6,7,2,8,3,4,1,5]=>[8]=>5040
[3,8,7,1,4,2,6,5]=>[8]=>5040
[3,7,8,1,4,2,6,5]=>[5,3]=>2688
[3,6,8,1,4,2,7,5]=>[5,2,1]=>4032
[3,5,7,8,2,4,1,6]=>[3,3,2]=>1120
[3,6,7,1,4,2,8,5]=>[6,2]=>3360
[7,6,2,8,3,1,4,5]=>[8]=>5040
[8,6,2,7,3,1,4,5]=>[6,2]=>3360
[8,1,7,5,4,3,2,6]=>[6,2]=>3360
[8,1,7,4,5,3,2,6]=>[6,1,1]=>3360
[5,8,3,7,1,4,2,6]=>[5,2,1]=>4032
[2,1,7,3,4,6,8,5]=>[5,2,1]=>4032
[6,7,3,2,4,1,8,5]=>[5,2,1]=>4032
[8,7,2,4,3,6,1,5]=>[6,1,1]=>3360
[7,1,2,3,5,6,8,4]=>[6,1,1]=>3360
[6,1,2,3,8,7,4,5]=>[6,2]=>3360
[5,1,2,3,7,8,6,4]=>[8]=>5040
[5,1,2,3,8,7,6,4]=>[6,2]=>3360
[5,1,2,3,8,6,7,4]=>[6,1,1]=>3360
[6,1,2,3,5,8,7,4]=>[6,1,1]=>3360
[8,6,2,4,3,1,7,5]=>[6,1,1]=>3360
[7,6,3,2,4,8,1,5]=>[5,2,1]=>4032
[2,1,6,3,4,8,7,5]=>[5,2,1]=>4032
[8,6,3,2,4,7,1,5]=>[7,1]=>5760
[7,6,2,4,3,1,8,5]=>[7,1]=>5760
[6,1,2,3,5,7,8,4]=>[7,1]=>5760
[5,1,2,3,6,8,7,4]=>[7,1]=>5760
[7,8,1,2,6,3,5,4]=>[5,3]=>2688
[1,4,8,2,7,3,5,6]=>[3,2,2,1]=>1680
[1,2,8,5,4,7,3,6]=>[4,2,1,1]=>2520
[1,3,8,5,4,2,7,6]=>[4,2,1,1]=>2520
[2,3,6,8,4,7,1,5]=>[5,3]=>2688
[1,3,6,8,4,7,5,2]=>[7,1]=>5760
[2,4,8,1,7,3,6,5]=>[5,3]=>2688
[3,4,8,5,7,6,1,2]=>[7,1]=>5760
[1,2,6,8,4,5,7,3]=>[5,1,1,1]=>1344
[7,5,1,2,4,3,6,8]=>[4,3,1]=>3360
[7,4,6,1,5,2,3,8]=>[6,1,1]=>3360
[7,1,4,2,6,3,5,8]=>[7,1]=>5760
[6,8,1,4,7,2,3,5]=>[7,1]=>5760
[1,6,4,2,8,3,5,7]=>[4,3,1]=>3360
[1,6,3,8,5,4,2,7]=>[5,1,1,1]=>1344
[6,8,1,7,3,5,4,2]=>[4,2,2]=>1260
[7,1,3,6,5,4,2,8]=>[3,2,1,1,1]=>1120
[7,3,1,6,5,4,2,8]=>[4,2,1,1]=>2520
[7,2,1,4,6,3,5,8]=>[5,1,1,1]=>1344
[7,2,3,6,5,1,4,8]=>[4,1,1,1,1]=>420
[7,1,2,3,6,5,4,8]=>[5,2,1]=>4032
[6,8,1,2,7,3,5,4]=>[3,3,2]=>1120
[1,6,2,3,8,5,4,7]=>[7,1]=>5760
[1,5,8,2,7,6,3,4]=>[6,1,1]=>3360
[5,1,8,2,7,6,3,4]=>[7,1]=>5760
[5,8,2,7,6,3,4,1]=>[6,2]=>3360
[6,2,8,1,7,3,5,4]=>[5,2,1]=>4032
[6,8,2,1,7,4,3,5]=>[5,3]=>2688
[3,6,4,1,2,8,5,7]=>[5,3]=>2688
[2,1,6,3,8,5,4,7]=>[6,2]=>3360
[2,5,1,8,7,6,3,4]=>[5,2,1]=>4032
[2,5,3,8,7,4,6,1]=>[7,1]=>5760
[1,2,5,3,8,7,4,6]=>[6,1,1]=>3360
[2,4,8,7,6,5,1,3]=>[4,2,2]=>1260
[2,5,3,8,7,1,6,4]=>[5,2,1]=>4032
[2,5,8,4,1,7,6,3]=>[3,2,2,1]=>1680
[3,5,8,7,1,4,2,6]=>[8]=>5040
[5,3,8,4,1,7,6,2]=>[3,2,2,1]=>1680
[4,2,8,7,6,3,5,1]=>[7,1]=>5760
[4,2,8,7,6,5,3,1]=>[5,2,1]=>4032
[4,1,8,7,6,5,3,2]=>[6,2]=>3360
[4,3,8,7,6,5,1,2]=>[3,3,2]=>1120
[6,3,1,8,7,2,5,4]=>[4,2,2]=>1260
[5,8,3,7,6,1,4,2]=>[3,2,2,1]=>1680
[5,1,3,8,7,6,2,4]=>[4,2,1,1]=>2520
[1,5,3,8,7,6,2,4]=>[3,2,1,1,1]=>1120
[1,5,8,4,7,2,6,3]=>[4,2,1,1]=>2520
[5,1,8,4,7,2,6,3]=>[5,2,1]=>4032
[5,8,7,4,6,1,2,3]=>[4,3,1]=>3360
[6,8,5,1,2,4,7,3]=>[4,3,1]=>3360
[5,6,3,1,2,4,8,7]=>[5,2,1]=>4032
[5,6,2,4,3,1,8,7]=>[5,2,1]=>4032
[5,6,1,2,4,3,8,7]=>[6,2]=>3360
[4,5,8,1,7,2,3,6]=>[6,2]=>3360
[4,5,8,1,7,2,6,3]=>[4,2,2]=>1260
[1,3,2,5,8,7,4,6]=>[5,2,1]=>4032
[3,5,1,8,7,4,6,2]=>[6,2]=>3360
[3,5,1,8,7,2,6,4]=>[4,2,2]=>1260
[4,3,6,1,2,8,5,7]=>[6,2]=>3360
[4,5,8,3,1,7,2,6]=>[8]=>5040
[4,5,2,8,7,1,3,6]=>[4,4]=>1260
[3,2,5,8,7,1,6,4]=>[5,2,1]=>4032
[3,4,8,7,6,2,1,5]=>[8]=>5040
[3,1,4,8,7,6,2,5]=>[7,1]=>5760
[3,4,8,7,6,5,1,2]=>[6,2]=>3360
[1,3,4,8,7,6,2,5]=>[6,1,1]=>3360
[3,4,8,7,6,2,5,1]=>[5,3]=>2688
[3,2,5,8,7,4,6,1]=>[7,1]=>5760
[4,5,8,3,1,7,6,2]=>[6,2]=>3360
[2,1,3,5,8,7,4,6]=>[5,2,1]=>4032
[1,2,7,5,8,6,4,3]=>[5,1,1,1]=>1344
[7,1,4,8,2,6,5,3]=>[4,3,1]=>3360
[6,8,1,3,7,5,2,4]=>[8]=>5040
[3,7,8,1,2,6,5,4]=>[4,3,1]=>3360
[1,3,7,8,2,6,5,4]=>[4,2,1,1]=>2520
[2,3,7,8,1,6,5,4]=>[5,2,1]=>4032
[2,7,8,1,3,6,5,4]=>[7,1]=>5760
[8,1,2,6,7,3,5,4]=>[6,2]=>3360
[8,1,2,6,7,5,3,4]=>[8]=>5040
[8,2,5,7,1,3,6,4]=>[7,1]=>5760
[2,8,1,6,7,3,5,4]=>[6,2]=>3360
[2,6,8,3,7,1,5,4]=>[3,3,2]=>1120
[2,8,6,4,7,1,5,3]=>[5,2,1]=>4032
[6,8,3,4,1,7,5,2]=>[4,2,1,1]=>2520
[6,8,3,7,4,1,5,2]=>[3,2,2,1]=>1680
[2,6,8,3,7,5,1,4]=>[5,3]=>2688
[2,8,1,6,7,5,3,4]=>[8]=>5040
[8,2,5,7,1,6,3,4]=>[6,1,1]=>3360
[8,4,7,2,3,6,1,5]=>[5,2,1]=>4032
[8,5,7,4,2,6,1,3]=>[4,2,1,1]=>2520
[8,3,5,7,4,1,6,2]=>[8]=>5040
[8,5,2,4,7,1,6,3]=>[7,1]=>5760
[8,2,3,5,7,1,6,4]=>[6,1,1]=>3360
[8,2,4,7,3,6,1,5]=>[6,1,1]=>3360
[8,2,7,1,4,6,3,5]=>[4,2,1,1]=>2520
[8,7,1,2,4,6,3,5]=>[7,1]=>5760
[8,7,1,4,6,2,3,5]=>[7,1]=>5760
[8,4,7,1,3,6,2,5]=>[7,1]=>5760
[1,6,8,3,7,2,5,4]=>[3,2,2,1]=>1680
[8,3,5,7,1,2,6,4]=>[8]=>5040
[5,8,7,1,3,6,2,4]=>[7,1]=>5760
[8,5,4,7,1,6,2,3]=>[7,1]=>5760
[8,5,4,7,1,2,6,3]=>[8]=>5040
[8,5,1,4,7,2,6,3]=>[4,3,1]=>3360
[1,4,6,8,2,7,5,3]=>[7,1]=>5760
[1,6,5,8,2,7,4,3]=>[7,1]=>5760
[8,5,6,3,1,7,4,2]=>[4,4]=>1260
[5,6,2,8,1,7,4,3]=>[6,2]=>3360
[1,8,4,5,7,2,6,3]=>[7,1]=>5760
[5,8,7,3,6,1,2,4]=>[5,3]=>2688
[8,3,5,7,1,6,2,4]=>[7,1]=>5760
[1,6,8,3,7,5,2,4]=>[4,3,1]=>3360
[6,3,8,2,7,5,1,4]=>[4,4]=>1260
[6,8,4,2,7,1,5,3]=>[4,2,2]=>1260
[8,6,4,7,3,1,5,2]=>[4,4]=>1260
[8,4,5,7,3,1,6,2]=>[6,2]=>3360
[8,4,2,5,7,1,6,3]=>[8]=>5040
[8,3,4,7,2,6,1,5]=>[7,1]=>5760
[8,7,1,3,4,6,2,5]=>[5,2,1]=>4032
[8,3,7,2,4,6,1,5]=>[7,1]=>5760
[2,8,4,5,7,1,6,3]=>[8]=>5040
[8,7,3,4,5,1,6,2]=>[5,1,1,1]=>1344
[8,7,4,5,2,6,1,3]=>[7,1]=>5760
[5,8,7,2,3,6,1,4]=>[4,3,1]=>3360
[8,7,2,3,4,6,1,5]=>[7,1]=>5760
[8,7,2,3,6,1,4,5]=>[4,4]=>1260
[1,3,2,8,5,4,7,6]=>[3,2,1,1,1]=>1120
[4,2,8,5,3,7,1,6]=>[7,1]=>5760
[5,2,1,8,4,3,7,6]=>[6,1,1]=>3360
[6,2,8,4,3,7,5,1]=>[6,1,1]=>3360
[7,2,8,4,3,1,6,5]=>[3,3,1,1]=>1120
[7,3,4,8,2,1,6,5]=>[5,3]=>2688
[6,3,4,8,2,7,5,1]=>[8]=>5040
[5,3,4,1,8,2,7,6]=>[7,1]=>5760
[8,1,4,5,2,3,7,6]=>[7,1]=>5760
[8,1,5,4,3,2,7,6]=>[4,2,1,1]=>2520
[3,5,4,2,8,1,7,6]=>[7,1]=>5760
[4,5,3,2,8,7,1,6]=>[7,1]=>5760
[6,4,3,2,8,7,5,1]=>[5,2,1]=>4032
[6,5,3,2,1,7,8,4]=>[7,1]=>5760
[5,6,3,2,7,8,4,1]=>[7,1]=>5760
[4,1,6,3,2,7,8,5]=>[8]=>5040
[3,6,4,2,7,8,1,5]=>[8]=>5040
[8,1,6,4,3,7,2,5]=>[7,1]=>5760
[8,1,7,4,3,6,5,2]=>[3,3,1,1]=>1120
[2,7,4,1,3,6,5,8]=>[6,1,1]=>3360
[3,7,4,2,6,1,5,8]=>[7,1]=>5760
[4,1,7,3,2,6,5,8]=>[6,1,1]=>3360
[5,7,3,2,6,4,8,1]=>[7,1]=>5760
[6,7,3,2,5,4,1,8]=>[5,1,1,1]=>1344
[7,6,3,2,1,5,4,8]=>[6,1,1]=>3360
[4,7,5,6,2,3,8,1]=>[8]=>5040
[3,1,7,5,6,2,4,8]=>[7,1]=>5760
[2,7,5,6,1,3,4,8]=>[7,1]=>5760
[2,6,5,7,1,3,8,4]=>[5,3]=>2688
[4,6,5,7,2,8,1,3]=>[5,3]=>2688
[5,6,4,7,2,8,3,1]=>[5,3]=>2688
[6,5,4,1,7,2,8,3]=>[8]=>5040
[7,5,4,6,2,1,8,3]=>[6,2]=>3360
[6,4,5,7,1,8,2,3]=>[5,3]=>2688
[5,4,6,1,7,8,2,3]=>[5,3]=>2688
[8,1,5,6,7,2,3,4]=>[5,3]=>2688
[2,1,4,6,8,7,3,5]=>[4,2,2]=>1260
[3,4,6,8,7,1,2,5]=>[5,3]=>2688
[4,3,1,6,8,7,2,5]=>[6,2]=>3360
[5,3,6,8,7,2,4,1]=>[5,3]=>2688
[6,3,5,1,8,7,2,4]=>[8]=>5040
[7,3,5,8,6,2,1,4]=>[4,2,2]=>1260
[7,2,8,5,6,3,1,4]=>[5,2,1]=>4032
[6,2,8,5,1,7,3,4]=>[7,1]=>5760
[4,2,1,8,6,7,3,5]=>[7,1]=>5760
[1,3,2,8,6,7,4,5]=>[5,2,1]=>4032
[2,3,8,6,7,1,4,5]=>[8]=>5040
[8,1,3,2,6,7,4,5]=>[7,1]=>5760
[2,3,8,7,1,6,5,4]=>[7,1]=>5760
[4,2,8,7,6,1,5,3]=>[5,2,1]=>4032
[5,2,8,7,6,4,1,3]=>[5,2,1]=>4032
[7,2,1,8,6,5,4,3]=>[5,2,1]=>4032
[7,3,6,1,8,5,4,2]=>[5,3]=>2688
[6,3,7,8,5,4,2,1]=>[4,3,1]=>3360
[5,3,7,8,6,4,1,2]=>[8]=>5040
[4,3,1,7,8,6,5,2]=>[7,1]=>5760
[3,4,7,8,6,1,5,2]=>[5,3]=>2688
[8,1,5,7,6,2,4,3]=>[6,2]=>3360
[3,5,7,6,8,1,4,2]=>[5,3]=>2688
[4,5,7,6,8,3,1,2]=>[5,3]=>2688
[5,4,1,7,6,8,3,2]=>[8]=>5040
[6,4,7,5,8,3,2,1]=>[8]=>5040
[7,4,6,5,1,8,3,2]=>[8]=>5040
[7,5,6,4,3,1,8,2]=>[7,1]=>5760
[6,5,1,7,4,3,8,2]=>[5,3]=>2688
[4,6,7,5,3,8,1,2]=>[5,3]=>2688
[3,6,7,5,1,4,8,2]=>[8]=>5040
[8,1,6,7,5,4,2,3]=>[7,1]=>5760
[8,1,7,6,5,4,3,2]=>[3,2,2,1]=>1680
[2,7,6,1,5,4,3,8]=>[6,1,1]=>3360
[3,7,6,5,1,4,2,8]=>[5,2,1]=>4032
[4,7,6,5,3,1,2,8]=>[5,2,1]=>4032
[8,6,4,3,1,5,7,2]=>[5,2,1]=>4032
[8,6,4,1,5,2,7,3]=>[4,2,1,1]=>2520
[8,6,5,1,3,2,7,4]=>[3,2,2,1]=>1680
[8,6,3,1,7,2,4,5]=>[5,2,1]=>4032
[8,7,3,1,5,2,4,6]=>[6,1,1]=>3360
[5,3,1,7,2,4,6,8]=>[4,3,1]=>3360
[8,7,1,2,4,5,3,6]=>[8]=>5040
[8,6,1,2,4,7,3,5]=>[8]=>5040
[8,5,1,2,6,7,3,4]=>[8]=>5040
[8,5,1,6,4,2,7,3]=>[4,3,1]=>3360
[8,5,1,3,6,4,7,2]=>[7,1]=>5760
[8,6,1,5,3,4,7,2]=>[7,1]=>5760
[8,6,1,5,2,4,7,3]=>[4,3,1]=>3360
[8,6,1,2,5,7,3,4]=>[7,1]=>5760
[8,6,1,2,7,4,3,5]=>[5,3]=>2688
[8,7,1,2,5,4,3,6]=>[7,1]=>5760
[5,1,4,2,3,8,6,7]=>[5,3]=>2688
[5,1,4,2,7,3,6,8]=>[7,1]=>5760
[7,1,5,8,2,6,3,4]=>[5,2,1]=>4032
[5,7,8,1,2,4,6,3]=>[6,2]=>3360
[5,7,8,1,3,4,6,2]=>[8]=>5040
[5,8,1,7,3,4,6,2]=>[3,3,2]=>1120
[8,1,5,7,2,4,6,3]=>[5,3]=>2688
[8,4,1,2,7,6,3,5]=>[5,2,1]=>4032
[1,4,2,3,8,7,5,6]=>[4,3,1]=>3360
[1,4,2,7,6,3,5,8]=>[6,1,1]=>3360
[6,1,2,8,7,5,3,4]=>[6,2]=>3360
[6,1,2,4,8,7,5,3]=>[7,1]=>5760
[3,1,8,4,6,7,5,2]=>[4,3,1]=>3360
[3,1,7,6,4,8,5,2]=>[8]=>5040
[7,1,2,4,6,8,5,3]=>[7,1]=>5760
[7,1,2,6,8,5,3,4]=>[4,4]=>1260
[6,1,2,7,8,5,3,4]=>[8]=>5040
[6,1,2,7,4,8,5,3]=>[5,3]=>2688
[3,1,6,4,7,8,5,2]=>[5,2,1]=>4032
[5,7,1,3,8,4,6,2]=>[8]=>5040
[5,7,1,8,4,2,6,3]=>[5,3]=>2688
[7,1,5,3,2,8,6,4]=>[8]=>5040
[7,1,4,5,2,8,6,3]=>[8]=>5040
[4,7,3,1,5,8,6,2]=>[4,2,1,1]=>2520
[4,8,7,3,1,5,6,2]=>[6,2]=>3360
[8,1,7,4,5,2,6,3]=>[6,1,1]=>3360
[8,1,7,5,3,2,6,4]=>[8]=>5040
[8,3,7,1,2,6,4,5]=>[7,1]=>5760
[3,1,2,8,4,7,5,6]=>[5,3]=>2688
[3,1,2,8,6,4,5,7]=>[5,3]=>2688
[3,1,7,2,6,4,5,8]=>[7,1]=>5760
[1,4,2,3,8,6,5,7]=>[3,3,1,1]=>1120
[1,4,2,3,8,5,7,6]=>[3,3,1,1]=>1120
[5,8,1,7,2,4,6,3]=>[5,3]=>2688
[5,8,1,3,4,7,6,2]=>[4,2,2]=>1260
[3,1,8,6,4,7,5,2]=>[4,4]=>1260
[8,1,2,6,7,4,5,3]=>[4,2,2]=>1260
[6,1,2,8,7,3,5,4]=>[4,2,2]=>1260
[1,2,3,5,8,4,7,6]=>[4,1,1,1,1]=>420
[1,2,3,5,8,6,4,7]=>[4,1,1,1,1]=>420
[7,1,2,8,3,6,5,4]=>[5,2,1]=>4032
[7,1,2,8,6,4,5,3]=>[8]=>5040
[3,1,7,8,4,6,5,2]=>[7,1]=>5760
[3,1,8,7,6,4,5,2]=>[4,4]=>1260
[8,1,2,7,4,6,5,3]=>[4,3,1]=>3360
[8,1,2,7,3,6,5,4]=>[7,1]=>5760
[1,2,3,5,8,7,4,6]=>[5,1,1,1]=>1344
[1,2,3,6,8,5,4,7]=>[5,1,1,1]=>1344
[7,8,5,6,3,1,4,2]=>[4,2,2]=>1260
[7,5,6,3,1,4,2,8]=>[4,3,1]=>3360
[7,5,8,3,1,4,2,6]=>[4,4]=>1260
[7,8,5,3,1,4,2,6]=>[8]=>5040
[7,8,5,3,1,6,2,4]=>[7,1]=>5760
[7,8,5,3,1,6,4,2]=>[5,2,1]=>4032
[7,8,5,3,6,1,4,2]=>[6,2]=>3360
[7,8,5,3,6,4,1,2]=>[4,2,2]=>1260
[7,5,8,3,4,1,6,2]=>[5,3]=>2688
[7,5,6,3,4,1,8,2]=>[8]=>5040
[7,5,6,3,1,2,8,4]=>[8]=>5040
[7,5,3,6,1,2,8,4]=>[7,1]=>5760
[7,5,3,1,6,4,8,2]=>[7,1]=>5760
[7,5,3,6,4,1,8,2]=>[7,1]=>5760
[7,5,3,6,4,8,1,2]=>[5,2,1]=>4032
[7,5,3,8,4,6,1,2]=>[4,2,1,1]=>2520
[7,5,3,1,8,4,6,2]=>[4,3,1]=>3360
[7,5,3,1,8,2,6,4]=>[7,1]=>5760
[7,5,3,1,6,4,2,8]=>[6,1,1]=>3360
[7,5,3,1,8,4,2,6]=>[7,1]=>5760
[7,5,3,1,8,6,2,4]=>[6,1,1]=>3360
[7,5,3,8,1,6,4,2]=>[6,1,1]=>3360
[7,5,3,8,6,1,4,2]=>[7,1]=>5760
[7,5,3,8,6,4,1,2]=>[5,2,1]=>4032
[7,5,8,3,6,1,4,2]=>[8]=>5040
[7,5,8,3,1,6,4,2]=>[7,1]=>5760
[7,5,3,6,1,4,2,8]=>[4,2,1,1]=>2520
[7,5,3,8,4,1,2,6]=>[7,1]=>5760
[7,5,8,6,3,1,2,4]=>[8]=>5040
[7,5,8,6,3,1,4,2]=>[4,4]=>1260
[7,5,8,6,3,4,1,2]=>[4,2,2]=>1260
[7,5,6,8,3,1,4,2]=>[8]=>5040
[7,5,6,3,8,1,2,4]=>[8]=>5040
[7,5,3,4,1,8,2,6]=>[4,2,1,1]=>2520
[7,5,6,3,1,8,2,4]=>[4,4]=>1260
[7,5,6,3,1,8,4,2]=>[8]=>5040
[7,5,6,3,8,1,4,2]=>[5,3]=>2688
[7,5,6,3,8,4,1,2]=>[3,3,2]=>1120
[7,5,3,6,1,8,4,2]=>[7,1]=>5760
[7,5,3,1,2,8,4,6]=>[3,2,2,1]=>1680
[7,5,3,1,2,8,6,4]=>[5,2,1]=>4032
[7,5,3,1,4,8,6,2]=>[7,1]=>5760
[7,5,3,4,8,1,6,2]=>[3,3,1,1]=>1120
[7,5,3,4,1,6,8,2]=>[5,1,1,1]=>1344
[7,5,3,1,4,6,8,2]=>[6,1,1]=>3360
[3,6,2,5,4,1,8,7]=>[4,2,2]=>1260
[3,5,2,8,4,7,6,1]=>[6,2]=>3360
[5,4,7,3,2,8,6,1]=>[8]=>5040
[5,4,8,3,2,7,6,1]=>[6,2]=>3360
[6,4,5,3,2,1,8,7]=>[4,2,2]=>1260
[5,3,2,6,4,1,8,7]=>[4,2,2]=>1260
[4,5,8,3,2,7,6,1]=>[4,2,2]=>1260
[4,7,6,3,8,5,2,1]=>[6,2]=>3360
[4,8,6,3,7,5,2,1]=>[8]=>5040
[4,8,5,3,2,7,6,1]=>[6,2]=>3360
[5,8,4,3,2,7,6,1]=>[4,2,2]=>1260
[5,3,2,8,4,7,6,1]=>[4,2,2]=>1260
[2,1,5,8,4,7,6,3]=>[4,2,2]=>1260
[5,3,2,7,4,8,6,1]=>[6,2]=>3360
[5,7,4,3,2,8,6,1]=>[6,2]=>3360
[4,7,5,3,2,8,6,1]=>[8]=>5040
[4,7,8,3,6,5,2,1]=>[4,2,2]=>1260
[4,6,8,3,7,5,2,1]=>[4,4]=>1260
[7,6,4,3,8,5,2,1]=>[6,2]=>3360
[7,3,2,6,8,5,4,1]=>[6,2]=>3360
[2,1,8,6,7,5,4,3]=>[4,2,2]=>1260
[8,3,2,6,7,5,4,1]=>[4,2,2]=>1260
[8,6,4,3,7,5,2,1]=>[4,2,2]=>1260
[8,5,7,6,4,3,2,1]=>[6,2]=>3360
[8,4,5,3,2,7,6,1]=>[4,2,2]=>1260
[8,4,7,3,6,5,2,1]=>[4,2,2]=>1260
[8,4,6,3,7,5,2,1]=>[6,2]=>3360
[7,4,6,3,8,5,2,1]=>[8]=>5040
[3,7,2,6,8,5,4,1]=>[8]=>5040
[3,8,2,6,7,5,4,1]=>[4,4]=>1260
[3,8,2,5,4,7,6,1]=>[4,2,2]=>1260
[3,7,2,8,6,5,4,1]=>[6,2]=>3360
[3,6,2,8,7,5,4,1]=>[8]=>5040
[6,4,7,3,8,5,2,1]=>[4,4]=>1260
[6,4,8,3,7,5,2,1]=>[8]=>5040
[7,4,8,3,6,5,2,1]=>[6,2]=>3360
[7,4,5,3,2,8,6,1]=>[4,4]=>1260
[7,5,4,3,2,8,6,1]=>[4,2,2]=>1260
[7,3,2,5,4,8,6,1]=>[4,2,2]=>1260
[2,1,7,5,4,8,6,3]=>[4,2,2]=>1260
[7,3,2,8,6,5,4,1]=>[4,2,2]=>1260
[7,8,4,3,6,5,2,1]=>[4,2,2]=>1260
[6,8,5,7,4,3,2,1]=>[8]=>5040
[6,8,4,3,7,5,2,1]=>[6,2]=>3360
[6,3,2,8,7,5,4,1]=>[6,2]=>3360
[6,3,2,7,8,5,4,1]=>[4,2,2]=>1260
[6,7,4,3,8,5,2,1]=>[4,2,2]=>1260
[2,3,1,4,5,6,7,8,9]=>[3,1,1,1,1,1,1]=>168
[2,3,4,1,5,6,7,8,9]=>[4,1,1,1,1,1]=>756
[2,3,4,5,1,6,7,8,9]=>[5,1,1,1,1]=>3024
[2,3,4,5,6,1,7,8,9]=>[6,1,1,1]=>10080
[2,3,1,4,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]=>240
[2,4,3,1,5,6,7,8,9]=>[3,1,1,1,1,1,1]=>168
[2,3,4,1,5,6,7,8,9,10]=>[4,1,1,1,1,1,1]=>1260
[2,3,4,5,1,6,7,8,9,10]=>[5,1,1,1,1,1]=>6048
[2,3,4,5,6,1,7,8,9,10]=>[6,1,1,1,1]=>25200
[2,3,4,5,6,7,1,8,9,10]=>[7,1,1,1]=>86400
[2,3,4,5,6,7,8,1,9,10]=>[8,1,1]=>226800
[2,3,4,5,6,7,9,8,1]=>[8,1]=>45360
[4,6,8,3,5,7,1,2]=>[7,1]=>5760
[6,8,1,2,4,5,7,3]=>[7,1]=>5760
[3,5,8,2,4,7,1,6]=>[5,3]=>2688
[8,3,5,2,4,1,6,7]=>[4,4]=>1260
[4,2,5,7,3,6,1,8]=>[3,2,1,1,1]=>1120
[4,5,2,8,3,1,6,7]=>[5,3]=>2688
[4,2,5,8,3,7,1,6]=>[5,2,1]=>4032
[2,1,6,8,4,7,3,5]=>[3,3,2]=>1120
[1,2,5,8,3,6,7,4]=>[2,2,1,1,1,1]=>210
[5,3,6,8,4,7,1,2]=>[8]=>5040
[1,6,5,8,2,4,7,3]=>[6,1,1]=>3360
[3,1,2,6,8,5,7,4]=>[4,3,1]=>3360
[1,4,3,8,2,6,7,5]=>[4,1,1,1,1]=>420
[5,4,8,3,2,1,6,7]=>[8]=>5040
[5,4,3,7,2,6,1,8]=>[5,1,1,1]=>1344
[4,3,6,2,7,5,1,8]=>[7,1]=>5760
[4,6,3,2,1,8,5,7]=>[7,1]=>5760
[4,1,7,3,2,5,8,6]=>[8]=>5040
[4,3,1,7,8,2,6,5]=>[6,2]=>3360
[3,5,1,2,7,8,6,4]=>[6,2]=>3360
[7,5,1,4,8,2,6,3]=>[7,1]=>5760
[5,4,7,3,8,6,1,2]=>[7,1]=>5760
[5,8,4,7,6,3,1,2]=>[6,2]=>3360
[5,8,7,1,4,2,6,3]=>[5,3]=>2688
[8,3,5,1,2,7,6,4]=>[3,3,2]=>1120
[4,8,3,1,7,2,6,5]=>[5,2,1]=>4032
[1,8,4,3,5,2,7,6]=>[3,2,1,1,1]=>1120
[4,6,3,1,5,2,8,7]=>[2,2,2,1,1]=>420
[4,7,3,6,5,2,1,8]=>[5,1,1,1]=>1344
[5,3,7,6,4,2,1,8]=>[7,1]=>5760
[1,6,3,4,2,8,7,5]=>[4,1,1,1,1]=>420
[1,8,3,6,2,7,5,4]=>[6,1,1]=>3360
[1,6,8,7,4,2,5,3]=>[3,2,2,1]=>1680
[6,4,8,7,5,3,1,2]=>[7,1]=>5760
[7,6,4,3,8,5,1,2]=>[4,2,2]=>1260
[1,7,6,2,8,4,5,3]=>[7,1]=>5760
[7,1,3,2,6,8,5,4]=>[7,1]=>5760
[1,5,3,2,7,4,8,6]=>[6,1,1]=>3360
[6,3,2,1,8,5,4,7]=>[6,2]=>3360
[6,5,3,2,7,4,1,8]=>[6,1,1]=>3360
[5,2,6,3,7,4,1,8]=>[3,3,1,1]=>1120
[2,8,5,3,1,6,4,7]=>[7,1]=>5760
[2,1,7,3,8,5,4,6]=>[3,3,2]=>1120
[1,6,2,3,7,8,5,4]=>[5,2,1]=>4032
[1,6,7,2,8,4,5,3]=>[4,3,1]=>3360
[5,7,1,8,2,4,6,3]=>[8]=>5040
[5,1,2,7,8,3,6,4]=>[8]=>5040
[2,4,1,7,8,6,3,5]=>[5,2,1]=>4032
[4,2,1,7,3,8,5,6]=>[5,2,1]=>4032
[6,2,8,4,3,1,5,7]=>[4,2,1,1]=>2520
[7,3,2,1,8,4,5,6]=>[6,2]=>3360
[7,8,3,2,5,6,1,4]=>[3,2,1,1,1]=>1120
[7,1,8,2,4,5,6,3]=>[6,2]=>3360
[8,7,6,1,2,4,5,3]=>[5,3]=>2688
[8,3,7,6,2,1,4,5]=>[8]=>5040
[3,2,8,7,5,1,4,6]=>[4,2,1,1]=>2520
[8,3,6,5,2,1,4,7]=>[8]=>5040
[7,6,3,5,2,4,1,8]=>[4,2,1,1]=>2520
[7,4,6,2,5,3,1,8]=>[2,2,2,1,1]=>420
[8,2,4,1,6,5,3,7]=>[5,2,1]=>4032
[4,2,8,1,7,5,3,6]=>[5,2,1]=>4032
[8,2,4,1,7,6,3,5]=>[6,1,1]=>3360
[8,7,1,5,6,2,4,3]=>[5,3]=>2688
[8,5,7,3,6,4,1,2]=>[8]=>5040
[6,8,3,7,5,4,1,2]=>[4,2,1,1]=>2520
[8,1,6,7,5,2,4,3]=>[5,2,1]=>4032
[8,1,2,6,4,3,7,5]=>[7,1]=>5760
[2,8,1,7,5,4,3,6]=>[7,1]=>5760
[2,5,1,8,6,4,3,7]=>[8]=>5040
[5,7,2,6,4,3,1,8]=>[7,1]=>5760
[6,2,7,5,4,3,1,8]=>[4,2,1,1]=>2520
[2,1,8,6,5,4,3,7]=>[3,2,2,1]=>1680
[1,2,7,5,4,3,8,6]=>[4,2,1,1]=>2520
[1,7,2,4,3,8,6,5]=>[6,1,1]=>3360
[1,7,2,8,3,6,5,4]=>[4,2,1,1]=>2520
[1,7,8,6,5,2,4,3]=>[4,2,1,1]=>2520
[7,3,8,6,5,4,1,2]=>[3,2,2,1]=>1680
[1,8,7,6,5,2,4,3]=>[6,1,1]=>3360
[8,1,7,3,2,6,5,4]=>[7,1]=>5760
[5,1,4,3,2,8,7,6]=>[3,2,2,1]=>1680
[8,6,5,3,2,1,7,4]=>[7,1]=>5760
[8,6,3,2,1,7,4,5]=>[4,3,1]=>3360
[8,6,5,4,1,7,2,3]=>[4,3,1]=>3360
[8,6,5,1,7,3,2,4]=>[5,3]=>2688
[8,6,1,7,4,3,2,5]=>[8]=>5040
[4,6,3,2,7,5,1,8]=>[6,1,1]=>3360
[1,4,3,7,2,5,8,6]=>[6,1,1]=>3360
[7,4,8,3,1,6,2,5]=>[7,1]=>5760
[7,1,5,8,3,2,6,4]=>[4,2,2]=>1260
[5,7,4,1,8,2,6,3]=>[5,3]=>2688
[5,7,4,3,1,8,6,2]=>[4,2,2]=>1260
[1,8,7,2,5,4,6,3]=>[6,1,1]=>3360
[1,8,5,3,7,2,6,4]=>[7,1]=>5760
[4,3,1,8,7,5,2,6]=>[8]=>5040
[1,4,8,6,3,5,2,7]=>[7,1]=>5760
[7,4,6,3,5,2,1,8]=>[4,2,1,1]=>2520
[1,3,5,6,8,4,2,7]=>[5,2,1]=>4032
[3,5,4,8,7,1,2,6]=>[5,3]=>2688
[3,1,4,6,8,7,2,5]=>[6,2]=>3360
[1,6,3,8,7,2,5,4]=>[2,2,2,1,1]=>420
[1,6,2,4,8,7,5,3]=>[6,1,1]=>3360
[8,4,1,6,7,5,3,2]=>[8]=>5040
[7,1,6,4,8,5,2,3]=>[4,3,1]=>3360
[7,3,6,8,5,1,2,4]=>[5,2,1]=>4032
[1,3,7,2,6,8,4,5]=>[4,3,1]=>3360
[3,6,5,2,8,1,4,7]=>[8]=>5040
[3,6,5,7,2,4,1,8]=>[7,1]=>5760
[4,2,6,3,8,1,5,7]=>[4,3,1]=>3360
[4,2,6,7,3,5,1,8]=>[3,3,1,1]=>1120
[3,6,2,4,7,5,1,8]=>[6,1,1]=>3360
[3,6,2,4,1,8,5,7]=>[7,1]=>5760
[7,3,8,2,1,6,4,5]=>[7,1]=>5760
[7,3,5,2,1,8,6,4]=>[8]=>5040
[8,7,6,4,3,1,5,2]=>[7,1]=>5760
[8,7,6,4,1,5,2,3]=>[5,2,1]=>4032
[3,8,7,2,1,4,6,5]=>[8]=>5040
[3,8,2,7,1,5,4,6]=>[6,2]=>3360
[3,6,8,2,1,5,4,7]=>[8]=>5040
[2,4,8,1,6,5,3,7]=>[3,3,2]=>1120
[4,2,8,1,5,7,3,6]=>[4,2,1,1]=>2520
[8,5,7,6,1,4,2,3]=>[6,2]=>3360
[8,6,1,7,3,5,4,2]=>[6,2]=>3360
[8,6,1,7,5,4,2,3]=>[4,3,1]=>3360
[1,6,2,8,7,3,5,4]=>[3,2,2,1]=>1680
[1,8,2,4,6,7,3,5]=>[6,1,1]=>3360
[2,8,5,4,7,1,3,6]=>[4,3,1]=>3360
[2,1,5,8,6,4,3,7]=>[6,2]=>3360
[7,2,5,6,4,3,1,8]=>[4,2,1,1]=>2520
[1,2,5,7,8,4,3,6]=>[6,1,1]=>3360
[1,2,7,4,8,6,3,5]=>[2,2,1,1,1,1]=>210
[1,2,7,8,3,6,5,4]=>[3,2,1,1,1]=>1120
[7,1,8,6,3,5,4,2]=>[8]=>5040
[1,8,7,6,3,5,2,4]=>[7,1]=>5760
[1,8,7,4,6,3,2,5]=>[6,1,1]=>3360
[7,1,6,4,2,3,5,8]=>[4,2,1,1]=>2520
[8,6,2,4,7,3,5,1]=>[3,2,2,1]=>1680
[8,6,2,4,5,7,3,1]=>[4,2,1,1]=>2520
[7,1,4,6,5,8,3,2]=>[7,1]=>5760
[7,1,2,3,8,5,4,6]=>[5,3]=>2688
[7,1,5,4,3,8,2,6]=>[3,2,2,1]=>1680
[7,1,5,4,6,2,8,3]=>[7,1]=>5760
[3,6,2,4,7,8,1,5]=>[7,1]=>5760
[6,5,8,7,2,3,1,4]=>[6,2]=>3360
[6,5,7,8,2,4,1,3]=>[6,2]=>3360
[3,4,7,2,5,8,1,6]=>[3,2,2,1]=>1680
[4,3,8,1,2,7,5,6]=>[6,2]=>3360
[2,8,3,1,5,6,4,7]=>[5,1,1,1]=>1344
[3,8,7,1,5,4,2,6]=>[7,1]=>5760
[3,4,1,5,7,6,2,8]=>[4,2,1,1]=>2520
[2,8,6,1,5,3,7,4]=>[4,2,1,1]=>2520
[7,6,5,1,3,8,2,4]=>[6,2]=>3360
[6,7,5,2,1,3,8,4]=>[4,4]=>1260
[8,4,5,3,7,2,6,1]=>[6,2]=>3360
[4,7,5,2,8,1,6,3]=>[5,3]=>2688
[7,3,8,4,1,5,2,6]=>[7,1]=>5760
[7,2,3,4,1,6,5,8]=>[3,1,1,1,1,1]=>112
[4,2,8,3,6,1,5,7]=>[7,1]=>5760
[6,8,5,7,2,1,3,4]=>[6,2]=>3360
[4,8,5,2,7,1,3,6]=>[5,3]=>2688
[6,3,5,2,1,7,4,8]=>[7,1]=>5760
[6,8,5,3,1,4,2,7]=>[5,3]=>2688
[3,6,5,4,2,8,1,7]=>[7,1]=>5760
[1,6,4,7,2,5,3,8]=>[3,3,1,1]=>1120
[1,6,4,8,2,5,3,7]=>[4,3,1]=>3360
[1,6,5,8,2,4,3,7]=>[7,1]=>5760
[1,6,8,2,4,3,7,5]=>[6,1,1]=>3360
[1,6,2,4,3,7,8,5]=>[6,1,1]=>3360
[1,5,6,2,4,7,3,8]=>[3,3,1,1]=>1120
[1,5,6,2,4,7,8,3]=>[4,3,1]=>3360
[1,5,8,2,4,7,3,6]=>[4,3,1]=>3360
[1,5,7,2,4,8,3,6]=>[3,2,2,1]=>1680
[1,6,5,7,2,4,3,8]=>[6,1,1]=>3360
[1,6,7,2,4,3,8,5]=>[7,1]=>5760
[1,5,6,7,2,4,8,3]=>[5,2,1]=>4032
[1,5,8,2,4,6,7,3]=>[3,2,1,1,1]=>1120
[1,5,7,2,4,6,8,3]=>[3,3,1,1]=>1120
[1,5,7,8,3,2,4,6]=>[7,1]=>5760
[1,5,8,3,2,4,6,7]=>[5,2,1]=>4032
[1,5,6,2,4,8,3,7]=>[4,3,1]=>3360
[1,7,6,2,8,3,4,5]=>[3,2,2,1]=>1680
[1,7,3,4,2,8,6,5]=>[5,1,1,1]=>1344
[1,6,2,4,3,8,7,5]=>[5,1,1,1]=>1344
[1,5,6,2,4,8,7,3]=>[3,3,1,1]=>1120
[1,5,8,7,3,2,4,6]=>[5,2,1]=>4032
[1,4,2,3,5,8,7,6]=>[3,2,1,1,1]=>1120
[1,5,2,3,4,8,7,6]=>[4,2,1,1]=>2520
[1,6,5,2,3,8,7,4]=>[4,2,1,1]=>2520
[1,7,4,2,8,6,5,3]=>[6,1,1]=>3360
[1,7,6,5,2,8,4,3]=>[4,3,1]=>3360
[1,6,7,5,2,3,8,4]=>[7,1]=>5760
[1,7,5,2,8,4,3,6]=>[7,1]=>5760
[1,7,5,6,2,8,3,4]=>[4,3,1]=>3360
[1,5,7,6,2,4,8,3]=>[3,2,2,1]=>1680
[1,5,8,3,2,4,7,6]=>[4,2,1,1]=>2520
[1,6,5,2,3,7,4,8]=>[4,2,1,1]=>2520
[1,6,5,2,3,7,8,4]=>[5,2,1]=>4032
[1,6,8,4,2,3,7,5]=>[5,1,1,1]=>1344
[1,7,4,6,2,8,3,5]=>[7,1]=>5760
[1,7,3,5,2,8,4,6]=>[4,2,1,1]=>2520
[1,6,8,5,2,3,7,4]=>[6,1,1]=>3360
[1,6,4,2,3,7,8,5]=>[7,1]=>5760
[1,6,4,2,3,7,5,8]=>[6,1,1]=>3360
[1,5,8,6,2,4,7,3]=>[2,2,2,1,1]=>420
[1,5,7,3,2,4,8,6]=>[5,2,1]=>4032
[1,7,3,4,2,8,5,6]=>[3,2,1,1,1]=>1120
[1,7,4,2,8,5,3,6]=>[4,3,1]=>3360
[1,6,7,4,2,3,8,5]=>[6,1,1]=>3360
[1,6,4,2,3,8,5,7]=>[7,1]=>5760
[1,7,6,4,2,8,5,3]=>[3,3,1,1]=>1120
[1,7,5,2,8,6,4,3]=>[3,3,1,1]=>1120
[1,6,4,2,3,8,7,5]=>[6,1,1]=>3360
[7,3,5,6,1,4,8,2]=>[6,2]=>3360
[3,7,5,6,1,4,8,2]=>[3,3,2]=>1120
[8,2,4,1,6,7,5,3]=>[4,3,1]=>3360
[8,6,1,4,2,7,5,3]=>[4,3,1]=>3360
[3,6,1,4,2,8,5,7]=>[5,2,1]=>4032
[1,6,7,4,3,5,8,2]=>[6,1,1]=>3360
[6,7,1,4,3,5,8,2]=>[4,3,1]=>3360
[7,6,1,4,3,5,8,2]=>[7,1]=>5760
[3,5,4,1,6,7,8,2]=>[5,3]=>2688
[4,7,1,6,3,5,8,2]=>[5,3]=>2688
[3,1,4,7,6,5,8,2]=>[6,2]=>3360
[6,1,7,4,3,5,8,2]=>[7,1]=>5760
[7,1,6,4,3,5,8,2]=>[4,3,1]=>3360
[1,7,6,4,3,5,8,2]=>[3,3,1,1]=>1120
[8,1,6,4,2,7,5,3]=>[7,1]=>5760
[8,4,1,3,7,2,5,6]=>[6,2]=>3360
[4,7,1,3,8,2,5,6]=>[5,3]=>2688
[7,4,1,3,8,2,5,6]=>[8]=>5040
[1,3,6,4,2,8,5,7]=>[6,1,1]=>3360
[4,7,3,1,2,8,5,6]=>[3,2,2,1]=>1680
[4,7,8,1,2,6,5,3]=>[3,2,2,1]=>1680
[6,8,1,4,2,7,5,3]=>[7,1]=>5760
[1,8,6,4,2,7,5,3]=>[6,1,1]=>3360
[4,8,1,3,7,2,5,6]=>[3,3,2]=>1120
[8,7,1,3,6,2,5,4]=>[4,4]=>1260
[6,8,5,7,3,2,1,4]=>[6,2]=>3360
[1,8,4,3,7,2,5,6]=>[3,2,2,1]=>1680
[2,8,3,4,7,6,1,5]=>[5,1,1,1]=>1344
[3,7,8,4,6,2,1,5]=>[7,1]=>5760
[3,7,4,6,8,2,1,5]=>[6,2]=>3360
[2,4,3,7,8,6,1,5]=>[4,2,1,1]=>2520
[1,4,7,3,8,2,5,6]=>[7,1]=>5760
[5,7,6,8,3,2,1,4]=>[6,2]=>3360
[2,5,3,4,8,6,1,7]=>[5,1,1,1]=>1344
[3,7,5,4,8,2,1,6]=>[7,1]=>5760
[7,1,3,4,2,8,5,6]=>[4,2,1,1]=>2520
[6,1,4,3,8,2,5,7]=>[3,3,2]=>1120
[4,1,7,3,8,2,5,6]=>[8]=>5040
[8,1,4,3,7,2,5,6]=>[4,2,2]=>1260
[8,2,3,4,7,6,1,5]=>[4,1,1,1,1]=>420
[4,2,3,7,8,6,1,5]=>[3,2,1,1,1]=>1120
[5,2,3,4,8,6,1,7]=>[4,1,1,1,1]=>420
[2,7,5,6,3,8,1,4]=>[3,3,2]=>1120
[5,7,2,6,3,8,1,4]=>[5,3]=>2688
[5,7,2,6,8,4,1,3]=>[6,2]=>3360
[7,2,5,6,8,4,1,3]=>[3,2,2,1]=>1680
[4,2,3,8,5,6,1,7]=>[4,1,1,1,1]=>420
[5,2,3,8,7,6,1,4]=>[3,2,1,1,1]=>1120
[8,2,3,7,5,6,1,4]=>[4,1,1,1,1]=>420
[6,1,8,3,7,2,5,4]=>[3,3,2]=>1120
[1,7,8,4,2,6,5,3]=>[3,2,1,1,1]=>1120
[4,7,1,8,2,5,6,3]=>[4,4]=>1260
[3,7,4,8,5,2,1,6]=>[7,1]=>5760
[2,4,3,8,5,6,1,7]=>[5,1,1,1]=>1344
[1,4,8,3,6,2,5,7]=>[7,1]=>5760
[7,5,8,6,3,2,1,4]=>[6,2]=>3360
[6,5,8,7,3,2,1,4]=>[8]=>5040
[8,5,7,6,3,2,1,4]=>[8]=>5040
[2,5,3,8,7,6,1,4]=>[4,2,1,1]=>2520
[3,7,5,8,6,2,1,4]=>[6,2]=>3360
[3,7,8,6,5,2,1,4]=>[7,1]=>5760
[1,8,7,3,6,2,5,4]=>[7,1]=>5760
[6,8,7,5,3,2,1,4]=>[8]=>5040
[5,7,6,8,3,4,1,2]=>[8]=>5040
[1,5,4,7,6,8,2,3]=>[7,1]=>5760
[1,7,4,6,5,8,2,3]=>[4,2,1,1]=>2520
[3,6,4,7,5,8,1,2]=>[4,3,1]=>3360
[1,6,2,7,5,8,3,4]=>[6,1,1]=>3360
[1,8,4,6,5,7,2,3]=>[6,1,1]=>3360
[7,8,1,5,2,4,3,6]=>[5,3]=>2688
[1,8,2,6,5,7,3,4]=>[6,1,1]=>3360
[1,7,2,8,5,6,3,4]=>[3,2,1,1,1]=>1120
[5,7,6,8,1,4,2,3]=>[4,2,2]=>1260
[7,8,5,6,1,3,2,4]=>[8]=>5040
[5,8,6,7,1,3,2,4]=>[4,2,2]=>1260
[1,3,2,7,6,8,4,5]=>[3,2,2,1]=>1680
[1,7,6,8,2,4,3,5]=>[7,1]=>5760
[7,8,1,6,2,4,3,5]=>[3,3,2]=>1120
[7,8,1,4,2,6,3,5]=>[3,3,1,1]=>1120
[7,8,1,4,2,5,3,6]=>[4,3,1]=>3360
[7,8,2,1,4,3,6,5]=>[8]=>5040
[7,8,1,2,4,3,5,6]=>[8]=>5040
[4,3,6,5,8,7,1,2]=>[8]=>5040
[3,4,6,5,7,8,1,2]=>[8]=>5040
[3,4,1,5,6,7,8,9,2]=>[7,2]=>25920
[3,4,5,1,6,7,8,9,2]=>[9]=>40320
[3,4,5,6,7,1,8,9,2]=>[9]=>40320
[3,4,5,6,7,8,1,9,2]=>[5,4]=>18144
[3,1,2,5,6,7,8,9,4]=>[6,3]=>20160
[3,4,1,5,6,7,8,9,10,2]=>[8,2]=>226800
[3,4,5,6,1,7,8,9,10,2]=>[7,3]=>172800
[3,4,5,6,7,1,2,9,8]=>[7,2]=>25920
[3,4,5,6,7,8,1,2,9]=>[4,4,1]=>11340
[3,4,5,6,7,8,9,1,10,2]=>[10]=>362880
[1,6,2,3,8,7,4,5]=>[5,2,1]=>4032
[1,7,4,3,2,8,6,5]=>[5,2,1]=>4032
[1,4,7,6,2,5,8,3]=>[4,3,1]=>3360
[1,2,6,5,3,7,4,8]=>[5,1,1,1]=>1344
[1,2,6,5,3,7,8,4]=>[6,1,1]=>3360
[1,3,7,5,2,6,8,4]=>[6,1,1]=>3360
[1,3,7,4,2,6,8,5]=>[5,1,1,1]=>1344
[1,2,6,4,3,7,8,5]=>[5,1,1,1]=>1344
[1,2,6,4,3,7,5,8]=>[4,1,1,1,1]=>420
[1,4,7,3,2,5,8,6]=>[7,1]=>5760
[1,4,3,2,5,8,6,7]=>[3,2,1,1,1]=>1120
[1,5,3,2,4,8,6,7]=>[3,3,1,1]=>1120
[1,7,5,3,2,8,6,4]=>[7,1]=>5760
[1,5,3,2,4,8,7,6]=>[3,2,1,1,1]=>1120
[7,6,5,4,3,1,8,2]=>[5,2,1]=>4032
[6,8,5,4,3,2,1,7]=>[5,2,1]=>4032
[8,7,6,5,4,3,1,9,2]=>[5,2,2]=>9072
[7,9,6,5,4,3,2,1,8]=>[5,2,2]=>9072
[9,8,7,6,5,4,3,1,10,2]=>[5,2,2,1]=>90720
[7,1,5,4,3,8,6,2]=>[5,2,1]=>4032
[2,8,5,4,3,7,1,6]=>[5,2,1]=>4032
[8,10,7,6,5,4,3,2,1,9]=>[5,2,2,1]=>90720
[1,8,7,6,5,4,3,10,9,2]=>[3,2,2,1,1,1]=>25200
[7,6,1,4,3,8,5,2]=>[4,3,1]=>3360
[3,8,5,4,7,2,1,6]=>[4,3,1]=>3360
[9,11,8,7,6,5,4,3,2,1,10]=>[5,2,2,2]=>166320
[7,6,5,1,3,8,4,2]=>[3,3,2]=>1120
[6,8,2,4,3,7,1,5]=>[4,3,1]=>3360
[1,8,3,4,7,2,6,5]=>[5,1,1,1]=>1344
[7,5,8,4,3,2,1,6]=>[5,2,1]=>4032
[4,8,5,7,3,2,1,6]=>[3,3,2]=>1120
[5,1,7,6,8,4,3,2]=>[4,2,2]=>1260
[8,4,7,5,2,6,1,3]=>[4,3,1]=>3360
[5,4,6,8,2,1,7,3]=>[7,1]=>5760
[8,4,6,5,2,1,7,3]=>[4,3,1]=>3360
[4,8,7,5,6,1,3,2]=>[4,2,2]=>1260
[2,7,5,1,8,4,3,6]=>[8]=>5040
[5,1,8,7,4,2,3,6]=>[8]=>5040
[2,8,6,7,4,3,5,1]=>[3,3,2]=>1120
[3,6,5,2,4,1,8,7]=>[6,2]=>3360
[5,2,3,6,4,1,8,7]=>[4,2,1,1]=>2520
[6,1,4,5,3,2,8,7]=>[3,3,2]=>1120
[3,8,7,1,4,6,5,2]=>[5,2,1]=>4032
[5,7,1,2,4,3,8,6]=>[8]=>5040
[4,3,7,6,8,2,5,1]=>[8]=>5040
[5,3,6,8,1,7,2,4]=>[4,2,2]=>1260
[3,2,6,8,5,7,1,4]=>[4,2,1,1]=>2520
[6,3,7,2,4,8,5,1]=>[5,3]=>2688
[7,4,8,6,5,2,1,3]=>[3,2,2,1]=>1680
[7,1,8,2,5,4,3,6]=>[7,1]=>5760
[2,5,3,7,4,1,8,6]=>[7,1]=>5760
[3,6,4,7,5,1,8,2]=>[7,1]=>5760
[8,4,7,6,2,3,1,5]=>[8]=>5040
[8,4,7,1,2,5,6,3]=>[8]=>5040
[4,2,8,7,3,5,6,1]=>[7,1]=>5760
[8,1,7,4,2,5,6,3]=>[7,1]=>5760
[7,4,3,8,2,5,6,1]=>[7,1]=>5760
[6,4,1,5,8,2,7,3]=>[7,1]=>5760
[2,5,8,7,3,6,1,4]=>[7,1]=>5760
[2,1,5,8,7,4,6,3]=>[6,2]=>3360
[8,3,5,6,7,4,1,2]=>[6,2]=>3360
[7,4,3,2,8,5,6,1]=>[5,2,1]=>4032
[4,2,7,1,8,5,6,3]=>[5,2,1]=>4032
[4,1,7,2,8,5,6,3]=>[5,3]=>2688
[2,4,8,7,3,5,6,1]=>[8]=>5040
[4,7,8,3,1,5,6,2]=>[8]=>5040
[3,4,7,2,8,5,6,1]=>[6,2]=>3360
[3,7,1,4,8,5,6,2]=>[5,2,1]=>4032
[7,2,3,4,8,5,6,1]=>[5,1,1,1]=>1344
[6,1,8,5,2,7,4,3]=>[6,2]=>3360
[2,1,7,4,5,8,6,3]=>[4,2,1,1]=>2520
[2,1,8,3,6,7,5,4]=>[3,3,2]=>1120
[8,2,1,6,4,7,5,3]=>[4,3,1]=>3360
[7,8,2,6,4,1,5,3]=>[5,3]=>2688
[2,6,3,5,8,7,1,4]=>[4,3,1]=>3360
[7,6,2,1,5,8,4,3]=>[4,3,1]=>3360
[4,5,2,7,6,1,8,3]=>[8]=>5040
[5,1,6,8,4,7,2,3]=>[8]=>5040
[3,6,8,7,5,2,1,4]=>[5,2,1]=>4032
[7,4,8,6,5,2,3,1]=>[4,3,1]=>3360
[8,1,6,4,7,3,2,5]=>[5,2,1]=>4032
[7,6,4,1,2,3,8,5]=>[8]=>5040
[2,6,4,8,5,3,7,1]=>[6,1,1]=>3360
[7,3,5,8,4,2,1,6]=>[6,2]=>3360
[3,2,5,8,4,1,7,6]=>[6,1,1]=>3360
[8,4,7,1,5,2,3,6]=>[5,2,1]=>4032
[4,8,7,5,6,1,2,3]=>[4,4]=>1260
[6,1,4,8,7,3,5,2]=>[6,2]=>3360
[7,2,8,4,3,5,6,1]=>[6,1,1]=>3360
[4,7,8,1,3,5,6,2]=>[6,2]=>3360
[8,7,3,4,1,5,6,2]=>[6,1,1]=>3360
[4,8,2,7,3,5,6,1]=>[8]=>5040
[3,1,8,7,2,5,6,4]=>[8]=>5040
[3,8,1,7,2,5,6,4]=>[6,2]=>3360
[8,2,3,7,1,5,6,4]=>[6,1,1]=>3360
[6,4,8,7,1,3,2,5]=>[5,3]=>2688
[2,8,4,6,7,3,1,5]=>[5,3]=>2688
[4,3,8,2,7,6,1,5]=>[7,1]=>5760
[6,8,4,2,1,3,7,5]=>[7,1]=>5760
[7,8,2,4,3,5,6,1]=>[7,1]=>5760
[2,8,3,7,1,5,6,4]=>[7,1]=>5760
[8,1,2,7,3,5,6,4]=>[8]=>5040
[6,4,1,3,2,8,5,7]=>[8]=>5040
[5,3,8,6,2,1,4,7]=>[8]=>5040
[4,6,5,2,8,3,1,7]=>[8]=>5040
[4,3,7,5,1,8,2,6]=>[3,3,2]=>1120
[6,8,5,2,7,4,3,1]=>[5,3]=>2688
[7,2,5,4,3,8,1,6]=>[2,2,2,1,1]=>420
[3,6,8,1,4,5,2,7]=>[8]=>5040
[6,8,1,2,4,5,3,7]=>[8]=>5040
[8,1,6,2,4,5,3,7]=>[8]=>5040
[3,8,6,1,2,5,4,7]=>[8]=>5040
[5,8,1,6,2,3,4,7]=>[8]=>5040
[4,1,6,5,8,2,3,7]=>[8]=>5040
[4,3,8,6,2,5,1,7]=>[8]=>5040
[8,3,6,1,4,5,2,7]=>[8]=>5040
[2,3,6,8,4,5,1,7]=>[8]=>5040
[2,7,5,4,3,8,1,6]=>[3,2,2,1]=>1680
[6,3,8,7,4,2,5,1]=>[5,3]=>2688
[5,8,4,3,7,6,1,2]=>[3,2,2,1]=>1680
[8,7,4,3,1,6,2,5]=>[3,2,2,1]=>1680
[1,7,4,3,8,6,2,5]=>[2,2,2,1,1]=>420
[7,1,5,3,4,8,2,6]=>[3,3,2]=>1120
[2,8,6,1,7,4,5,3]=>[6,2]=>3360
[4,8,6,5,7,2,1,3]=>[4,4]=>1260
[4,7,6,8,2,1,5,3]=>[5,3]=>2688
[6,1,8,7,4,3,5,2]=>[5,3]=>2688
[8,5,4,3,1,6,7,2]=>[4,2,1,1]=>2520
[1,5,8,6,3,4,7,2]=>[4,2,1,1]=>2520
[2,5,8,6,3,4,7,1]=>[5,2,1]=>4032
[4,1,3,8,5,6,7,2]=>[4,1,1,1,1]=>420
[6,5,8,4,3,1,7,2]=>[4,2,1,1]=>2520
[4,6,5,2,8,1,7,3]=>[4,3,1]=>3360
[7,2,8,1,3,6,4,5]=>[3,3,1,1]=>1120
[1,8,5,2,3,6,7,4]=>[3,2,1,1,1]=>1120
[1,8,3,2,5,6,7,4]=>[3,1,1,1,1,1]=>112
[2,8,3,1,5,6,7,4]=>[4,1,1,1,1]=>420
[4,8,3,2,5,6,7,1]=>[4,1,1,1,1]=>420
[8,2,3,1,5,6,7,4]=>[3,1,1,1,1,1]=>112
[2,1,8,3,5,6,7,4]=>[3,2,1,1,1]=>1120
[1,4,8,2,3,6,7,5]=>[3,2,1,1,1]=>1120
[3,1,2,7,8,6,4,5]=>[3,2,2,1]=>1680
[7,5,1,8,2,4,3,6]=>[3,3,2]=>1120
[3,5,8,1,2,4,7,6]=>[5,2,1]=>4032
[4,5,8,1,2,3,7,6]=>[3,2,2,1]=>1680
[4,2,7,1,8,6,3,5]=>[2,2,2,1,1]=>420
[3,8,4,1,2,6,7,5]=>[3,3,1,1]=>1120
[5,4,8,2,3,6,7,1]=>[4,2,1,1]=>2520
[5,8,3,6,7,4,1,2]=>[3,2,2,1]=>1680
[2,3,1,6,8,4,7,5]=>[3,2,2,1]=>1680
[2,4,3,7,1,8,5,6]=>[5,2,1]=>4032
[1,4,7,3,2,8,5,6]=>[5,2,1]=>4032
[2,7,1,4,3,8,5,6]=>[5,2,1]=>4032
[2,4,1,8,6,3,7,5]=>[7,1]=>5760
[8,4,1,3,6,2,7,5]=>[7,1]=>5760
[6,8,5,1,7,2,3,4]=>[5,3]=>2688
[7,3,6,5,8,2,1,4]=>[3,3,2]=>1120
[7,6,3,5,8,2,1,4]=>[3,2,2,1]=>1680
[4,5,8,7,3,6,1,2]=>[4,3,1]=>3360
[3,5,2,8,6,1,7,4]=>[5,2,1]=>4032
[8,2,5,6,1,4,7,3]=>[4,2,1,1]=>2520
[8,6,5,4,1,2,7,3]=>[4,2,1,1]=>2520
[2,6,1,8,3,7,5,4]=>[6,2]=>3360
[4,7,1,6,2,8,5,3]=>[5,3]=>2688
[6,1,5,3,8,7,2,4]=>[4,4]=>1260
[2,8,6,3,7,1,5,4]=>[6,2]=>3360
[7,6,1,5,8,2,3,4]=>[3,3,2]=>1120
[3,6,8,5,1,2,7,4]=>[5,2,1]=>4032
[6,5,2,4,8,1,7,3]=>[4,2,1,1]=>2520
[5,1,4,8,2,6,7,3]=>[3,3,1,1]=>1120
[4,8,2,5,1,6,7,3]=>[3,3,1,1]=>1120
[3,4,8,5,2,6,7,1]=>[3,3,1,1]=>1120
[4,2,1,8,5,6,7,3]=>[4,1,1,1,1]=>420
[1,5,4,8,2,6,7,3]=>[3,2,1,1,1]=>1120
[7,2,1,5,8,6,3,4]=>[3,3,1,1]=>1120
[2,8,4,5,1,6,7,3]=>[6,1,1]=>3360
[5,4,8,3,7,6,1,2]=>[4,3,1]=>3360
[3,1,5,8,6,2,7,4]=>[5,2,1]=>4032
[6,3,4,8,5,1,7,2]=>[4,2,1,1]=>2520
[5,3,4,8,1,6,7,2]=>[4,2,1,1]=>2520
[7,6,1,2,8,3,5,4]=>[8]=>5040
[7,5,8,4,1,2,6,3]=>[5,2,1]=>4032
[7,5,8,4,6,1,3,2]=>[7,1]=>5760
[6,5,4,8,7,1,3,2]=>[6,2]=>3360
[6,5,4,8,1,2,7,3]=>[4,3,1]=>3360
[7,5,1,6,2,3,8,4]=>[6,2]=>3360
[7,5,1,6,8,2,4,3]=>[8]=>5040
[6,5,4,1,8,2,7,3]=>[7,1]=>5760
[6,5,4,7,1,2,8,3]=>[4,4]=>1260
[6,5,4,7,8,1,3,2]=>[3,3,2]=>1120
[6,5,3,7,1,4,2,8]=>[6,1,1]=>3360
[6,5,3,1,8,4,2,7]=>[4,3,1]=>3360
[7,5,1,4,8,3,2,6]=>[7,1]=>5760
[8,1,6,4,7,3,5,2]=>[3,2,2,1]=>1680
[7,5,1,4,8,3,6,2]=>[4,3,1]=>3360
[6,5,3,7,1,4,8,2]=>[7,1]=>5760
[6,4,3,1,5,8,7,2]=>[5,1,1,1]=>1344
[7,4,1,5,3,8,6,2]=>[8]=>5040
[8,1,5,4,3,7,6,2]=>[3,2,2,1]=>1680
[8,1,5,4,3,7,2,6]=>[5,2,1]=>4032
[7,4,1,5,3,8,2,6]=>[6,2]=>3360
[7,4,1,5,3,2,6,8]=>[7,1]=>5760
[8,1,5,4,3,2,6,7]=>[5,2,1]=>4032
[8,1,6,4,2,5,3,7]=>[7,1]=>5760
[6,5,3,1,2,7,4,8]=>[4,2,1,1]=>2520
[6,5,3,8,1,4,2,7]=>[7,1]=>5760
[7,6,8,1,4,3,2,5]=>[8]=>5040
[8,1,7,2,5,4,3,6]=>[5,2,1]=>4032
[8,1,7,2,5,4,6,3]=>[7,1]=>5760
[7,6,1,2,5,4,8,3]=>[4,3,1]=>3360
[6,5,3,8,1,4,7,2]=>[6,1,1]=>3360
[6,5,3,1,2,7,8,4]=>[5,2,1]=>4032
[7,5,1,4,2,6,8,3]=>[4,2,1,1]=>2520
[8,1,6,4,2,5,7,3]=>[6,1,1]=>3360
[7,4,1,5,3,2,8,6]=>[8]=>5040
[6,4,3,1,5,2,8,7]=>[4,2,1,1]=>2520
[6,4,3,1,5,7,2,8]=>[5,1,1,1]=>1344
[7,4,1,5,3,6,2,8]=>[6,1,1]=>3360
[8,1,5,4,3,6,2,7]=>[4,2,1,1]=>2520
[8,1,5,4,3,6,7,2]=>[3,2,1,1,1]=>1120
[7,4,1,5,3,6,8,2]=>[7,1]=>5760
[6,4,3,1,5,7,8,2]=>[6,1,1]=>3360
[6,7,3,8,4,5,1,2]=>[7,1]=>5760
[6,7,4,5,1,8,2,3]=>[6,2]=>3360
[4,7,5,6,1,8,2,3]=>[6,2]=>3360
[4,7,5,6,3,8,1,2]=>[6,2]=>3360
[4,5,3,8,6,7,1,2]=>[7,1]=>5760
[5,6,4,7,1,8,2,3]=>[6,2]=>3360
[5,6,1,8,4,7,2,3]=>[5,3]=>2688
[4,5,1,8,6,7,2,3]=>[4,4]=>1260
[7,8,4,5,1,6,2,3]=>[7,1]=>5760
[3,6,4,5,2,7,1,8]=>[7,1]=>5760
[3,6,4,5,1,8,2,7]=>[4,4]=>1260
[2,6,4,8,1,5,3,7]=>[4,4]=>1260
[2,8,3,6,1,5,4,7]=>[7,1]=>5760
[7,8,1,5,3,6,2,4]=>[7,1]=>5760
[1,8,3,6,2,7,4,5]=>[3,3,1,1]=>1120
[2,6,4,7,3,5,1,8]=>[7,1]=>5760
[1,7,3,6,4,8,2,5]=>[4,2,1,1]=>2520
[1,7,5,8,4,6,2,3]=>[4,2,1,1]=>2520
[6,7,1,5,3,8,2,4]=>[6,2]=>3360
[6,7,5,8,1,4,2,3]=>[6,2]=>3360
[5,8,6,7,2,3,1,4]=>[6,2]=>3360
[6,7,2,3,1,8,4,5]=>[4,4]=>1260
[6,7,2,8,1,4,3,5]=>[5,3]=>2688
[3,4,2,7,5,6,1,8]=>[5,1,1,1]=>1344
[2,3,1,8,4,7,5,6]=>[5,3]=>2688
[7,8,2,3,1,6,4,5]=>[7,1]=>5760
[2,8,6,7,1,4,3,5]=>[4,4]=>1260
[2,8,1,4,3,7,5,6]=>[7,1]=>5760
[3,7,2,5,4,6,1,8]=>[4,2,1,1]=>2520
[4,5,2,7,3,6,1,8]=>[3,3,1,1]=>1120
[4,5,1,8,2,7,3,6]=>[6,2]=>3360
[3,4,1,8,6,7,2,5]=>[6,2]=>3360
[3,4,2,5,1,8,6,7]=>[5,3]=>2688
[4,5,2,8,1,6,3,7]=>[7,1]=>5760
[4,5,3,6,1,8,2,7]=>[7,1]=>5760
[7,1,5,8,4,6,2,3]=>[4,3,1]=>3360
[8,6,7,1,4,2,5,3]=>[6,2]=>3360
[8,6,3,7,5,1,2,4]=>[6,1,1]=>3360
[8,6,1,7,3,2,5,4]=>[6,2]=>3360
[7,6,1,8,3,5,2,4]=>[6,2]=>3360
[7,6,1,3,8,5,2,4]=>[8]=>5040
[7,6,8,2,4,5,1,3]=>[4,2,2]=>1260
[7,6,2,8,3,5,1,4]=>[4,2,2]=>1260
[7,6,2,3,8,5,1,4]=>[6,2]=>3360
[8,7,1,5,2,6,3,4]=>[7,1]=>5760
[8,7,1,5,2,3,6,4]=>[8]=>5040
[8,5,2,3,1,7,6,4]=>[6,2]=>3360
[8,6,2,3,7,1,5,4]=>[6,2]=>3360
[8,6,2,7,3,1,5,4]=>[8]=>5040
[8,6,7,2,4,1,5,3]=>[8]=>5040
[6,8,7,3,4,1,5,2]=>[4,2,2]=>1260
[8,7,2,5,1,6,3,4]=>[4,3,1]=>3360
[8,7,2,1,4,6,3,5]=>[4,3,1]=>3360
[8,4,2,1,7,6,3,5]=>[7,1]=>5760
[8,5,2,7,1,6,3,4]=>[7,1]=>5760
[8,5,7,2,1,4,3,6]=>[6,2]=>3360
[5,8,7,3,1,4,2,6]=>[6,2]=>3360
[5,8,7,3,1,4,6,2]=>[4,2,2]=>1260
[8,5,7,2,1,4,6,3]=>[8]=>5040
[8,5,2,7,1,3,6,4]=>[8]=>5040
[8,4,2,1,3,7,6,5]=>[6,2]=>3360
[8,7,4,1,2,3,6,5]=>[8]=>5040
[8,7,4,1,2,6,3,5]=>[7,1]=>5760
[8,4,3,1,7,2,6,5]=>[7,1]=>5760
[8,4,3,1,2,7,6,5]=>[5,2,1]=>4032
[8,6,1,3,7,2,5,4]=>[4,2,2]=>1260
[8,5,1,3,2,7,6,4]=>[4,2,2]=>1260
[8,5,7,4,1,6,2,3]=>[6,1,1]=>3360
[8,5,7,4,1,2,6,3]=>[7,1]=>5760
[8,1,5,4,2,7,6,3]=>[5,2,1]=>4032
[8,1,6,4,7,2,5,3]=>[5,2,1]=>4032
[6,1,5,8,4,2,7,3]=>[4,3,1]=>3360
[5,8,3,6,4,1,2,7]=>[4,3,1]=>3360
[5,2,8,6,4,1,3,7]=>[4,3,1]=>3360
[8,4,7,5,1,6,2,3]=>[7,1]=>5760
[8,4,7,5,1,2,6,3]=>[8]=>5040
[8,4,7,5,1,2,3,6]=>[6,2]=>3360
[8,7,3,5,1,2,6,4]=>[4,3,1]=>3360
[8,3,2,6,5,1,4,7]=>[5,2,1]=>4032
[4,8,6,3,5,1,2,7]=>[4,3,1]=>3360
[4,8,7,3,1,5,2,6]=>[8]=>5040
[8,4,7,2,1,5,3,6]=>[4,2,2]=>1260
[8,3,2,7,1,5,4,6]=>[4,2,2]=>1260
[8,3,2,1,7,6,4,5]=>[5,2,1]=>4032
[8,7,3,1,4,2,6,5]=>[4,3,1]=>3360
[8,7,3,1,6,2,4,5]=>[7,1]=>5760
[8,7,3,1,2,6,4,5]=>[6,1,1]=>3360
[8,7,3,1,2,4,6,5]=>[7,1]=>5760
[8,3,2,1,4,7,6,5]=>[4,2,2]=>1260
[8,3,2,1,7,4,6,5]=>[6,2]=>3360
[8,3,2,7,1,5,6,4]=>[6,2]=>3360
[8,4,7,2,1,5,6,3]=>[6,2]=>3360
[3,8,7,4,1,2,5,6]=>[4,3,1]=>3360
[8,7,2,1,6,3,4,5]=>[8]=>5040
[8,7,2,1,3,6,4,5]=>[7,1]=>5760
[8,7,2,1,3,4,6,5]=>[8]=>5040
[3,6,5,4,1,2,8,7]=>[3,2,2,1]=>1680
[3,8,5,6,7,4,1,2]=>[4,2,2]=>1260
[4,7,5,8,6,2,1,3]=>[8]=>5040
[2,5,7,8,6,3,4,1]=>[8]=>5040
[4,8,5,7,6,3,1,2]=>[3,3,2]=>1120
[4,6,3,2,1,5,8,7]=>[5,2,1]=>4032
[6,2,1,5,3,4,8,7]=>[5,2,1]=>4032
[5,8,1,3,7,6,4,2]=>[5,2,1]=>4032
[4,7,2,3,6,1,8,5]=>[8]=>5040
[3,7,4,2,8,1,5,6]=>[8]=>5040
[4,2,6,8,5,7,3,1]=>[3,3,1,1]=>1120
[6,4,2,7,3,8,5,1]=>[5,3]=>2688
[8,1,6,7,5,3,4,2]=>[3,2,2,1]=>1680
[2,1,5,8,7,6,3,4]=>[3,2,2,1]=>1680
[2,1,4,7,6,3,8,5]=>[6,2]=>3360
[6,4,7,8,5,3,2,1]=>[7,1]=>5760
[4,1,3,7,6,2,8,5]=>[7,1]=>5760
[8,5,1,6,3,2,7,4]=>[7,1]=>5760
[6,3,7,1,5,2,8,4]=>[7,1]=>5760
[3,2,6,8,4,7,5,1]=>[7,1]=>5760
[8,4,6,1,3,2,5,7]=>[8]=>5040
[4,2,8,6,7,3,1,5]=>[7,1]=>5760
[7,4,3,8,2,1,5,6]=>[7,1]=>5760
[4,7,5,8,1,6,3,2]=>[7,1]=>5760
[6,4,3,2,7,8,1,5]=>[5,2,1]=>4032
[4,2,5,1,6,7,8,3]=>[5,2,1]=>4032
[2,4,8,5,7,1,3,6]=>[8]=>5040
[3,7,1,4,6,8,5,2]=>[5,2,1]=>4032
[7,8,2,5,6,1,4,3]=>[5,3]=>2688
[2,4,3,8,7,5,6,1]=>[4,3,1]=>3360
[2,6,7,3,5,1,8,4]=>[4,3,1]=>3360
[7,6,8,4,2,5,3,1]=>[4,3,1]=>3360
[8,5,7,1,6,3,2,4]=>[5,3]=>2688
[6,5,7,2,8,4,3,1]=>[6,2]=>3360
[3,4,8,6,5,2,1,7]=>[4,3,1]=>3360
[2,7,6,1,4,5,8,3]=>[8]=>5040
[6,5,8,2,1,7,3,4]=>[8]=>5040
[7,4,3,5,1,6,8,2]=>[6,1,1]=>3360
[4,1,6,3,5,8,7,2]=>[6,1,1]=>3360
[6,2,5,8,4,3,7,1]=>[6,1,1]=>3360
[8,6,7,1,5,4,3,2]=>[5,2,1]=>4032
[2,1,6,5,8,4,7,3]=>[5,2,1]=>4032
[2,1,6,8,5,4,3,7]=>[5,2,1]=>4032
[4,1,8,5,6,2,3,7]=>[5,3]=>2688
[2,6,4,8,7,3,5,1]=>[6,2]=>3360
[6,2,8,4,3,5,1,7]=>[6,1,1]=>3360
[4,8,2,7,6,1,3,5]=>[8]=>5040
[3,1,8,2,7,5,4,6]=>[8]=>5040
[3,8,1,2,6,7,4,5]=>[6,2]=>3360
[5,8,4,3,2,7,1,6]=>[6,2]=>3360
[7,4,8,6,3,2,5,1]=>[5,3]=>2688
[5,8,4,7,2,1,3,6]=>[5,3]=>2688
[2,1,8,4,3,7,5,6]=>[5,2,1]=>4032
[6,3,8,2,4,5,7,1]=>[7,1]=>5760
[5,8,4,2,3,6,1,7]=>[7,1]=>5760
[5,8,2,4,3,1,6,7]=>[7,1]=>5760
[2,8,3,1,6,4,5,7]=>[7,1]=>5760
[8,2,1,3,4,7,5,6]=>[7,1]=>5760
[1,4,8,2,6,3,5,7]=>[5,2,1]=>4032
[1,2,7,3,5,4,8,6]=>[5,1,1,1]=>1344
[1,2,3,8,4,5,7,6]=>[4,1,1,1,1]=>420
[1,2,8,3,4,5,7,6]=>[5,1,1,1]=>1344
[1,3,8,2,6,4,5,7]=>[7,1]=>5760
[1,5,7,2,3,6,4,8]=>[5,1,1,1]=>1344
[1,7,2,3,5,4,8,6]=>[6,1,1]=>3360
[1,3,8,2,4,5,7,6]=>[6,1,1]=>3360
[1,2,3,8,4,6,7,5]=>[3,1,1,1,1,1]=>112
[1,8,2,3,5,4,6,7]=>[6,1,1]=>3360
[1,7,8,2,3,6,4,5]=>[3,3,1,1]=>1120
[1,6,7,8,2,3,5,4]=>[5,2,1]=>4032
[1,7,8,2,5,3,6,4]=>[6,1,1]=>3360
[1,7,8,2,4,5,3,6]=>[7,1]=>5760
[1,2,8,3,6,4,5,7]=>[6,1,1]=>3360
[1,8,2,3,6,4,5,7]=>[7,1]=>5760
[1,2,8,3,5,4,6,7]=>[5,1,1,1]=>1344
[1,2,7,8,3,6,4,5]=>[5,1,1,1]=>1344
[1,5,2,7,8,3,6,4]=>[7,1]=>5760
[1,3,2,8,4,6,7,5]=>[3,2,1,1,1]=>1120
[1,8,2,3,4,6,7,5]=>[5,1,1,1]=>1344
[1,7,8,2,4,3,6,5]=>[7,1]=>5760
[6,7,3,1,5,2,8,4]=>[6,1,1]=>3360
[6,8,3,1,5,2,7,4]=>[5,1,1,1]=>1344
[6,7,4,5,1,2,8,3]=>[8]=>5040
[7,3,6,1,5,2,4,8]=>[3,3,1,1]=>1120
[6,7,5,4,1,2,8,3]=>[7,1]=>5760
[5,8,6,4,1,7,2,3]=>[5,2,1]=>4032
[5,7,6,4,1,8,2,3]=>[3,2,2,1]=>1680
[6,4,7,5,1,2,8,3]=>[5,3]=>2688
[6,3,8,1,5,2,7,4]=>[6,1,1]=>3360
[5,6,8,4,1,7,2,3]=>[3,2,2,1]=>1680
[4,6,8,5,7,1,2,3]=>[6,2]=>3360
[5,4,8,6,1,7,2,3]=>[4,2,2]=>1260
[5,3,8,1,6,7,2,4]=>[8]=>5040
[5,4,7,6,1,8,2,3]=>[6,2]=>3360
[4,8,6,5,7,1,2,3]=>[8]=>5040
[4,6,5,7,8,1,2,3]=>[5,3]=>2688
[5,7,4,6,1,8,2,3]=>[4,2,2]=>1260
[5,8,4,6,1,7,2,3]=>[6,2]=>3360
[5,8,3,1,6,7,2,4]=>[7,1]=>5760
[5,7,3,1,6,8,2,4]=>[5,2,1]=>4032
[5,6,3,1,7,8,2,4]=>[7,1]=>5760
[5,8,3,1,7,6,2,4]=>[6,1,1]=>3360
[5,7,4,8,1,6,2,3]=>[3,2,2,1]=>1680
[5,4,6,8,1,7,2,3]=>[6,2]=>3360
[4,8,6,7,5,1,2,3]=>[7,1]=>5760
[5,2,1,7,8,6,3,4]=>[6,1,1]=>3360
[5,3,8,1,7,6,2,4]=>[7,1]=>5760
[5,4,8,7,1,6,2,3]=>[3,2,2,1]=>1680
[4,6,8,7,5,1,2,3]=>[5,2,1]=>4032
[4,8,7,6,5,1,2,3]=>[4,3,1]=>3360
[2,5,4,7,3,6,1,8]=>[6,1,1]=>3360
[2,4,6,3,7,5,1,8]=>[7,1]=>5760
[4,2,7,3,6,5,1,8]=>[4,2,1,1]=>2520
[4,2,6,3,1,5,8,7]=>[5,2,1]=>4032
[2,5,3,1,6,4,8,7]=>[5,2,1]=>4032
[2,5,3,7,6,4,1,8]=>[6,1,1]=>3360
[2,6,5,3,7,4,1,8]=>[7,1]=>5760
[4,2,7,6,3,5,1,8]=>[6,1,1]=>3360
[2,7,5,3,6,4,1,8]=>[4,3,1]=>3360
[2,6,3,7,5,4,1,8]=>[5,1,1,1]=>1344
[1,7,5,2,3,8,4,6]=>[3,2,2,1]=>1680
[2,1,3,7,5,4,8,6]=>[4,2,1,1]=>2520
[2,3,1,8,6,5,4,7]=>[3,3,2]=>1120
[2,5,3,1,8,6,4,7]=>[6,1,1]=>3360
[4,2,8,3,1,6,5,7]=>[6,1,1]=>3360
[8,3,2,6,4,1,5,7]=>[6,2]=>3360
[3,6,8,2,1,4,5,7]=>[5,3]=>2688
[1,5,2,8,3,4,7,6]=>[3,3,1,1]=>1120
[1,2,6,3,8,7,4,5]=>[4,2,1,1]=>2520
[1,2,8,3,6,4,7,5]=>[5,1,1,1]=>1344
[1,2,7,6,3,4,8,5]=>[4,2,1,1]=>2520
[2,1,3,8,7,5,4,6]=>[5,2,1]=>4032
[1,2,3,8,6,4,7,5]=>[4,1,1,1,1]=>420
[1,2,3,7,4,8,6,5]=>[5,1,1,1]=>1344
[1,2,7,6,3,8,4,5]=>[6,1,1]=>3360
[1,2,3,6,4,8,7,5]=>[4,1,1,1,1]=>420
[1,2,3,7,6,4,8,5]=>[5,1,1,1]=>1344
[2,6,3,1,8,5,4,7]=>[7,1]=>5760
[2,1,3,8,5,4,7,6]=>[3,2,1,1,1]=>1120
[7,1,8,4,2,3,5,6]=>[4,3,1]=>3360
[2,1,8,4,3,5,7,6]=>[4,2,1,1]=>2520
[4,2,6,3,1,8,5,7]=>[7,1]=>5760
[5,4,2,8,3,1,6,7]=>[8]=>5040
[3,5,8,2,4,1,6,7]=>[5,3]=>2688
[2,5,4,8,3,1,6,7]=>[8]=>5040
[4,2,1,8,3,5,7,6]=>[6,1,1]=>3360
[1,8,7,4,2,3,5,6]=>[6,1,1]=>3360
[1,5,2,8,7,3,4,6]=>[7,1]=>5760
[1,2,7,3,6,4,8,5]=>[6,1,1]=>3360
[1,2,8,6,3,7,4,5]=>[3,3,1,1]=>1120
[1,2,7,3,8,6,4,5]=>[3,2,1,1,1]=>1120
[1,2,3,8,4,7,6,5]=>[3,2,1,1,1]=>1120
[1,2,7,3,4,8,6,5]=>[6,1,1]=>3360
[1,2,6,3,8,4,7,5]=>[3,2,1,1,1]=>1120
[1,5,2,3,8,7,4,6]=>[7,1]=>5760
[4,2,1,8,3,7,5,6]=>[7,1]=>5760
[8,3,2,1,7,4,5,6]=>[4,2,2]=>1260
[1,8,4,2,7,3,5,6]=>[5,2,1]=>4032
[1,2,8,6,3,4,7,5]=>[3,2,1,1,1]=>1120
[1,2,7,3,8,4,6,5]=>[4,2,1,1]=>2520
[1,2,3,8,7,4,6,5]=>[5,1,1,1]=>1344
[1,2,3,8,7,6,4,5]=>[4,1,1,1,1]=>420
[2,5,3,8,1,6,4,7]=>[3,3,1,1]=>1120
[2,6,4,7,1,5,3,8]=>[4,3,1]=>3360
[2,6,5,7,1,4,3,8]=>[7,1]=>5760
[3,8,5,7,1,2,6,4]=>[5,3]=>2688
[3,8,5,7,2,6,4,1]=>[5,2,1]=>4032
[3,4,8,6,2,5,7,1]=>[4,3,1]=>3360
[3,4,8,6,1,2,5,7]=>[5,3]=>2688
[2,5,7,1,4,8,6,3]=>[4,4]=>1260
[2,4,8,1,5,7,6,3]=>[3,2,2,1]=>1680
[2,4,3,8,1,6,5,7]=>[6,1,1]=>3360
[2,8,1,7,5,6,4,3]=>[4,2,1,1]=>2520
[2,3,8,1,6,5,7,4]=>[5,2,1]=>4032
[2,4,8,1,3,5,7,6]=>[4,3,1]=>3360
[3,5,7,6,1,2,4,8]=>[7,1]=>5760
[3,5,7,6,2,4,8,1]=>[4,2,2]=>1260
[4,8,6,7,2,3,5,1]=>[6,2]=>3360
[4,8,6,7,1,2,3,5]=>[8]=>5040
[4,8,6,7,1,3,5,2]=>[4,2,2]=>1260
[3,4,8,6,1,5,7,2]=>[7,1]=>5760
[3,8,5,7,1,6,4,2]=>[3,2,2,1]=>1680
[3,2,8,5,6,1,7,4]=>[6,1,1]=>3360
[3,8,5,7,2,1,6,4]=>[8]=>5040
[3,4,8,6,2,1,5,7]=>[8]=>5040
[3,5,7,6,2,1,4,8]=>[5,2,1]=>4032
[4,8,6,7,2,1,3,5]=>[5,3]=>2688
[4,8,6,7,3,5,2,1]=>[5,3]=>2688
[5,8,6,7,3,4,2,1]=>[8]=>5040
[5,8,6,7,2,1,3,4]=>[8]=>5040
[5,8,6,7,2,1,4,3]=>[6,2]=>3360
[4,8,6,7,2,1,5,3]=>[8]=>5040
[4,3,1,7,5,2,8,6]=>[7,1]=>5760
[4,3,2,8,5,1,7,6]=>[4,2,1,1]=>2520
[4,3,8,5,1,6,7,2]=>[3,3,1,1]=>1120
[4,8,6,7,1,5,3,2]=>[6,2]=>3360
[5,8,6,7,1,4,3,2]=>[4,2,2]=>1260
[5,8,6,7,2,3,4,1]=>[4,2,2]=>1260
[5,8,6,7,2,4,3,1]=>[4,4]=>1260
[5,8,6,7,1,2,4,3]=>[4,2,2]=>1260
[4,2,3,8,5,1,6,7]=>[5,1,1,1]=>1344
[4,2,8,5,1,7,6,3]=>[3,2,2,1]=>1680
[3,4,2,8,5,6,1,7]=>[6,1,1]=>3360
[3,2,4,8,6,1,5,7]=>[7,1]=>5760
[3,2,5,7,6,1,4,8]=>[4,2,1,1]=>2520
[4,8,6,7,1,3,2,5]=>[6,2]=>3360
[4,8,6,7,1,2,5,3]=>[4,4]=>1260
[4,8,6,7,2,5,3,1]=>[8]=>5040
[4,3,8,5,2,6,7,1]=>[6,1,1]=>3360
[4,3,8,5,1,2,6,7]=>[5,3]=>2688
[4,2,6,7,5,1,3,8]=>[5,1,1,1]=>1344
[3,8,5,7,1,4,2,6]=>[5,3]=>2688
[3,8,4,7,1,5,2,6]=>[8]=>5040
[3,5,2,8,4,6,1,7]=>[7,1]=>5760
[3,5,1,7,4,6,2,8]=>[4,2,1,1]=>2520
[3,8,4,7,2,5,1,6]=>[4,4]=>1260
[4,1,3,8,5,2,6,7]=>[6,1,1]=>3360
[4,1,2,6,7,5,3,8]=>[7,1]=>5760
[4,2,6,7,5,3,8,1]=>[4,2,1,1]=>2520
[4,8,6,7,3,2,5,1]=>[8]=>5040
[4,8,6,7,3,1,2,5]=>[8]=>5040
[3,1,5,7,6,2,4,8]=>[5,2,1]=>4032
[3,4,1,7,5,6,2,8]=>[3,2,1,1,1]=>1120
[4,1,7,5,2,8,6,3]=>[4,4]=>1260
[4,1,6,7,5,2,3,8]=>[6,1,1]=>3360
[4,8,6,7,2,3,1,5]=>[3,3,2]=>1120
[5,8,6,7,3,2,4,1]=>[6,2]=>3360
[5,8,6,7,4,2,3,1]=>[8]=>5040
[5,8,6,7,4,1,2,3]=>[8]=>5040
[5,8,6,7,4,1,3,2]=>[6,2]=>3360
[5,8,6,7,3,1,4,2]=>[4,2,2]=>1260
[4,8,6,7,3,1,5,2]=>[6,2]=>3360
[4,1,6,7,5,3,8,2]=>[5,2,1]=>4032
[4,1,7,5,3,2,8,6]=>[8]=>5040
[4,2,8,5,3,1,7,6]=>[6,1,1]=>3360
[4,2,1,6,7,5,3,8]=>[6,1,1]=>3360
[4,8,6,7,3,2,1,5]=>[5,3]=>2688
[5,8,6,7,4,2,1,3]=>[4,4]=>1260
[5,8,6,7,4,3,1,2]=>[4,2,2]=>1260
[3,8,7,6,1,4,2,5]=>[6,2]=>3360
[5,1,8,3,6,7,2,4]=>[5,3]=>2688
[3,6,1,4,7,8,5,2]=>[3,2,2,1]=>1680
[1,6,8,4,7,5,2,3]=>[4,2,1,1]=>2520
[6,8,1,3,5,7,2,4]=>[7,1]=>5760
[3,8,1,6,5,4,2,7]=>[3,2,2,1]=>1680
[6,1,7,3,8,4,2,5]=>[6,2]=>3360
[3,1,7,6,5,8,4,2]=>[7,1]=>5760
[7,4,1,6,8,2,5,3]=>[5,3]=>2688
[6,1,3,2,7,8,4,5]=>[7,1]=>5760
[1,8,6,2,5,3,4,7]=>[4,2,1,1]=>2520
[4,7,2,6,8,1,5,3]=>[5,3]=>2688
[8,7,3,6,4,5,2,1]=>[3,2,2,1]=>1680
[5,7,8,6,2,1,4,3]=>[6,2]=>3360
[2,7,4,1,6,8,3,5]=>[5,3]=>2688
[1,8,6,4,5,2,3,7]=>[5,1,1,1]=>1344
[2,5,4,3,6,8,1,7]=>[6,2]=>3360
[8,3,7,4,5,2,6,1]=>[4,2,1,1]=>2520
[4,3,7,8,5,1,6,2]=>[7,1]=>5760
[5,8,2,6,3,4,1,7]=>[6,2]=>3360
[4,1,7,5,8,6,2,3]=>[7,1]=>5760
[5,1,7,8,4,3,6,2]=>[5,3]=>2688
[1,4,3,5,7,8,2,6]=>[4,2,1,1]=>2520
[6,5,8,7,1,3,4,2]=>[6,2]=>3360
[1,5,2,7,4,3,8,6]=>[7,1]=>5760
[2,8,5,6,4,3,1,7]=>[4,4]=>1260
[1,8,6,5,4,3,2,7]=>[3,2,2,1]=>1680
[6,1,5,2,8,4,7,3]=>[4,3,1]=>3360
[4,6,1,8,5,7,2,3]=>[4,3,1]=>3360
[4,7,1,2,8,5,6,3]=>[8]=>5040
[1,4,7,2,8,5,6,3]=>[5,2,1]=>4032
[1,7,3,5,8,6,2,4]=>[3,2,1,1,1]=>1120
[7,3,5,8,6,1,2,4]=>[6,2]=>3360
[3,6,8,1,5,7,2,4]=>[4,3,1]=>3360
[3,4,6,5,8,1,7,2]=>[4,3,1]=>3360
[6,8,1,5,7,2,3,4]=>[8]=>5040
[7,1,2,5,8,6,3,4]=>[4,3,1]=>3360
[1,7,2,5,8,6,3,4]=>[3,3,1,1]=>1120
[1,7,6,8,2,3,5,4]=>[3,2,2,1]=>1680
[7,6,8,1,2,3,5,4]=>[8]=>5040
[2,7,1,5,8,6,3,4]=>[4,3,1]=>3360
[2,4,7,1,8,5,6,3]=>[5,3]=>2688
[4,7,5,8,3,1,6,2]=>[6,2]=>3360
[4,7,2,1,8,5,6,3]=>[6,2]=>3360
[7,6,8,2,1,3,5,4]=>[5,3]=>2688
[1,2,7,6,8,3,5,4]=>[6,1,1]=>3360
[3,7,6,8,2,1,5,4]=>[3,3,2]=>1120
[7,4,2,1,6,8,5,3]=>[8]=>5040
[6,7,4,1,8,5,3,2]=>[8]=>5040
[6,7,4,3,1,8,5,2]=>[6,2]=>3360
[2,7,4,1,6,8,5,3]=>[8]=>5040
[2,3,7,6,8,1,5,4]=>[8]=>5040
[7,4,2,6,8,5,1,3]=>[6,2]=>3360
[7,3,2,5,8,6,1,4]=>[3,2,2,1]=>1680
[3,1,7,6,8,2,5,4]=>[8]=>5040
[3,7,6,8,1,2,5,4]=>[6,2]=>3360
[1,3,7,6,8,2,5,4]=>[7,1]=>5760
[1,7,4,2,6,8,5,3]=>[7,1]=>5760
[7,4,1,2,6,8,5,3]=>[6,2]=>3360
[7,1,4,2,8,5,6,3]=>[8]=>5040
[7,1,8,2,5,4,6,3]=>[5,2,1]=>4032
[7,3,8,4,6,1,5,2]=>[4,3,1]=>3360
[7,2,8,1,6,4,5,3]=>[5,2,1]=>4032
[7,1,6,8,5,4,2,3]=>[4,3,1]=>3360
[7,1,2,6,8,5,4,3]=>[8]=>5040
[1,7,2,6,8,5,4,3]=>[7,1]=>5760
[1,7,6,8,3,2,5,4]=>[5,2,1]=>4032
[7,6,8,3,1,2,5,4]=>[3,3,2]=>1120
[7,1,5,8,6,3,2,4]=>[3,3,2]=>1120
[7,2,5,8,6,3,1,4]=>[3,2,2,1]=>1680
[3,6,7,1,8,5,4,2]=>[4,4]=>1260
[7,2,6,8,5,4,1,3]=>[4,2,1,1]=>2520
[7,6,8,2,3,1,5,4]=>[8]=>5040
[2,7,6,8,3,1,5,4]=>[6,2]=>3360
[2,7,1,6,8,5,4,3]=>[8]=>5040
[6,7,3,1,8,5,4,2]=>[7,1]=>5760
[6,7,1,8,5,4,3,2]=>[7,1]=>5760
[7,2,1,6,8,5,4,3]=>[7,1]=>5760
[7,6,8,3,2,1,5,4]=>[5,3]=>2688
[4,7,8,5,6,1,3,2]=>[4,4]=>1260
[4,6,5,8,7,1,3,2]=>[5,3]=>2688
[5,6,4,8,1,2,7,3]=>[3,2,2,1]=>1680
[8,1,5,6,7,2,4,3]=>[8]=>5040
[6,4,5,1,8,2,7,3]=>[4,3,1]=>3360
[5,4,6,7,1,2,8,3]=>[6,2]=>3360
[4,3,6,7,2,1,5,8]=>[7,1]=>5760
[5,3,6,7,1,4,2,8]=>[5,2,1]=>4032
[8,1,4,6,7,3,2,5]=>[5,3]=>2688
[8,1,3,6,7,4,5,2]=>[3,2,2,1]=>1680
[7,2,1,6,8,4,5,3]=>[5,2,1]=>4032
[5,2,6,7,1,4,8,3]=>[5,2,1]=>4032
[4,2,6,7,3,1,8,5]=>[7,1]=>5760
[6,2,4,1,5,8,7,3]=>[5,1,1,1]=>1344
[7,2,1,5,4,8,6,3]=>[5,2,1]=>4032
[8,1,4,5,3,7,2,6]=>[5,3]=>2688
[7,3,1,5,4,8,2,6]=>[4,2,2]=>1260
[6,3,4,1,5,8,2,7]=>[7,1]=>5760
[5,3,4,2,1,8,6,7]=>[3,3,2]=>1120
[4,3,5,2,7,1,6,8]=>[7,1]=>5760
[5,6,3,8,1,4,2,7]=>[5,2,1]=>4032
[8,1,7,2,4,5,6,3]=>[8]=>5040
[7,6,1,2,4,5,8,3]=>[4,4]=>1260
[4,7,8,2,3,1,6,5]=>[5,3]=>2688
[5,6,2,8,1,4,7,3]=>[5,2,1]=>4032
[6,5,2,1,3,7,8,4]=>[5,3]=>2688
[7,5,1,3,2,6,8,4]=>[5,2,1]=>4032
[8,1,6,3,2,5,7,4]=>[7,1]=>5760
[7,4,1,3,5,2,8,6]=>[7,1]=>5760
[5,4,2,3,1,6,8,7]=>[3,2,2,1]=>1680
[7,3,1,4,5,6,2,8]=>[4,1,1,1,1]=>420
[8,1,4,3,5,6,2,7]=>[4,2,1,1]=>2520
[6,2,3,1,5,7,8,4]=>[5,1,1,1]=>1344
[7,8,4,2,1,6,5,3]=>[4,3,1]=>3360
[7,8,4,2,1,5,6,3]=>[4,4]=>1260
[6,2,3,4,8,7,1,5]=>[3,2,1,1,1]=>1120
[6,2,3,4,7,8,1,5]=>[5,1,1,1]=>1344
[7,8,3,4,6,2,1,5]=>[4,2,1,1]=>2520
[7,8,3,6,4,2,1,5]=>[5,2,1]=>4032
[7,8,3,5,6,2,1,4]=>[5,2,1]=>4032
[6,2,3,8,7,5,1,4]=>[4,2,1,1]=>2520
[6,2,3,7,8,5,1,4]=>[6,1,1]=>3360
[5,2,6,3,8,1,7,4]=>[6,1,1]=>3360
[6,3,2,5,8,7,1,4]=>[3,3,2]=>1120
[6,3,2,8,4,7,1,5]=>[3,3,2]=>1120
[6,4,3,8,7,5,1,2]=>[4,3,1]=>3360
[6,4,3,7,8,5,1,2]=>[7,1]=>5760
[6,2,4,1,7,3,5,8]=>[4,2,1,1]=>2520
[6,3,2,7,4,8,1,5]=>[6,2]=>3360
[6,3,2,5,7,8,1,4]=>[6,2]=>3360
[5,7,2,3,6,1,8,4]=>[5,3]=>2688
[5,8,2,3,6,1,7,4]=>[4,3,1]=>3360
[4,7,5,8,3,2,1,6]=>[6,2]=>3360
[4,5,6,8,3,2,1,7]=>[4,4]=>1260
[4,6,8,5,3,2,1,7]=>[6,2]=>3360
[5,6,1,4,2,3,7,8]=>[5,1,1,1]=>1344
[5,6,8,4,3,7,1,2]=>[7,1]=>5760
[5,6,1,4,2,3,8,7]=>[5,2,1]=>4032
[5,2,8,3,4,1,7,6]=>[6,1,1]=>3360
[4,5,8,6,3,2,1,7]=>[8]=>5040
[4,6,5,8,3,2,1,7]=>[4,2,2]=>1260
[4,7,5,6,3,2,1,8]=>[5,2,1]=>4032
[6,2,3,4,5,8,1,7]=>[4,1,1,1,1]=>420
[5,1,4,3,6,2,8,7]=>[4,2,2]=>1260
[5,1,4,3,7,2,8,6]=>[6,2]=>3360
[5,1,4,3,8,2,7,6]=>[5,2,1]=>4032
[5,6,2,4,1,7,8,3]=>[5,2,1]=>4032
[5,6,2,4,1,8,7,3]=>[4,2,1,1]=>2520
[5,7,2,4,1,8,6,3]=>[5,2,1]=>4032
[6,1,4,2,8,7,5,3]=>[8]=>5040
[6,1,4,2,7,8,5,3]=>[6,2]=>3360
[5,8,2,4,1,7,6,3]=>[3,2,2,1]=>1680
[5,2,7,4,1,6,8,3]=>[3,2,1,1,1]=>1120
[5,4,1,3,7,2,6,8]=>[7,1]=>5760
[5,1,4,3,6,2,7,8]=>[4,2,1,1]=>2520
[5,8,6,4,3,7,1,2]=>[5,2,1]=>4032
[5,8,1,4,2,3,7,6]=>[6,1,1]=>3360
[5,1,6,3,4,2,7,8]=>[6,1,1]=>3360
[4,8,6,5,3,2,1,7]=>[8]=>5040
[4,8,5,6,3,2,1,7]=>[6,2]=>3360
[5,4,7,8,3,2,1,6]=>[4,4]=>1260
[5,4,8,7,3,2,1,6]=>[8]=>5040
[4,6,8,7,3,2,1,5]=>[3,3,2]=>1120
[4,6,7,8,3,2,1,5]=>[6,2]=>3360
[4,7,6,8,3,2,1,5]=>[8]=>5040
[4,7,8,5,3,2,1,6]=>[8]=>5040
[5,7,1,3,4,2,6,8]=>[4,3,1]=>3360
[5,1,8,4,2,3,6,7]=>[4,3,1]=>3360
[5,1,7,4,2,3,6,8]=>[3,3,1,1]=>1120
[5,8,1,3,4,2,6,7]=>[4,4]=>1260
[4,8,7,5,3,2,1,6]=>[5,3]=>2688
[4,7,8,6,3,2,1,5]=>[5,3]=>2688
[4,8,7,6,3,2,1,5]=>[8]=>5040
[4,8,2,6,3,7,5,1]=>[8]=>5040
[4,3,8,1,6,2,5,7]=>[6,2]=>3360
[4,3,8,7,2,5,1,6]=>[5,3]=>2688
[5,8,4,3,7,1,6,2]=>[4,2,2]=>1260
[6,8,1,2,4,3,5,7]=>[5,3]=>2688
[5,8,7,1,3,4,2,6]=>[8]=>5040
[4,3,8,2,7,5,6,1]=>[5,3]=>2688
[1,4,3,8,2,6,5,7]=>[5,1,1,1]=>1344
[4,3,2,8,1,6,5,7]=>[5,2,1]=>4032
[4,1,3,8,2,6,5,7]=>[6,1,1]=>3360
[4,1,8,3,7,5,6,2]=>[5,3]=>2688
[3,7,8,1,5,4,2,6]=>[5,2,1]=>4032
[7,3,8,1,5,4,6,2]=>[4,3,1]=>3360
[3,4,8,1,6,2,5,7]=>[8]=>5040
[3,4,2,1,8,6,5,7]=>[4,3,1]=>3360
[3,6,7,8,4,1,2,5]=>[5,3]=>2688
[4,1,7,8,5,3,2,6]=>[7,1]=>5760
[3,7,6,8,4,2,1,5]=>[5,3]=>2688
[4,3,1,8,2,6,5,7]=>[7,1]=>5760
[4,3,7,8,5,2,1,6]=>[7,1]=>5760
[2,6,8,4,7,3,1,5]=>[7,1]=>5760
[7,3,6,8,4,2,1,5]=>[3,3,2]=>1120
[7,6,2,8,3,5,4,1]=>[4,4]=>1260
[3,2,4,8,1,6,5,7]=>[6,1,1]=>3360
[2,4,8,3,6,1,5,7]=>[8]=>5040
[7,4,1,8,5,2,6,3]=>[7,1]=>5760
[1,3,2,4,8,6,5,7]=>[3,2,1,1,1]=>1120
[3,1,2,4,8,6,5,7]=>[3,3,1,1]=>1120
[3,1,4,8,2,6,5,7]=>[7,1]=>5760
[3,7,4,8,5,1,2,6]=>[5,2,1]=>4032
[6,7,2,8,3,5,4,1]=>[8]=>5040
[2,1,3,4,8,6,5,7]=>[3,2,1,1,1]=>1120
[1,2,3,4,8,6,5,7]=>[3,1,1,1,1,1]=>112
[4,8,3,6,2,1,5,7]=>[4,3,1]=>3360
[3,5,8,2,6,1,4,7]=>[8]=>5040
[3,6,5,8,2,4,1,7]=>[8]=>5040
[5,3,8,7,2,4,6,1]=>[5,3]=>2688
[2,8,4,5,7,3,6,1]=>[5,3]=>2688
[2,4,5,7,3,8,1,6]=>[4,2,2]=>1260
[6,2,4,5,8,3,1,7]=>[7,1]=>5760
[4,8,1,2,5,6,3,7]=>[6,1,1]=>3360
[8,1,3,5,2,6,4,7]=>[6,1,1]=>3360
[5,2,1,6,3,8,4,7]=>[4,3,1]=>3360
[6,2,5,1,8,4,3,7]=>[4,3,1]=>3360
[3,6,1,5,8,4,2,7]=>[6,2]=>3360
[6,1,4,5,8,3,2,7]=>[8]=>5040
[5,6,4,8,1,3,2,7]=>[6,2]=>3360
[6,5,4,3,8,2,1,7]=>[6,2]=>3360
[5,4,3,7,2,8,1,6]=>[5,2,1]=>4032
[5,8,4,3,7,2,6,1]=>[6,2]=>3360
[4,6,8,3,7,2,5,1]=>[4,2,2]=>1260
[7,4,6,3,2,8,1,5]=>[6,2]=>3360
[1,4,3,6,2,7,8,5]=>[6,1,1]=>3360
[1,5,4,3,7,2,8,6]=>[5,2,1]=>4032
[4,7,8,5,3,1,2,6]=>[6,2]=>3360
[5,7,3,4,1,2,8,6]=>[4,2,1,1]=>2520
[8,5,4,7,6,2,1,3]=>[5,3]=>2688
[8,5,7,4,3,6,1,2]=>[6,1,1]=>3360
[4,3,8,1,6,7,5,2]=>[3,3,2]=>1120
[4,7,8,3,6,1,5,2]=>[8]=>5040
[5,3,8,6,7,4,1,2]=>[3,3,2]=>1120
[1,3,8,6,4,7,5,2]=>[4,3,1]=>3360
[8,6,2,7,4,1,5,3]=>[5,3]=>2688
[7,6,2,1,4,3,8,5]=>[5,3]=>2688
[7,6,1,3,4,2,8,5]=>[6,2]=>3360
[1,5,7,3,2,6,8,4]=>[4,2,1,1]=>2520
[1,6,7,3,2,5,8,4]=>[4,3,1]=>3360
[3,2,6,8,5,7,4,1]=>[6,1,1]=>3360
[5,8,2,3,6,7,4,1]=>[8]=>5040
[7,5,2,3,1,6,8,4]=>[7,1]=>5760
[1,6,4,7,2,3,8,5]=>[7,1]=>5760
[3,1,7,5,2,8,4,6]=>[6,2]=>3360
[2,5,7,4,1,8,3,6]=>[3,2,2,1]=>1680
[4,2,6,1,7,8,3,5]=>[5,2,1]=>4032
[4,2,7,6,3,8,1,5]=>[7,1]=>5760
[6,4,8,7,2,3,5,1]=>[4,4]=>1260
[3,2,6,8,7,4,5,1]=>[5,2,1]=>4032
[3,2,7,4,1,6,8,5]=>[5,1,1,1]=>1344
[6,3,2,1,7,8,4,5]=>[6,2]=>3360
[3,7,1,8,4,2,5,6]=>[6,2]=>3360
[4,2,1,3,7,5,8,6]=>[4,3,1]=>3360
[8,1,3,7,4,2,6,5]=>[7,1]=>5760
[8,4,3,7,6,2,1,5]=>[7,1]=>5760
[8,3,5,2,7,6,1,4]=>[7,1]=>5760
[3,6,2,8,7,1,5,4]=>[4,2,2]=>1260
[7,3,2,8,1,6,5,4]=>[3,2,2,1]=>1680
[3,8,7,2,6,5,4,1]=>[6,2]=>3360
[4,2,7,8,6,1,5,3]=>[7,1]=>5760
[6,8,2,4,7,1,5,3]=>[3,2,2,1]=>1680
[5,2,1,8,7,3,6,4]=>[5,2,1]=>4032
[8,2,1,6,3,7,5,4]=>[7,1]=>5760
[6,8,3,1,7,5,2,4]=>[7,1]=>5760
[5,8,1,6,7,2,4,3]=>[8]=>5040
[6,2,8,1,5,7,4,3]=>[4,2,1,1]=>2520
[5,7,8,2,6,1,4,3]=>[3,3,2]=>1120
[8,7,2,5,6,4,3,1]=>[3,3,2]=>1120
[8,6,7,5,2,4,3,1]=>[4,2,2]=>1260
[7,2,6,8,1,5,4,3]=>[7,1]=>5760
[1,2,7,8,5,6,4,3]=>[4,1,1,1,1]=>420
[7,4,8,1,6,2,5,3]=>[6,2]=>3360
[3,7,1,8,2,6,5,4]=>[3,2,2,1]=>1680
[2,1,7,3,8,6,5,4]=>[5,2,1]=>4032
[8,2,1,7,6,5,4,3]=>[3,2,2,1]=>1680
[8,1,4,7,6,5,3,2]=>[3,3,2]=>1120
[8,6,7,5,1,4,3,2]=>[6,2]=>3360
[7,8,6,5,4,1,3,2]=>[4,2,2]=>1260
[5,8,4,3,2,1,6,7]=>[6,2]=>3360
[6,4,7,3,2,1,8,5]=>[6,2]=>3360
[5,4,7,3,2,1,6,8]=>[7,1]=>5760
[6,5,3,7,2,1,4,8]=>[2,2,2,1,1]=>420
[5,8,3,6,2,1,4,7]=>[7,1]=>5760
[6,3,7,8,2,1,4,5]=>[6,2]=>3360
[5,3,7,6,2,1,4,8]=>[7,1]=>5760
[3,8,7,6,2,1,4,5]=>[5,3]=>2688
[5,8,4,2,6,1,3,7]=>[5,3]=>2688
[4,8,7,2,5,1,3,6]=>[5,2,1]=>4032
[5,8,3,2,6,1,4,7]=>[4,3,1]=>3360
[4,8,3,2,5,1,7,6]=>[5,1,1,1]=>1344
[4,3,7,2,5,1,8,6]=>[7,1]=>5760
[3,8,7,2,5,1,4,6]=>[7,1]=>5760
[6,4,2,7,5,1,3,8]=>[4,2,1,1]=>2520
[6,3,2,7,5,1,4,8]=>[2,2,2,1,1]=>420
[5,3,2,6,7,1,4,8]=>[5,2,1]=>4032
[3,8,2,6,5,1,4,7]=>[7,1]=>5760
[6,2,7,8,5,1,3,4]=>[2,2,2,1,1]=>420
[5,2,7,6,8,1,3,4]=>[5,2,1]=>4032
[4,2,7,6,5,1,3,8]=>[3,2,1,1,1]=>1120
[2,8,7,6,5,1,3,4]=>[5,2,1]=>4032
[6,5,4,3,1,7,8,2]=>[6,2]=>3360
[6,4,7,3,1,5,8,2]=>[5,3]=>2688
[5,4,7,3,1,8,6,2]=>[6,2]=>3360
[6,4,3,7,1,5,8,2]=>[4,3,1]=>3360
[5,4,3,6,1,8,7,2]=>[4,2,1,1]=>2520
[6,3,7,8,1,4,5,2]=>[8]=>5040
[5,3,7,6,1,4,8,2]=>[4,2,2]=>1260
[4,3,7,6,1,5,8,2]=>[4,4]=>1260
[3,8,7,6,1,4,5,2]=>[4,2,2]=>1260
[6,5,4,2,1,7,3,8]=>[7,1]=>5760
[6,4,7,2,1,5,3,8]=>[3,2,2,1]=>1680
[4,8,7,2,1,5,3,6]=>[6,2]=>3360
[5,8,3,2,1,4,7,6]=>[4,2,1,1]=>2520
[4,8,3,2,1,5,7,6]=>[6,1,1]=>3360
[5,3,7,2,1,4,8,6]=>[6,2]=>3360
[3,8,7,2,1,4,5,6]=>[4,4]=>1260
[6,5,2,7,1,4,3,8]=>[7,1]=>5760
[5,8,2,6,1,4,3,7]=>[4,2,2]=>1260
[6,4,2,7,1,5,3,8]=>[4,3,1]=>3360
[5,4,2,6,1,8,3,7]=>[6,2]=>3360
[4,3,2,6,1,5,8,7]=>[4,2,2]=>1260
[6,2,7,8,1,4,3,5]=>[5,2,1]=>4032
[4,2,7,6,1,5,3,8]=>[4,2,1,1]=>2520
[3,2,7,6,1,4,5,8]=>[4,2,1,1]=>2520
[6,5,4,1,8,7,3,2]=>[5,3]=>2688
[5,8,4,1,6,7,3,2]=>[6,2]=>3360
[6,4,7,1,5,8,3,2]=>[5,2,1]=>4032
[5,4,7,1,6,8,3,2]=>[6,2]=>3360
[4,8,7,1,5,6,3,2]=>[2,2,2,1,1]=>420
[5,4,3,1,6,8,7,2]=>[6,1,1]=>3360
[4,8,3,1,5,6,7,2]=>[2,2,1,1,1,1]=>210
[3,8,7,1,5,4,6,2]=>[5,2,1]=>4032
[5,8,2,1,6,4,3,7]=>[4,4]=>1260
[6,3,2,1,5,4,8,7]=>[3,2,2,1]=>1680
[5,3,2,1,6,4,8,7]=>[4,2,2]=>1260
[3,8,2,1,5,4,6,7]=>[7,1]=>5760
[6,2,7,1,5,4,3,8]=>[3,2,1,1,1]=>1120
[5,2,7,1,6,4,3,8]=>[4,2,1,1]=>2520
[4,2,7,1,5,6,3,8]=>[2,2,1,1,1,1]=>210
[3,2,7,1,5,4,6,8]=>[5,1,1,1]=>1344
[2,8,7,1,5,4,3,6]=>[5,2,1]=>4032
[6,5,1,7,8,4,3,2]=>[5,3]=>2688
[5,8,1,6,7,4,3,2]=>[4,2,2]=>1260
[6,4,1,7,5,8,3,2]=>[7,1]=>5760
[5,4,1,6,7,8,3,2]=>[4,4]=>1260
[4,8,1,6,5,7,3,2]=>[5,2,1]=>4032
[6,3,1,7,5,4,8,2]=>[7,1]=>5760
[5,3,1,6,7,4,8,2]=>[6,2]=>3360
[4,3,1,6,5,7,8,2]=>[7,1]=>5760
[3,8,1,6,5,4,7,2]=>[2,2,2,1,1]=>420
[5,2,1,6,7,4,3,8]=>[4,2,1,1]=>2520
[4,2,1,6,5,7,3,8]=>[5,1,1,1]=>1344
[2,8,1,6,5,4,3,7]=>[5,2,1]=>4032
[6,1,7,8,5,4,3,2]=>[5,2,1]=>4032
[4,1,7,6,5,8,3,2]=>[5,2,1]=>4032
[3,1,7,6,5,4,8,2]=>[5,2,1]=>4032
[4,5,8,1,2,6,3,7]=>[3,2,2,1]=>1680
[1,4,5,7,2,6,3,8]=>[5,1,1,1]=>1344
[1,7,3,5,6,2,4,8]=>[5,1,1,1]=>1344
[8,1,3,5,7,2,4,6]=>[4,3,1]=>3360
[3,6,8,1,7,2,4,5]=>[6,2]=>3360
[3,4,5,6,8,1,7,2]=>[7,1]=>5760
[4,5,8,2,6,7,1,3]=>[6,2]=>3360
[8,2,3,5,6,7,1,4]=>[6,1,1]=>3360
[1,7,2,3,5,4,6,8]=>[5,1,1,1]=>1344
[8,1,2,3,5,4,6,7]=>[7,1]=>5760
[2,7,8,1,3,5,4,6]=>[4,4]=>1260
[2,7,8,3,5,6,1,4]=>[3,3,1,1]=>1120
[2,4,5,7,8,1,6,3]=>[5,3]=>2688
[4,5,8,1,7,6,3,2]=>[5,2,1]=>4032
[4,5,8,7,2,1,6,3]=>[4,2,2]=>1260
[8,7,3,5,6,2,1,4]=>[7,1]=>5760
[8,7,2,1,3,5,4,6]=>[8]=>5040
[3,6,8,7,2,1,5,4]=>[8]=>5040
[8,6,4,1,7,5,3,2]=>[8]=>5040
[7,6,4,3,1,8,5,2]=>[3,3,2]=>1120
[2,3,6,7,8,1,5,4]=>[4,4]=>1260
[3,6,8,1,2,5,4,7]=>[5,3]=>2688
[1,3,6,7,2,5,4,8]=>[4,2,1,1]=>2520
[7,4,1,8,5,2,3,6]=>[4,3,1]=>3360
[7,1,4,2,8,3,6,5]=>[6,2]=>3360
[7,1,8,2,5,3,6,4]=>[7,1]=>5760
[8,1,7,5,4,2,3,6]=>[4,2,2]=>1260
[1,7,2,6,5,4,3,8]=>[3,2,1,1,1]=>1120
[1,7,6,3,2,5,4,8]=>[6,1,1]=>3360
[8,6,3,1,2,5,4,7]=>[4,3,1]=>3360
[8,1,7,6,3,2,4,5]=>[8]=>5040
[8,2,5,7,6,3,1,4]=>[4,3,1]=>3360
[3,6,8,1,7,5,4,2]=>[8]=>5040
[8,2,6,7,5,4,1,3]=>[6,1,1]=>3360
[2,7,8,6,3,1,5,4]=>[8]=>5040
[2,7,8,1,6,5,4,3]=>[4,2,2]=>1260
[7,3,1,8,6,5,4,2]=>[6,2]=>3360
[8,7,2,1,6,5,4,3]=>[6,2]=>3360
[8,7,6,3,2,1,5,4]=>[5,3]=>2688
[2,1,8,6,3,7,4,5]=>[3,3,2]=>1120
[8,6,1,5,2,7,4,3]=>[5,3]=>2688
[8,5,1,7,4,2,6,3]=>[5,3]=>2688
[2,1,7,5,4,3,8,6]=>[4,2,2]=>1260
[2,1,7,8,3,6,5,4]=>[3,2,2,1]=>1680
[6,4,1,5,2,3,8,7]=>[3,3,2]=>1120
[8,3,7,5,2,6,1,4]=>[7,1]=>5760
[5,3,7,4,6,8,1,2]=>[7,1]=>5760
[5,8,3,7,6,2,1,4]=>[7,1]=>5760
[4,2,6,3,8,5,1,7]=>[7,1]=>5760
[3,8,2,4,7,5,1,6]=>[7,1]=>5760
[5,8,2,1,7,6,4,3]=>[4,3,1]=>3360
[8,3,2,4,1,7,5,6]=>[5,2,1]=>4032
[7,8,3,1,5,4,6,2]=>[4,2,1,1]=>2520
[7,2,8,1,4,6,5,3]=>[4,2,1,1]=>2520
[5,6,1,4,3,2,8,7]=>[3,2,2,1]=>1680
[5,7,1,8,3,6,2,4]=>[3,2,2,1]=>1680
[6,8,1,4,5,3,2,7]=>[3,3,1,1]=>1120
[8,2,6,1,4,7,3,5]=>[4,3,1]=>3360
[8,3,5,6,1,7,4,2]=>[5,3]=>2688
[8,7,3,6,5,1,4,2]=>[6,1,1]=>3360
[2,7,4,3,6,1,8,5]=>[6,2]=>3360
[4,2,3,5,8,1,6,7]=>[6,1,1]=>3360
[3,8,4,7,1,6,5,2]=>[5,2,1]=>4032
[3,2,4,6,1,5,8,7]=>[5,2,1]=>4032
[8,3,4,5,7,6,1,2]=>[7,1]=>5760
[3,2,4,5,6,8,1,7]=>[7,1]=>5760
[5,6,8,1,4,2,7,3]=>[3,2,2,1]=>1680
[1,5,7,8,4,6,2,3]=>[6,1,1]=>3360
[1,3,5,7,8,6,2,4]=>[6,1,1]=>3360
[3,5,7,8,6,1,2,4]=>[6,2]=>3360
[3,5,1,6,8,2,7,4]=>[5,2,1]=>4032
[3,1,5,6,8,2,7,4]=>[7,1]=>5760
[2,3,5,6,8,1,7,4]=>[7,1]=>5760
[5,6,4,8,2,1,7,3]=>[4,3,1]=>3360
[5,1,6,3,8,4,7,2]=>[4,3,1]=>3360
[2,5,1,6,8,3,7,4]=>[7,1]=>5760
[5,1,2,6,8,3,7,4]=>[7,1]=>5760
[5,7,1,8,6,2,3,4]=>[6,2]=>3360
[1,5,2,7,8,6,3,4]=>[6,1,1]=>3360
[1,6,7,5,2,8,3,4]=>[5,2,1]=>4032
[6,1,7,5,2,8,3,4]=>[6,2]=>3360
[2,6,7,5,1,8,3,4]=>[6,2]=>3360
[5,7,2,8,6,1,3,4]=>[3,3,2]=>1120
[3,5,7,8,6,2,1,4]=>[3,3,2]=>1120
[5,1,7,8,6,3,4,2]=>[8]=>5040
[5,1,3,7,8,6,4,2]=>[4,2,1,1]=>2520
[5,2,7,8,4,6,1,3]=>[6,1,1]=>3360
[3,2,5,7,8,6,1,4]=>[6,1,1]=>3360
[6,2,7,5,1,8,3,4]=>[5,2,1]=>4032
[1,2,6,7,5,8,3,4]=>[5,1,1,1]=>1344
[6,2,7,5,4,1,8,3]=>[3,2,2,1]=>1680
[6,7,5,2,4,1,8,3]=>[6,2]=>3360
[6,7,2,5,3,8,1,4]=>[8]=>5040
[6,7,4,5,2,1,8,3]=>[6,2]=>3360
[5,1,7,8,6,4,3,2]=>[6,2]=>3360
[2,5,7,8,6,3,1,4]=>[6,2]=>3360
[5,1,7,8,6,3,2,4]=>[6,2]=>3360
[6,3,7,5,1,8,2,4]=>[5,3]=>2688
[1,6,7,5,3,8,2,4]=>[7,1]=>5760
[1,6,7,5,4,2,8,3]=>[3,2,2,1]=>1680
[6,7,5,1,4,2,8,3]=>[8]=>5040
[5,7,8,6,4,1,2,3]=>[4,2,2]=>1260
[4,1,7,2,6,5,8,3]=>[3,3,2]=>1120
[2,4,7,1,5,6,8,3]=>[3,3,1,1]=>1120
[6,7,4,1,5,2,8,3]=>[7,1]=>5760
[1,6,7,4,5,2,8,3]=>[3,2,1,1,1]=>1120
[1,6,3,7,5,8,2,4]=>[5,1,1,1]=>1344
[6,3,1,7,5,8,2,4]=>[7,1]=>5760
[2,5,3,7,8,6,1,4]=>[6,1,1]=>3360
[6,7,5,4,2,1,8,3]=>[5,2,1]=>4032
[6,3,2,7,5,8,1,4]=>[5,2,1]=>4032
[6,7,4,2,5,1,8,3]=>[5,2,1]=>4032
[6,2,7,4,5,1,8,3]=>[3,2,1,1,1]=>1120
[6,2,3,7,5,8,1,4]=>[5,1,1,1]=>1344
[2,7,6,1,3,8,5,4]=>[8]=>5040
[7,3,5,1,8,2,6,4]=>[8]=>5040
[7,3,5,1,8,2,4,6]=>[5,3]=>2688
[3,7,5,1,8,6,2,4]=>[5,2,1]=>4032
[2,6,7,4,1,8,3,5]=>[5,2,1]=>4032
[3,6,5,1,8,4,7,2]=>[7,1]=>5760
[3,6,5,1,8,4,2,7]=>[8]=>5040
[3,7,5,4,8,1,6,2]=>[7,1]=>5760
[4,6,1,5,8,7,3,2]=>[8]=>5040
[7,5,1,6,2,8,4,3]=>[6,2]=>3360
[2,3,4,7,8,1,6,5]=>[6,2]=>3360
[6,8,5,4,3,2,7,1]=>[4,2,1,1]=>2520
[10,11,9,8,7,6,5,4,3,2,1]=>[4,2,2,2,1]=>207900
[7,9,6,5,4,3,2,8,1]=>[4,2,2,1]=>11340
[8,9,6,5,4,3,2,1,7]=>[3,2,2,2]=>2520
[6,8,5,4,3,7,2,1]=>[5,2,1]=>4032
[5,8,4,3,2,1,7,6]=>[5,2,1]=>4032
[6,5,4,3,1,8,7,2]=>[5,2,1]=>4032
[8,7,6,5,4,3,9,1,2]=>[3,2,2,2]=>2520
[8,7,5,4,3,1,6,2]=>[5,2,1]=>4032
[9,7,6,5,4,3,1,8,2]=>[4,2,2,1]=>11340
[11,10,9,8,7,6,5,4,3,1,2]=>[4,2,2,2,1]=>207900
[8,3,4,6,2,1,5,7]=>[8]=>5040
[3,5,6,2,1,8,4,7]=>[8]=>5040
[3,5,2,6,8,4,1,7]=>[6,2]=>3360
[7,5,3,2,8,4,1,6]=>[5,2,1]=>4032
[7,5,3,2,8,4,6,1]=>[7,1]=>5760
[2,4,5,7,3,8,6,1]=>[6,2]=>3360
[4,2,5,6,8,3,1,7]=>[7,1]=>5760
[4,2,8,1,5,6,3,7]=>[3,2,1,1,1]=>1120
[2,5,6,1,8,4,3,7]=>[8]=>5040
[5,3,6,8,1,4,2,7]=>[6,2]=>3360
[4,5,6,8,1,3,2,7]=>[6,2]=>3360
[1,4,5,6,8,3,2,7]=>[7,1]=>5760
[4,5,6,3,8,2,1,7]=>[8]=>5040
[4,5,3,7,2,8,6,1]=>[5,2,1]=>4032
[6,4,7,3,2,8,5,1]=>[5,3]=>2688
[6,1,4,7,3,2,8,5]=>[5,3]=>2688
[1,7,8,4,5,3,2,6]=>[3,2,1,1,1]=>1120
[5,1,7,3,8,4,2,6]=>[8]=>5040
[2,5,1,7,4,3,8,6]=>[8]=>5040
[2,5,7,4,1,8,6,3]=>[4,3,1]=>3360
[5,3,7,1,4,8,6,2]=>[5,3]=>2688
[6,4,3,1,7,8,5,2]=>[5,2,1]=>4032
[6,4,1,7,3,8,5,2]=>[8]=>5040
[5,6,3,7,8,4,2,1]=>[4,3,1]=>3360
[5,1,6,3,7,8,4,2]=>[8]=>5040
[5,6,1,3,7,8,4,2]=>[5,3]=>2688
[5,6,1,7,8,3,4,2]=>[6,2]=>3360
[1,6,3,7,4,8,5,2]=>[3,3,1,1]=>1120
[6,7,2,4,1,8,5,3]=>[7,1]=>5760
[6,7,2,1,4,3,8,5]=>[8]=>5040
[6,4,7,3,1,2,8,5]=>[8]=>5040
[5,6,3,1,2,7,8,4]=>[7,1]=>5760
[5,6,1,3,2,7,8,4]=>[8]=>5040
[5,6,3,2,1,7,8,4]=>[5,2,1]=>4032
[2,5,6,3,7,8,4,1]=>[8]=>5040
[2,5,6,3,1,7,8,4]=>[5,3]=>2688
[2,6,4,7,3,1,8,5]=>[5,3]=>2688
[6,3,7,2,8,4,5,1]=>[8]=>5040
[6,3,7,2,8,4,1,5]=>[6,2]=>3360
[6,3,2,7,1,8,4,5]=>[4,2,2]=>1260
[7,5,3,2,1,8,4,6]=>[5,2,1]=>4032
[7,3,8,4,2,1,5,6]=>[7,1]=>5760
[4,7,2,1,3,8,6,5]=>[6,2]=>3360
[1,3,7,8,6,4,2,5]=>[4,3,1]=>3360
[7,3,8,4,6,2,1,5]=>[5,2,1]=>4032
[5,7,3,8,2,1,6,4]=>[5,2,1]=>4032
[6,3,7,8,5,2,1,4]=>[5,2,1]=>4032
[4,6,2,7,8,5,3,1]=>[8]=>5040
[4,6,2,1,7,8,5,3]=>[4,2,2]=>1260
[7,4,5,8,1,2,6,3]=>[8]=>5040
[2,5,1,7,3,8,6,4]=>[4,4]=>1260
[6,7,2,1,3,8,5,4]=>[4,4]=>1260
[5,1,6,7,8,2,4,3]=>[6,2]=>3360
[6,3,7,1,8,5,2,4]=>[5,3]=>2688
[6,2,1,7,3,8,5,4]=>[7,1]=>5760
[6,2,7,1,8,5,4,3]=>[7,1]=>5760
[6,3,1,7,8,5,4,2]=>[6,2]=>3360
[4,1,3,6,8,2,5,7]=>[4,3,1]=>3360
[4,2,3,6,8,1,5,7]=>[3,3,1,1]=>1120
[5,3,2,1,8,4,7,6]=>[5,2,1]=>4032
[3,6,5,8,2,1,7,4]=>[5,2,1]=>4032
[4,5,2,1,3,8,7,6]=>[3,2,2,1]=>1680
[3,2,6,4,5,8,1,7]=>[5,1,1,1]=>1344
[2,4,6,5,8,1,3,7]=>[8]=>5040
[1,6,2,4,5,8,3,7]=>[5,1,1,1]=>1344
[5,3,2,1,6,8,4,7]=>[6,2]=>3360
[6,2,4,5,8,1,3,7]=>[5,2,1]=>4032
[1,3,4,6,5,8,2,7]=>[6,1,1]=>3360
[1,6,3,4,5,8,2,7]=>[4,1,1,1,1]=>420
[3,4,1,8,5,2,7,6]=>[4,2,1,1]=>2520
[2,8,4,1,7,6,3,5]=>[7,1]=>5760
[8,1,4,2,7,3,6,5]=>[8]=>5040
[1,5,3,2,8,7,4,6]=>[6,1,1]=>3360
[8,2,1,7,5,3,4,6]=>[4,2,1,1]=>2520
[1,7,6,4,5,8,3,2]=>[5,1,1,1]=>1344
[5,8,7,4,1,2,6,3]=>[5,2,1]=>4032
[5,8,7,4,6,2,1,3]=>[7,1]=>5760
[3,4,2,5,8,6,7,1]=>[6,1,1]=>3360
[4,1,3,5,6,8,7,2]=>[6,1,1]=>3360
[2,4,8,6,7,1,3,5]=>[4,4]=>1260
[4,3,6,2,8,1,7,5]=>[5,2,1]=>4032
[3,7,4,8,2,1,6,5]=>[8]=>5040
[2,3,5,8,6,7,1,4]=>[6,2]=>3360
[3,2,5,6,8,7,1,4]=>[7,1]=>5760
[2,1,8,5,6,7,3,4]=>[6,2]=>3360
[1,2,8,3,5,6,7,4]=>[3,1,1,1,1,1]=>112
[4,2,3,7,1,8,6,5]=>[6,1,1]=>3360
[3,2,6,4,8,1,7,5]=>[3,2,1,1,1]=>1120
[8,2,1,6,7,3,4,5]=>[7,1]=>5760
[2,7,8,5,4,1,3,6]=>[6,2]=>3360
[1,7,5,3,8,4,2,6]=>[5,2,1]=>4032
[4,7,5,3,1,2,8,6]=>[4,4]=>1260
[7,2,4,8,5,3,1,6]=>[4,2,1,1]=>2520
[4,8,3,1,2,7,6,5]=>[3,2,2,1]=>1680
[3,5,2,7,4,1,8,6]=>[8]=>5040
[8,4,2,3,7,1,5,6]=>[3,3,2]=>1120
[2,8,4,7,1,3,5,6]=>[8]=>5040
[8,2,4,6,7,1,3,5]=>[7,1]=>5760
[4,8,2,3,6,7,1,5]=>[8]=>5040
[3,5,2,7,6,1,8,4]=>[5,3]=>2688
[1,6,3,2,5,8,7,4]=>[4,1,1,1,1]=>420
[5,8,3,2,1,6,7,4]=>[3,2,1,1,1]=>1120
[5,8,7,3,4,6,2,1]=>[7,1]=>5760
[5,8,2,7,4,1,6,3]=>[5,3]=>2688
[5,1,4,2,8,7,6,3]=>[6,2]=>3360
[4,7,6,5,8,2,1,3]=>[8]=>5040
[5,3,7,1,6,2,8,4]=>[8]=>5040
[5,2,6,8,7,1,3,4]=>[5,2,1]=>4032
[6,3,2,1,8,5,7,4]=>[5,2,1]=>4032
[2,7,5,4,1,8,6,3]=>[7,1]=>5760
[4,2,5,6,8,7,1,3]=>[4,3,1]=>3360
[1,8,4,2,5,6,7,3]=>[4,1,1,1,1]=>420
[3,8,4,1,5,6,7,2]=>[3,2,1,1,1]=>1120
[4,2,8,5,6,7,1,3]=>[5,2,1]=>4032
[5,2,4,7,1,8,6,3]=>[5,2,1]=>4032
[5,3,4,7,1,8,6,2]=>[6,2]=>3360
[8,6,4,1,3,2,5,7]=>[6,2]=>3360
[8,1,3,6,5,2,4,7]=>[6,1,1]=>3360
[8,1,4,3,6,5,2,7]=>[4,2,2]=>1260
[3,6,5,2,1,8,7,4]=>[4,3,1]=>3360
[8,3,2,4,6,5,1,7]=>[3,2,2,1]=>1680
[8,4,2,1,6,5,3,7]=>[6,2]=>3360
[8,4,1,2,6,5,3,7]=>[4,2,2]=>1260
[8,6,4,2,1,5,3,7]=>[8]=>5040
[8,3,6,4,1,5,2,7]=>[7,1]=>5760
[8,2,6,3,4,5,1,7]=>[4,3,1]=>3360
[1,3,4,8,5,7,2,6]=>[6,1,1]=>3360
[5,8,4,7,6,2,3,1]=>[5,3]=>2688
[1,3,4,7,5,8,2,6]=>[4,2,1,1]=>2520
[1,3,5,2,4,8,7,6]=>[4,2,1,1]=>2520
[2,6,5,1,3,8,7,4]=>[5,2,1]=>4032
[4,7,1,6,5,8,3,2]=>[7,1]=>5760
[5,4,8,7,6,3,1,2]=>[8]=>5040
[2,8,5,1,4,7,6,3]=>[6,2]=>3360
[4,3,1,5,8,6,7,2]=>[6,1,1]=>3360
[4,1,3,5,8,6,7,2]=>[5,1,1,1]=>1344
[6,5,3,8,4,7,1,2]=>[4,3,1]=>3360
[5,4,2,1,6,8,7,3]=>[7,1]=>5760
[6,8,4,3,2,7,1,5]=>[3,3,2]=>1120
[3,4,7,8,2,1,6,5]=>[4,4]=>1260
[5,1,3,2,8,6,7,4]=>[5,1,1,1]=>1344
[5,3,1,2,8,6,7,4]=>[6,1,1]=>3360
[5,2,3,1,6,8,7,4]=>[5,1,1,1]=>1344
[5,3,2,1,8,6,7,4]=>[4,2,1,1]=>2520
[5,2,1,3,6,8,7,4]=>[6,1,1]=>3360
[2,4,7,3,8,1,6,5]=>[6,2]=>3360
[6,3,8,2,7,4,1,5]=>[8]=>5040
[8,2,1,3,6,4,7,5]=>[6,1,1]=>3360
[3,5,1,7,8,4,2,6]=>[6,2]=>3360
[2,7,4,5,8,3,1,6]=>[5,3]=>2688
[1,8,4,3,7,2,6,5]=>[5,2,1]=>4032
[3,4,8,7,2,1,6,5]=>[8]=>5040
[5,4,7,8,3,6,2,1]=>[7,1]=>5760
[6,4,3,8,7,2,1,5]=>[7,1]=>5760
[6,3,8,7,4,1,2,5]=>[6,2]=>3360
[3,5,7,2,4,8,1,6]=>[3,3,2]=>1120
[8,4,7,2,3,1,5,6]=>[3,3,2]=>1120
[8,4,7,1,3,2,5,6]=>[5,3]=>2688
[8,4,7,2,1,3,5,6]=>[6,2]=>3360
[8,6,4,2,1,3,7,5]=>[4,3,1]=>3360
[8,6,4,1,3,2,7,5]=>[5,2,1]=>4032
[8,6,4,2,3,1,7,5]=>[7,1]=>5760
[3,5,7,2,6,1,8,4]=>[8]=>5040
[6,1,3,8,5,7,2,4]=>[4,2,1,1]=>2520
[5,8,3,2,6,7,1,4]=>[4,3,1]=>3360
[4,8,5,3,6,2,7,1]=>[7,1]=>5760
[2,8,1,5,4,7,6,3]=>[4,2,2]=>1260
[1,5,8,7,4,6,2,3]=>[4,2,1,1]=>2520
[2,1,7,6,4,5,8,3]=>[3,3,2]=>1120
[1,7,2,4,6,5,8,3]=>[4,2,1,1]=>2520
[3,5,1,7,6,8,2,4]=>[6,2]=>3360
[5,8,2,6,1,3,7,4]=>[5,2,1]=>4032
[6,3,5,8,7,2,1,4]=>[6,2]=>3360
[2,5,7,8,4,1,6,3]=>[8]=>5040
[4,2,8,1,5,6,7,3]=>[2,2,1,1,1,1]=>210
[4,1,5,2,6,8,7,3]=>[4,3,1]=>3360
[3,4,5,1,6,8,7,2]=>[7,1]=>5760
[4,2,8,5,1,6,7,3]=>[3,2,1,1,1]=>1120
[4,1,8,5,2,6,7,3]=>[4,2,1,1]=>2520
[2,7,1,8,5,4,6,3]=>[7,1]=>5760
[5,8,6,2,1,3,7,4]=>[3,2,2,1]=>1680
[8,2,4,1,5,6,7,3]=>[4,1,1,1,1]=>420
[4,6,3,5,8,1,7,2]=>[6,1,1]=>3360
[1,7,8,3,5,4,6,2]=>[6,1,1]=>3360
[3,4,5,1,8,6,7,2]=>[6,1,1]=>3360
[3,8,1,4,5,6,7,2]=>[2,2,1,1,1,1]=>210
[3,4,5,7,8,2,6,1]=>[4,4]=>1260
[3,4,6,8,1,5,2,7]=>[4,4]=>1260
[3,4,7,2,1,8,6,5]=>[6,2]=>3360
[3,4,8,2,1,5,6,7]=>[6,2]=>3360
[3,5,6,2,8,4,1,7]=>[8]=>5040
[3,5,6,8,4,1,2,7]=>[5,3]=>2688
[3,5,7,2,4,8,6,1]=>[5,3]=>2688
[3,5,7,8,4,1,6,2]=>[4,4]=>1260
[3,6,2,1,8,5,4,7]=>[8]=>5040
[3,6,7,2,8,5,4,1]=>[8]=>5040
[3,6,8,2,4,5,1,7]=>[4,4]=>1260
[3,7,2,1,4,8,6,5]=>[8]=>5040
[3,8,2,1,4,5,6,7]=>[8]=>5040
[4,1,5,6,7,8,3,2]=>[5,3]=>2688
[4,1,6,3,8,5,2,7]=>[8]=>5040
[4,1,6,7,3,8,5,2]=>[8]=>5040
[4,1,7,3,2,8,6,5]=>[8]=>5040
[4,1,8,3,2,5,6,7]=>[8]=>5040
[4,5,2,6,8,1,3,7]=>[5,3]=>2688
[4,5,7,3,8,1,6,2]=>[5,3]=>2688
[4,5,8,3,2,1,6,7]=>[6,2]=>3360
[4,6,7,3,2,8,5,1]=>[8]=>5040
[4,7,2,8,3,5,6,1]=>[5,3]=>2688
[4,7,8,3,2,5,6,1]=>[4,4]=>1260
[4,8,2,3,1,5,6,7]=>[8]=>5040
[5,1,2,6,8,4,3,7]=>[6,2]=>3360
[5,1,6,7,4,8,2,3]=>[5,3]=>2688
[5,6,2,3,8,4,1,7]=>[4,4]=>1260
[5,6,2,7,8,4,1,3]=>[8]=>5040
[5,6,8,3,4,2,1,7]=>[6,2]=>3360
[5,7,2,3,4,8,6,1]=>[8]=>5040
[5,7,8,3,4,2,6,1]=>[5,3]=>2688
[5,8,2,3,4,1,6,7]=>[8]=>5040
[6,1,2,3,7,8,5,4]=>[6,2]=>3360
[6,1,2,3,8,5,4,7]=>[8]=>5040
[6,1,2,7,8,5,4,3]=>[6,2]=>3360
[6,1,7,3,8,5,4,2]=>[5,3]=>2688
[6,1,7,8,4,5,3,2]=>[6,2]=>3360
[6,1,8,3,4,5,2,7]=>[8]=>5040
[6,7,2,3,8,5,4,1]=>[4,4]=>1260
[6,7,2,8,4,5,3,1]=>[5,3]=>2688
[7,1,2,3,4,8,6,5]=>[8]=>5040
[7,1,2,8,4,5,6,3]=>[8]=>5040
[7,1,8,3,4,5,6,2]=>[8]=>5040
[6,4,1,8,2,3,7,5]=>[4,3,1]=>3360
[5,8,1,2,4,3,7,6]=>[7,1]=>5760
[1,3,5,7,2,6,4,8]=>[3,2,1,1,1]=>1120
[3,5,8,6,1,2,4,7]=>[8]=>5040
[3,1,6,8,2,4,7,5]=>[7,1]=>5760
[3,6,2,8,1,5,7,4]=>[5,2,1]=>4032
[2,6,1,3,8,4,7,5]=>[5,2,1]=>4032
[1,7,5,2,3,4,6,8]=>[4,2,1,1]=>2520
[2,7,5,1,3,8,4,6]=>[4,2,2]=>1260
[8,2,5,7,4,6,1,3]=>[6,1,1]=>3360
[8,2,1,3,7,6,4,5]=>[6,1,1]=>3360
[8,2,5,1,3,7,4,6]=>[5,2,1]=>4032
[8,2,7,5,3,1,6,4]=>[7,1]=>5760
[8,2,6,5,4,7,1,3]=>[5,2,1]=>4032
[7,6,5,2,4,8,1,3]=>[6,2]=>3360
[7,8,2,5,3,1,6,4]=>[5,3]=>2688
[7,1,8,6,3,2,4,5]=>[5,3]=>2688
[6,8,1,5,3,2,4,7]=>[8]=>5040
[1,6,7,5,3,2,4,8]=>[4,2,1,1]=>2520
[6,5,1,2,4,8,3,7]=>[5,3]=>2688
[7,8,1,6,4,2,3,5]=>[5,3]=>2688
[8,4,1,2,5,6,3,7]=>[4,2,1,1]=>2520
[1,7,3,6,5,2,4,8]=>[4,1,1,1,1]=>420
[8,1,3,7,2,6,4,5]=>[4,2,1,1]=>2520
[7,3,2,6,5,1,8,4]=>[5,2,1]=>4032
[7,8,4,2,5,6,1,3]=>[4,2,1,1]=>2520
[8,2,7,4,5,6,1,3]=>[4,1,1,1,1]=>420
[8,2,3,6,5,1,7,4]=>[4,1,1,1,1]=>420
[7,9,8,6,5,4,3,2,1]=>[6,2,1]=>30240
[6,9,8,7,5,4,3,2,1]=>[8,1]=>45360
[5,9,8,7,6,4,3,2,1]=>[9]=>40320
[4,9,8,7,6,5,3,2,1]=>[7,2]=>25920
[3,9,8,7,6,5,4,2,1]=>[5,2,2]=>9072
[2,9,8,7,6,5,4,3,1]=>[3,2,2,2]=>2520
[8,10,9,7,6,5,4,3,2,1]=>[6,2,2]=>75600
[6,9,7,8,5,4,3,2,1]=>[6,2,1]=>30240
[7,10,9,8,6,5,4,3,2,1]=>[8,2]=>226800
[4,8,6,5,7,3,2,1]=>[6,2]=>3360
[5,9,8,6,7,4,3,2,1]=>[7,2]=>25920
[6,10,9,8,7,5,4,3,2,1]=>[10]=>362880
[3,8,7,5,4,6,2,1]=>[5,2,1]=>4032
[4,8,5,6,7,3,2,1]=>[8]=>5040
[4,9,8,7,5,6,3,2,1]=>[7,1,1]=>25920
[5,10,9,8,7,6,4,3,2,1]=>[9,1]=>403200
[2,8,7,6,4,3,5,1]=>[5,3]=>2688
[3,8,7,4,5,6,2,1]=>[5,1,1,1]=>1344
[3,9,8,7,6,4,5,2,1]=>[5,4]=>18144
[4,10,9,8,7,6,5,3,2,1]=>[7,2,1]=>259200
[1,8,7,6,5,3,2,4]=>[6,1,1]=>3360
[2,8,7,6,3,4,5,1]=>[3,3,2]=>1120
[2,9,8,7,6,5,3,4,1]=>[4,3,2]=>15120
[3,10,9,8,7,6,5,4,2,1]=>[5,2,2,1]=>90720
[1,8,7,6,5,2,3,4]=>[4,2,1,1]=>2520
[1,9,8,7,6,5,4,2,3]=>[4,2,2,1]=>11340
[2,10,9,8,7,6,5,4,3,1]=>[3,2,2,2,1]=>25200
[7,2,8,6,5,4,1,3]=>[2,2,2,1,1]=>420
[7,2,8,5,4,6,1,3]=>[2,2,2,1,1]=>420
[6,3,2,8,5,1,7,4]=>[2,2,2,1,1]=>420
[8,4,7,2,5,6,3,1]=>[2,2,2,1,1]=>420
[6,8,5,4,3,1,7,2]=>[2,2,2,1,1]=>420
[5,8,6,4,1,3,7,2]=>[2,2,2,1,1]=>420
[4,8,6,1,5,3,7,2]=>[2,2,2,1,1]=>420
[3,6,1,8,5,2,7,4]=>[2,2,2,1,1]=>420
[3,4,1,2,8,6,7,5]=>[2,2,2,1,1]=>420
[6,8,3,5,4,1,7,2]=>[2,2,2,1,1]=>420
[7,2,5,8,3,6,1,4]=>[2,2,2,1,1]=>420
[1,7,5,6,3,4,2,8]=>[2,2,2,1,1]=>420
[7,2,6,8,5,3,1,4]=>[2,2,2,1,1]=>420
[7,6,3,8,5,2,1,4]=>[2,2,2,1,1]=>420
[7,2,6,4,8,3,1,5]=>[2,2,2,1,1]=>420
[1,5,7,4,2,6,3,8]=>[2,2,1,1,1,1]=>210
[4,2,3,1,7,8,5,6]=>[2,2,2,1,1]=>420
[5,2,8,4,1,7,6,3]=>[2,2,2,1,1]=>420
[8,6,3,4,7,2,5,1]=>[2,2,2,1,1]=>420
[6,8,3,4,5,1,7,2]=>[2,2,1,1,1,1]=>210
[1,6,3,2,5,8,4,7]=>[5,1,1,1]=>1344
[8,3,2,1,5,4,7,6]=>[4,2,1,1]=>2520
[6,3,7,1,5,8,4,2]=>[7,1]=>5760
[2,5,1,8,4,3,7,6]=>[7,1]=>5760
[6,2,5,4,8,1,3,7]=>[4,2,1,1]=>2520
[4,3,1,6,5,8,2,7]=>[7,1]=>5760
[1,3,5,4,6,8,2,7]=>[6,1,1]=>3360
[6,1,3,4,5,8,2,7]=>[5,1,1,1]=>1344
[8,3,4,1,5,2,7,6]=>[6,1,1]=>3360
[7,5,4,2,6,8,3,1]=>[8]=>5040
[8,2,6,4,1,7,3,5]=>[3,3,1,1]=>1120
[7,3,8,4,5,2,1,6]=>[4,2,1,1]=>2520
[7,2,5,1,8,4,3,6]=>[7,1]=>5760
[1,7,3,2,5,4,8,6]=>[5,1,1,1]=>1344
[8,7,2,1,5,3,4,6]=>[7,1]=>5760
[3,6,1,5,8,7,4,2]=>[6,2]=>3360
[8,3,6,4,5,1,7,2]=>[5,1,1,1]=>1344
[5,4,6,8,1,2,7,3]=>[5,2,1]=>4032
[6,4,7,2,3,5,8,1]=>[6,2]=>3360
[6,8,4,1,3,5,7,2]=>[5,2,1]=>4032
[3,4,7,8,6,2,5,1]=>[8]=>5040
[4,1,3,5,7,8,6,2]=>[7,1]=>5760
[6,5,1,8,4,7,3,2]=>[4,4]=>1260
[5,3,1,8,4,7,6,2]=>[6,2]=>3360
[8,2,7,4,6,1,3,5]=>[4,2,1,1]=>2520
[4,7,3,2,8,1,6,5]=>[5,2,1]=>4032
[6,3,1,4,7,2,8,5]=>[4,3,1]=>3360
[8,7,3,6,1,5,2,4]=>[5,2,1]=>4032
[7,4,3,6,8,2,5,1]=>[4,3,1]=>3360
[2,4,7,3,8,5,6,1]=>[8]=>5040
[2,8,6,1,5,7,3,4]=>[4,3,1]=>3360
[7,8,2,5,4,3,1,6]=>[4,2,2]=>1260
[1,8,3,4,2,7,6,5]=>[3,2,1,1,1]=>1120
[8,5,3,7,4,2,6,1]=>[5,2,1]=>4032
[5,7,3,2,4,1,8,6]=>[7,1]=>5760
[2,8,3,4,7,1,5,6]=>[4,2,1,1]=>2520
[4,1,3,6,7,8,2,5]=>[7,1]=>5760
[1,7,6,3,2,5,8,4]=>[7,1]=>5760
[3,8,1,5,6,2,7,4]=>[5,2,1]=>4032
[8,2,5,6,1,7,4,3]=>[4,3,1]=>3360
[7,1,5,2,8,6,4,3]=>[4,3,1]=>3360
[6,5,4,8,7,2,1,3]=>[5,3]=>2688
[1,8,6,4,5,2,7,3]=>[4,1,1,1,1]=>420
[1,8,5,3,6,2,7,4]=>[6,1,1]=>3360
[3,6,2,1,7,5,8,4]=>[8]=>5040
[2,5,4,1,8,7,6,3]=>[6,2]=>3360
[4,7,2,6,5,8,1,3]=>[7,1]=>5760
[6,8,1,4,2,7,3,5]=>[4,3,1]=>3360
[6,3,4,7,1,8,2,5]=>[4,4]=>1260
[3,4,7,8,2,5,6,1]=>[8]=>5040
[1,8,2,4,5,6,7,3]=>[3,1,1,1,1,1]=>112
[5,2,4,1,6,8,7,3]=>[6,1,1]=>3360
[3,2,5,7,6,1,8,4]=>[4,3,1]=>3360
[4,3,5,6,1,8,7,2]=>[7,1]=>5760
[5,3,4,1,7,6,8,2]=>[7,1]=>5760
[3,1,4,6,5,7,8,2]=>[7,1]=>5760
[1,4,7,3,5,6,8,2]=>[5,1,1,1]=>1344
[1,3,2,7,5,8,6,4]=>[4,2,1,1]=>2520
[1,4,2,5,8,3,7,6]=>[6,1,1]=>3360
[4,1,2,6,8,5,3,7]=>[8]=>5040
[1,5,2,4,8,7,6,3]=>[4,2,1,1]=>2520
[1,2,6,4,8,7,5,3]=>[5,1,1,1]=>1344
[1,2,7,4,8,6,5,3]=>[4,1,1,1,1]=>420
[1,3,2,7,5,8,4,6]=>[2,2,2,1,1]=>420
[1,3,2,8,5,7,4,6]=>[4,2,1,1]=>2520
[1,5,2,4,8,7,3,6]=>[6,1,1]=>3360
[1,2,6,4,8,7,3,5]=>[3,2,1,1,1]=>1120
[1,2,7,8,5,6,3,4]=>[2,2,1,1,1,1]=>210
[1,3,8,2,6,7,4,5]=>[7,1]=>5760
[1,6,7,8,2,5,3,4]=>[3,2,2,1]=>1680
[1,5,7,8,2,3,6,4]=>[3,2,2,1]=>1680
[1,5,2,7,8,4,6,3]=>[4,3,1]=>3360
[1,3,6,2,4,8,7,5]=>[6,1,1]=>3360
[1,6,7,3,4,8,5,2]=>[4,3,1]=>3360
[1,5,3,7,4,8,6,2]=>[6,1,1]=>3360
[2,8,4,1,5,3,7,6]=>[6,1,1]=>3360
[1,3,8,4,2,7,6,5]=>[4,2,1,1]=>2520
[1,2,7,4,8,3,6,5]=>[3,2,1,1,1]=>1120
[1,2,6,4,8,3,7,5]=>[2,2,1,1,1,1]=>210
[1,5,2,4,8,3,7,6]=>[5,1,1,1]=>1344
[1,8,3,5,2,7,4,6]=>[6,1,1]=>3360
[1,3,8,6,2,7,4,5]=>[4,3,1]=>3360
[1,2,6,8,5,3,7,4]=>[2,2,1,1,1,1]=>210
[1,2,7,8,6,3,5,4]=>[4,2,1,1]=>2520
[1,6,7,8,5,2,3,4]=>[2,2,2,1,1]=>420
[1,5,7,8,6,2,3,4]=>[3,2,2,1]=>1680
[1,2,7,8,6,5,3,4]=>[2,2,2,1,1]=>420
[5,2,6,7,3,4,8,1]=>[7,1]=>5760
[5,2,4,7,6,3,8,1]=>[7,1]=>5760
[5,6,2,1,7,8,3,4]=>[8]=>5040
[5,6,2,1,4,8,7,3]=>[4,3,1]=>3360
[2,6,1,4,5,8,7,3]=>[5,1,1,1]=>1344
[5,4,2,7,6,3,8,1]=>[8]=>5040
[2,3,7,6,4,5,8,1]=>[5,3]=>2688
[2,6,1,7,5,8,3,4]=>[7,1]=>5760
[2,6,1,7,4,8,5,3]=>[5,3]=>2688
[5,1,2,7,8,4,3,6]=>[8]=>5040
[2,6,1,7,4,8,3,5]=>[8]=>5040
[3,6,4,1,7,8,2,5]=>[5,3]=>2688
[5,4,6,1,3,8,7,2]=>[7,1]=>5760
[3,6,4,1,5,8,7,2]=>[3,3,1,1]=>1120
[2,6,1,5,4,8,7,3]=>[5,2,1]=>4032
[2,6,1,4,7,8,5,3]=>[5,2,1]=>4032
[5,1,2,4,8,6,7,3]=>[5,1,1,1]=>1344
[5,1,2,4,8,7,3,6]=>[7,1]=>5760
[5,1,2,4,8,7,6,3]=>[5,2,1]=>4032
[1,2,3,8,5,4,7,6]=>[3,1,1,1,1,1]=>112
[4,3,1,2,8,5,7,6]=>[4,3,1]=>3360
[2,1,5,3,8,6,4,7]=>[5,2,1]=>4032
[1,2,3,8,5,6,4,7]=>[3,1,1,1,1,1]=>112
[1,2,3,8,6,4,5,7]=>[5,1,1,1]=>1344
[1,2,3,8,6,5,4,7]=>[3,2,1,1,1]=>1120
[1,2,3,8,5,4,6,7]=>[4,1,1,1,1]=>420
[2,6,1,5,4,8,3,7]=>[6,2]=>3360
[5,1,2,4,8,6,3,7]=>[6,1,1]=>3360
[5,1,2,4,8,3,7,6]=>[6,1,1]=>3360
[5,6,3,1,4,8,2,7]=>[4,3,1]=>3360
[2,5,4,3,1,8,6,7]=>[3,3,2]=>1120
[5,4,6,3,1,8,7,2]=>[5,2,1]=>4032
[3,6,4,5,1,8,7,2]=>[4,3,1]=>3360
[3,6,5,4,1,8,7,2]=>[3,3,1,1]=>1120
[5,2,6,1,7,8,4,3]=>[4,3,1]=>3360
[5,1,6,2,8,7,3,4]=>[5,3]=>2688
[2,1,3,7,8,6,4,5]=>[2,2,2,1,1]=>420
[2,1,3,7,8,5,6,4]=>[5,2,1]=>4032
[5,2,4,1,7,8,6,3]=>[7,1]=>5760
[4,3,1,2,8,6,7,5]=>[4,2,1,1]=>2520
[5,1,4,2,8,6,7,3]=>[6,1,1]=>3360
[2,1,3,6,8,5,7,4]=>[4,2,1,1]=>2520
[1,2,3,8,6,7,4,5]=>[5,1,1,1]=>1344
[1,2,3,8,7,5,4,6]=>[5,1,1,1]=>1344
[1,2,3,8,7,4,5,6]=>[3,2,1,1,1]=>1120
[1,2,3,8,5,7,4,6]=>[4,1,1,1,1]=>420
[2,1,3,6,8,7,4,5]=>[3,2,2,1]=>1680
[5,4,1,2,8,7,6,3]=>[4,2,2]=>1260
[3,1,6,2,8,7,5,4]=>[8]=>5040
[1,2,3,4,5,9,6,7,8]=>[4,1,1,1,1,1]=>756
[1,2,3,4,9,5,6,7,8]=>[5,1,1,1,1]=>3024
[1,2,3,9,4,5,6,7,8]=>[6,1,1,1]=>10080
[1,2,9,3,4,5,6,7,8]=>[7,1,1]=>25920
[1,2,3,4,5,6,7,10,8,9]=>[3,1,1,1,1,1,1,1]=>240
[1,2,3,4,5,9,7,6,8]=>[3,1,1,1,1,1,1]=>168
[1,2,3,4,5,6,10,7,8,9]=>[4,1,1,1,1,1,1]=>1260
[1,2,3,4,9,6,5,7,8]=>[4,1,1,1,1,1]=>756
[1,2,3,4,5,10,6,7,8,9]=>[5,1,1,1,1,1]=>6048
[1,2,3,9,5,4,6,7,8]=>[5,1,1,1,1]=>3024
[1,2,3,4,10,5,6,7,8,9]=>[6,1,1,1,1]=>25200
[1,8,3,4,2,5,6,7]=>[5,1,1,1]=>1344
[1,2,9,4,3,5,6,7,8]=>[6,1,1,1]=>10080
[1,2,3,10,4,5,6,7,8,9]=>[7,1,1,1]=>86400
[1,8,4,3,2,5,6,7]=>[5,2,1]=>4032
[1,9,3,2,4,5,6,7,8]=>[7,1,1]=>25920
[1,2,10,3,4,5,6,7,8,9]=>[8,1,1]=>226800
[8,4,7,6,5,3,2,1]=>[5,2,1]=>4032
[8,5,7,4,6,3,2,1]=>[5,2,1]=>4032
[8,5,7,3,6,4,2,1]=>[6,2]=>3360
[8,1,7,4,6,5,3,2]=>[3,2,2,1]=>1680
[8,2,7,3,6,5,4,1]=>[3,2,2,1]=>1680
[8,3,7,2,6,5,4,1]=>[4,2,2]=>1260
[8,5,7,2,6,4,3,1]=>[4,2,2]=>1260
[8,7,6,2,5,4,3,1]=>[5,2,1]=>4032
[8,4,7,1,6,5,3,2]=>[4,2,2]=>1260
[8,3,7,1,6,5,4,2]=>[6,2]=>3360
[8,2,7,1,6,5,4,3]=>[5,2,1]=>4032
[8,1,7,6,5,3,4,2]=>[4,3,1]=>3360
[8,3,7,6,5,2,4,1]=>[5,2,1]=>4032
[8,4,7,6,5,2,3,1]=>[3,2,2,1]=>1680
[8,5,7,6,4,2,3,1]=>[4,2,2]=>1260
[8,6,7,5,4,1,3,2]=>[4,2,2]=>1260
[8,3,7,6,5,1,4,2]=>[7,1]=>5760
[8,7,6,1,5,2,4,3]=>[7,1]=>5760
[6,8,1,3,2,5,4,7]=>[8]=>5040
[6,8,1,4,2,5,3,7]=>[7,1]=>5760
[7,8,3,6,1,4,2,5]=>[5,2,1]=>4032
[7,8,2,5,3,6,1,4]=>[5,2,1]=>4032
[7,8,2,5,1,4,3,6]=>[8]=>5040
[7,8,1,4,3,6,2,5]=>[6,1,1]=>3360
[5,8,1,4,3,7,2,6]=>[4,3,1]=>3360
[6,8,2,5,1,4,3,7]=>[4,4]=>1260
[6,8,2,5,3,7,1,4]=>[5,3]=>2688
[6,8,2,5,4,7,1,3]=>[3,3,2]=>1120
[2,5,4,7,6,8,1,3]=>[8]=>5040
[2,5,3,7,6,8,1,4]=>[7,1]=>5760
[2,5,1,4,3,7,6,8]=>[4,2,1,1]=>2520
[2,6,1,4,3,7,5,8]=>[6,1,1]=>3360
[2,6,5,8,1,4,3,7]=>[8]=>5040
[2,6,1,5,3,7,4,8]=>[7,1]=>5760
[2,6,3,7,4,8,1,5]=>[7,1]=>5760
[2,6,4,7,5,8,1,3]=>[7,1]=>5760
[5,8,3,6,4,7,1,2]=>[5,2,1]=>4032
[5,8,2,6,4,7,1,3]=>[5,3]=>2688
[4,8,2,6,3,7,1,5]=>[4,4]=>1260
[4,8,1,5,3,7,2,6]=>[4,4]=>1260
[4,8,1,5,2,6,3,7]=>[7,1]=>5760
[4,8,3,7,1,5,2,6]=>[7,1]=>5760
[6,8,3,7,1,4,2,5]=>[7,1]=>5760
[5,8,1,3,2,6,4,7]=>[7,1]=>5760
[5,8,4,7,1,3,2,6]=>[6,2]=>3360
[6,8,4,7,1,3,2,5]=>[8]=>5040
[6,8,5,7,1,3,2,4]=>[4,4]=>1260
[5,7,6,8,2,4,1,3]=>[4,4]=>1260
[4,7,6,8,1,3,2,5]=>[4,2,2]=>1260
[4,7,5,8,1,3,2,6]=>[6,2]=>3360
[4,7,1,3,2,6,5,8]=>[3,3,1,1]=>1120
[3,7,1,4,2,6,5,8]=>[3,2,1,1,1]=>1120
[3,7,5,8,1,4,2,6]=>[3,3,2]=>1120
[3,7,6,8,1,4,2,5]=>[6,2]=>3360
[3,7,6,8,2,5,1,4]=>[6,2]=>3360
[4,7,6,8,2,5,1,3]=>[8]=>5040
[4,7,5,8,3,6,1,2]=>[5,2,1]=>4032
[4,7,5,8,2,6,1,3]=>[7,1]=>5760
[3,7,5,8,2,6,1,4]=>[5,2,1]=>4032
[3,7,4,8,2,6,1,5]=>[7,1]=>5760
[3,7,4,8,1,5,2,6]=>[6,2]=>3360
[3,7,1,5,2,6,4,8]=>[4,2,1,1]=>2520
[3,7,2,6,1,5,4,8]=>[7,1]=>5760
[3,7,2,6,5,8,1,4]=>[4,3,1]=>3360
[4,7,3,6,5,8,1,2]=>[6,1,1]=>3360
[3,6,5,8,4,7,1,2]=>[8]=>5040
[2,6,5,8,4,7,1,3]=>[4,4]=>1260
[2,6,5,8,3,7,1,4]=>[4,2,2]=>1260
[2,6,3,7,1,5,4,8]=>[4,2,1,1]=>2520
[7,6,4,2,8,5,3,1]=>[8]=>5040
[7,6,4,3,8,2,5,1]=>[4,2,2]=>1260
[7,6,4,8,5,2,3,1]=>[5,2,1]=>4032
[6,8,4,3,7,2,1,5]=>[6,2]=>3360
[6,7,4,3,5,1,8,2]=>[3,2,2,1]=>1680
[6,7,3,5,4,8,2,1]=>[3,2,2,1]=>1680
[6,8,3,7,5,2,4,1]=>[4,2,1,1]=>2520
[7,6,8,3,5,2,4,1]=>[5,2,1]=>4032
[7,6,3,5,8,2,4,1]=>[5,2,1]=>4032
[7,6,3,5,2,4,8,1]=>[4,3,1]=>3360
[7,6,4,2,5,1,8,3]=>[7,1]=>5760
[7,6,2,8,4,1,5,3]=>[8]=>5040
[7,6,3,8,2,4,1,5]=>[5,2,1]=>4032
[7,6,3,4,8,2,5,1]=>[4,2,1,1]=>2520
[6,8,3,7,4,5,2,1]=>[7,1]=>5760
[6,7,3,5,8,4,2,1]=>[5,2,1]=>4032
[5,7,8,3,6,2,1,4]=>[5,3]=>2688
[5,8,3,6,7,2,1,4]=>[4,3,1]=>3360
[6,3,4,8,7,2,5,1]=>[6,2]=>3360
[6,3,8,4,7,2,1,5]=>[7,1]=>5760
[6,2,8,4,1,7,5,3]=>[4,2,1,1]=>2520
[6,2,7,4,1,5,3,8]=>[3,2,1,1,1]=>1120
[6,3,4,7,5,8,2,1]=>[4,3,1]=>3360
[6,3,5,7,8,4,2,1]=>[8]=>5040
[5,7,3,6,8,2,1,4]=>[7,1]=>5760
[5,6,8,3,7,2,1,4]=>[3,3,2]=>1120
[5,6,7,3,4,1,8,2]=>[8]=>5040
[4,6,7,8,3,5,2,1]=>[5,3]=>2688
[4,6,8,3,5,7,2,1]=>[4,3,1]=>3360
[4,7,3,5,6,8,2,1]=>[5,2,1]=>4032
[4,7,3,5,8,2,6,1]=>[4,3,1]=>3360
[5,3,4,7,8,2,1,6]=>[8]=>5040
[5,3,8,2,4,1,6,7]=>[8]=>5040
[5,3,4,8,2,6,1,7]=>[7,1]=>5760
[4,8,3,6,2,5,7,1]=>[6,1,1]=>3360
[4,8,3,5,7,2,6,1]=>[7,1]=>5760
[4,8,3,5,6,7,2,1]=>[7,1]=>5760
[4,7,8,3,5,6,2,1]=>[4,2,1,1]=>2520
[4,7,8,3,6,2,5,1]=>[4,4]=>1260
[4,8,3,6,7,2,5,1]=>[5,2,1]=>4032
[4,8,3,7,2,5,6,1]=>[7,1]=>5760
[5,3,4,8,2,7,6,1]=>[6,2]=>3360
[5,3,8,2,4,1,7,6]=>[7,1]=>5760
[5,2,8,4,1,7,3,6]=>[4,2,1,1]=>2520
[6,4,2,5,1,8,7,3]=>[7,1]=>5760
[6,4,3,5,8,2,1,7]=>[7,1]=>5760
[6,3,5,8,7,2,4,1]=>[8]=>5040
[5,8,3,7,2,6,4,1]=>[4,2,1,1]=>2520
[5,7,3,4,8,2,1,6]=>[6,1,1]=>3360
[5,8,4,2,3,1,6,7]=>[8]=>5040
[5,8,4,2,3,1,7,6]=>[7,1]=>5760
[6,4,5,3,8,2,1,7]=>[8]=>5040
[6,4,8,5,3,7,2,1]=>[8]=>5040
[6,4,3,8,5,7,2,1]=>[6,1,1]=>3360
[6,4,2,8,5,3,1,7]=>[7,1]=>5760
[6,4,2,7,3,1,8,5]=>[6,2]=>3360
[6,4,3,7,8,5,2,1]=>[4,3,1]=>3360
[6,4,5,3,7,1,8,2]=>[6,2]=>3360
[5,7,4,2,3,1,6,8]=>[7,1]=>5760
[5,6,3,7,1,8,2,4]=>[5,2,1]=>4032
[5,6,3,4,7,1,8,2]=>[6,1,1]=>3360
[5,6,3,4,8,2,1,7]=>[4,2,1,1]=>2520
[6,3,5,7,4,8,2,1]=>[5,3]=>2688
[6,3,5,4,7,8,2,1]=>[4,3,1]=>3360
[6,4,3,5,7,1,8,2]=>[5,2,1]=>4032
[6,4,2,5,1,7,3,8]=>[7,1]=>5760
[5,3,7,2,4,1,6,8]=>[7,1]=>5760
[5,3,4,7,2,6,1,8]=>[6,1,1]=>3360
[4,7,3,6,2,5,8,1]=>[7,1]=>5760
[4,7,3,6,8,2,5,1]=>[7,1]=>5760
[4,6,7,3,5,8,2,1]=>[7,1]=>5760
[4,5,7,8,3,6,2,1]=>[4,3,1]=>3360
[4,5,8,3,6,7,2,1]=>[4,4]=>1260
[4,5,8,3,7,2,6,1]=>[4,4]=>1260
[5,3,4,6,8,2,1,7]=>[4,4]=>1260
[5,3,6,8,2,1,4,7]=>[5,3]=>2688
[5,3,6,7,1,8,2,4]=>[6,2]=>3360
[5,3,4,6,7,1,8,2]=>[8]=>5040
[4,6,3,5,7,8,2,1]=>[7,1]=>5760
[4,5,7,3,6,8,2,1]=>[8]=>5040
[4,5,6,8,3,7,2,1]=>[5,3]=>2688
[5,7,4,8,6,3,2,1]=>[6,2]=>3360
[4,5,6,7,8,9,3,2,1]=>[6,3]=>20160
[3,2,1,6,5,4,9,8,7]=>[2,2,2,1,1,1]=>1260
[3,2,5,4,7,6,9,8,1]=>[5,1,1,1,1]=>3024
[3,4,5,6,7,8,9,2,1]=>[5,4]=>18144
[5,4,3,2,1,10,9,8,7,6]=>[2,2,2,2,1,1]=>4725
[4,5,6,7,8,9,10,3,2,1]=>[6,4]=>151200
[3,4,5,6,7,8,9,10,2,1]=>[10]=>362880
[1,6,2,5,3,4,8,7]=>[5,2,1]=>4032
[1,3,8,2,4,6,5,7]=>[6,1,1]=>3360
[1,7,2,3,6,4,8,5]=>[7,1]=>5760
[1,6,8,2,5,3,7,4]=>[5,1,1,1]=>1344
[1,8,2,5,3,4,7,6]=>[6,1,1]=>3360
[1,8,2,3,6,4,7,5]=>[6,1,1]=>3360
[1,3,5,2,8,4,7,6]=>[6,1,1]=>3360
[1,2,7,3,5,4,6,8]=>[4,1,1,1,1]=>420
[1,8,2,7,3,4,6,5]=>[4,3,1]=>3360
[1,5,8,2,3,7,4,6]=>[7,1]=>5760
[1,6,8,2,3,5,4,7]=>[7,1]=>5760
[5,3,6,1,2,4,8,7]=>[6,2]=>3360
[7,1,5,8,4,2,3,6]=>[8]=>5040
[8,1,5,7,4,2,3,6]=>[4,4]=>1260
[7,1,4,5,8,2,3,6]=>[8]=>5040
[7,4,1,6,2,8,3,5]=>[5,3]=>2688
[8,4,1,7,2,6,3,5]=>[7,1]=>5760
[8,1,4,7,5,2,3,6]=>[4,3,1]=>3360
[8,1,5,4,7,2,3,6]=>[4,3,1]=>3360
[2,1,7,5,8,3,4,6]=>[6,2]=>3360
[7,1,5,4,8,2,3,6]=>[7,1]=>5760
[7,1,4,8,5,2,3,6]=>[7,1]=>5760
[6,4,1,7,2,3,8,5]=>[5,3]=>2688
[7,8,3,1,2,4,6,5]=>[4,3,1]=>3360
[8,7,1,6,4,2,3,5]=>[8]=>5040
[8,6,1,7,4,2,3,5]=>[6,2]=>3360
[7,6,1,8,4,2,3,5]=>[3,3,2]=>1120
[7,3,8,1,2,4,6,5]=>[4,4]=>1260
[8,3,7,1,2,4,6,5]=>[8]=>5040
[8,3,6,1,2,4,7,5]=>[7,1]=>5760
[8,3,7,5,1,2,4,6]=>[8]=>5040
[7,3,6,1,2,4,8,5]=>[8]=>5040
[6,7,1,8,4,2,3,5]=>[5,3]=>2688
[6,8,1,7,4,2,3,5]=>[8]=>5040
[7,1,8,5,4,2,3,6]=>[6,2]=>3360
[7,1,8,4,5,2,3,6]=>[6,1,1]=>3360
[2,1,7,8,5,3,4,6]=>[5,2,1]=>4032
[7,6,3,1,2,4,8,5]=>[7,1]=>5760
[6,1,2,3,8,7,5,4]=>[8]=>5040
[6,8,1,4,2,3,7,5]=>[3,3,1,1]=>1120
[6,8,3,1,2,7,4,5]=>[4,3,1]=>3360
[6,7,3,1,2,8,4,5]=>[7,1]=>5760
[6,7,1,4,2,3,8,5]=>[4,3,1]=>3360
[4,3,6,8,5,7,1,2]=>[7,1]=>5760
[1,3,6,8,7,4,2,5]=>[7,1]=>5760
[1,2,8,5,7,3,4,6]=>[3,3,1,1]=>1120
[2,6,1,5,8,3,4,7]=>[4,4]=>1260
[5,7,1,6,8,4,3,2]=>[6,2]=>3360
[4,8,1,2,5,7,3,6]=>[7,1]=>5760
[8,4,6,2,5,7,3,1]=>[3,2,2,1]=>1680
[8,3,6,4,7,2,5,1]=>[3,2,2,1]=>1680
[3,8,1,4,7,2,5,6]=>[3,2,2,1]=>1680
[1,7,8,4,6,2,5,3]=>[4,2,1,1]=>2520
[3,7,4,8,5,1,6,2]=>[7,1]=>5760
[3,7,1,6,5,4,8,2]=>[3,2,2,1]=>1680
[2,7,3,1,5,8,4,6]=>[4,2,1,1]=>2520
[2,7,4,6,8,1,3,5]=>[6,2]=>3360
[2,7,5,8,6,4,1,3]=>[5,3]=>2688
[8,2,6,7,5,4,3,1]=>[4,2,1,1]=>2520
[3,8,7,1,6,4,5,2]=>[6,2]=>3360
[3,6,8,2,7,4,1,5]=>[5,3]=>2688
[1,5,2,8,7,4,6,3]=>[7,1]=>5760
[3,4,2,7,8,1,6,5]=>[6,2]=>3360
[4,1,3,7,5,6,8,2]=>[5,1,1,1]=>1344
[6,3,8,1,7,4,2,5]=>[5,3]=>2688
[6,5,8,7,1,4,2,3]=>[6,2]=>3360
[4,1,7,3,8,5,2,6]=>[5,3]=>2688
[3,6,1,4,5,8,2,7]=>[4,2,1,1]=>2520
[1,6,7,4,5,3,8,2]=>[5,1,1,1]=>1344
[6,1,7,3,5,4,8,2]=>[7,1]=>5760
[6,3,1,2,5,8,4,7]=>[7,1]=>5760
[1,4,7,2,8,5,3,6]=>[3,2,2,1]=>1680
[5,6,8,7,2,4,1,3]=>[6,2]=>3360
[6,8,5,7,1,2,4,3]=>[6,2]=>3360
[2,8,4,1,7,5,6,3]=>[5,3]=>2688
[8,2,4,3,7,5,6,1]=>[3,2,2,1]=>1680
[6,8,2,1,5,7,3,4]=>[7,1]=>5760
[7,2,8,4,1,6,3,5]=>[5,1,1,1]=>1344
[1,2,4,8,6,5,3,7]=>[4,2,1,1]=>2520
[7,1,5,6,8,4,3,2]=>[6,2]=>3360
[2,7,8,1,4,6,3,5]=>[7,1]=>5760
[4,8,2,5,7,1,6,3]=>[5,3]=>2688
[4,1,6,8,5,3,7,2]=>[4,2,1,1]=>2520
[5,2,6,4,8,3,1,7]=>[4,2,1,1]=>2520
[6,7,1,3,4,5,8,2]=>[5,3]=>2688
[1,7,3,2,4,8,5,6]=>[4,2,1,1]=>2520
[1,3,6,5,2,8,4,7]=>[7,1]=>5760
[7,1,6,5,3,4,8,2]=>[4,4]=>1260
[6,3,4,2,8,7,5,1]=>[5,3]=>2688
[4,3,8,7,5,2,6,1]=>[7,1]=>5760
[6,8,7,4,2,3,5,1]=>[7,1]=>5760
[3,6,4,5,2,8,7,1]=>[7,1]=>5760
[8,6,1,3,5,4,2,7]=>[7,1]=>5760
[5,3,8,6,1,2,4,7]=>[6,2]=>3360
[2,5,6,3,4,8,7,1]=>[7,1]=>5760
[2,5,3,6,8,7,4,1]=>[4,3,1]=>3360
[4,8,7,3,5,2,6,1]=>[7,1]=>5760
[3,8,7,2,6,4,5,1]=>[8]=>5040
[6,3,5,4,8,7,2,1]=>[7,1]=>5760
[4,3,8,6,1,5,2,7]=>[4,4]=>1260
[4,7,6,2,5,3,8,1]=>[5,2,1]=>4032
[7,5,2,6,8,1,4,3]=>[4,4]=>1260
[8,5,2,7,1,4,3,6]=>[8]=>5040
[1,8,5,3,6,2,4,7]=>[7,1]=>5760
[5,1,7,2,4,3,8,6]=>[4,4]=>1260
[1,5,3,4,8,6,2,7]=>[4,1,1,1,1]=>420
[5,4,1,3,8,6,2,7]=>[7,1]=>5760
[5,1,8,6,3,4,2,7]=>[6,2]=>3360
[4,5,2,8,3,7,6,1]=>[3,3,2]=>1120
[8,2,3,7,6,4,5,1]=>[4,2,1,1]=>2520
[5,8,2,4,7,6,3,1]=>[6,1,1]=>3360
[6,8,2,5,3,4,7,1]=>[7,1]=>5760
[7,2,5,6,4,8,1,3]=>[5,2,1]=>4032
[1,6,7,4,8,2,3,5]=>[2,2,2,1,1]=>420
[7,1,3,5,8,2,6,4]=>[4,3,1]=>3360
[8,2,1,3,5,6,7,4]=>[4,1,1,1,1]=>420
[6,3,1,4,7,5,8,2]=>[7,1]=>5760
[4,1,3,8,2,6,7,5]=>[5,1,1,1]=>1344
[2,8,3,6,7,5,4,1]=>[4,3,1]=>3360
[3,1,7,2,8,5,4,6]=>[5,3]=>2688
[3,6,1,4,7,2,8,5]=>[3,2,2,1]=>1680
[1,5,8,4,7,2,3,6]=>[6,1,1]=>3360
[7,1,3,6,2,8,4,5]=>[7,1]=>5760
[6,2,7,4,5,8,1,3]=>[5,1,1,1]=>1344
[2,1,8,4,5,7,3,6]=>[4,2,1,1]=>2520
[1,8,5,7,3,2,4,6]=>[3,2,2,1]=>1680
[2,1,8,5,4,3,6,7]=>[4,2,2]=>1260
[2,7,4,1,5,3,8,6]=>[7,1]=>5760
[7,4,8,6,2,3,1,5]=>[6,2]=>3360
[2,7,1,4,6,3,8,5]=>[7,1]=>5760
[4,7,5,6,8,1,3,2]=>[5,3]=>2688
[7,1,3,2,8,5,4,6]=>[4,3,1]=>3360
[2,8,5,4,1,3,6,7]=>[7,1]=>5760
[5,1,7,4,2,3,8,6]=>[4,3,1]=>3360
[3,8,6,5,1,4,2,7]=>[5,3]=>2688
[1,3,4,8,6,5,2,7]=>[5,2,1]=>4032
[4,1,8,6,5,3,2,7]=>[7,1]=>5760
[4,8,5,2,7,3,6,1]=>[4,4]=>1260
[7,2,8,5,3,6,4,1]=>[6,1,1]=>3360
[5,2,8,4,3,7,6,1]=>[4,2,1,1]=>2520
[8,4,7,5,2,3,6,1]=>[3,3,2]=>1120
[7,5,2,8,4,6,1,3]=>[5,2,1]=>4032
[5,7,4,3,6,2,8,1]=>[6,2]=>3360
[6,7,5,1,2,8,3,4]=>[4,4]=>1260
[5,2,6,8,3,4,7,1]=>[6,1,1]=>3360
[7,6,2,4,5,8,3,1]=>[6,1,1]=>3360
[3,6,8,4,7,2,5,1]=>[3,2,2,1]=>1680
[7,6,3,8,4,2,5,1]=>[5,2,1]=>4032
[2,6,3,8,4,7,5,1]=>[7,1]=>5760
[7,2,3,6,5,8,4,1]=>[5,1,1,1]=>1344
[6,2,7,5,8,3,1,4]=>[4,3,1]=>3360
[2,8,3,6,4,5,7,1]=>[3,3,1,1]=>1120
[2,1,5,6,8,3,7,4]=>[5,2,1]=>4032
[5,8,1,2,6,4,7,3]=>[7,1]=>5760
[1,6,8,3,2,7,4,5]=>[7,1]=>5760
[6,5,7,2,8,4,1,3]=>[8]=>5040
[7,5,1,2,8,4,6,3]=>[8]=>5040
[5,4,8,3,6,2,7,1]=>[7,1]=>5760
[5,8,2,7,4,3,6,1]=>[8]=>5040
[6,4,5,8,2,7,3,1]=>[8]=>5040
[5,7,3,6,4,8,2,1]=>[5,2,1]=>4032
[1,5,6,4,8,2,7,3]=>[5,1,1,1]=>1344
[3,1,5,6,4,8,7,2]=>[7,1]=>5760
[3,5,1,6,4,7,8,2]=>[6,2]=>3360
[3,6,1,4,2,7,8,5]=>[5,2,1]=>4032
[1,2,6,4,3,8,5,7]=>[5,1,1,1]=>1344
[1,2,6,3,5,8,7,4]=>[4,1,1,1,1]=>420
[2,3,5,1,8,4,7,6]=>[7,1]=>5760
[2,3,6,1,8,5,4,7]=>[8]=>5040
[3,1,7,5,4,8,6,2]=>[6,2]=>3360
[1,2,7,6,4,8,5,3]=>[6,1,1]=>3360
[1,2,7,3,6,8,5,4]=>[6,1,1]=>3360
[2,3,6,1,8,5,7,4]=>[7,1]=>5760
[1,2,5,8,4,7,3,6]=>[6,1,1]=>3360
[1,2,6,8,5,4,3,7]=>[5,1,1,1]=>1344
[1,3,5,8,2,4,7,6]=>[3,3,1,1]=>1120
[1,4,6,8,3,2,5,7]=>[7,1]=>5760
[1,3,7,5,6,8,2,4]=>[4,3,1]=>3360
[1,2,6,7,3,8,5,4]=>[6,1,1]=>3360
[3,1,5,7,6,8,4,2]=>[6,2]=>3360
[3,5,4,6,8,2,7,1]=>[7,1]=>5760
[2,3,6,5,8,7,1,4]=>[5,3]=>2688
[1,2,7,5,6,8,4,3]=>[6,1,1]=>3360
[3,1,6,7,5,8,4,2]=>[5,2,1]=>4032
[4,6,2,7,5,8,3,1]=>[7,1]=>5760
[2,4,7,6,8,3,5,1]=>[8]=>5040
[1,3,5,8,2,7,4,6]=>[4,3,1]=>3360
[1,2,5,8,4,7,6,3]=>[4,2,1,1]=>2520
[1,2,5,8,7,4,3,6]=>[3,3,1,1]=>1120
[1,3,5,8,7,2,4,6]=>[7,1]=>5760
[5,7,1,2,8,6,4,3]=>[4,3,1]=>3360
[6,4,5,7,2,8,1,3]=>[8]=>5040
[5,3,6,2,7,1,4,8]=>[7,1]=>5760
[3,7,4,5,6,8,1,2]=>[8]=>5040
[4,7,6,2,3,8,1,5]=>[4,4]=>1260
[7,3,5,2,4,8,1,6]=>[4,2,2]=>1260
[5,3,1,2,8,4,7,6]=>[7,1]=>5760
[5,2,1,8,3,4,6,7]=>[4,3,1]=>3360
[6,3,2,8,4,5,7,1]=>[5,2,1]=>4032
[7,3,1,2,8,4,6,5]=>[6,2]=>3360
[6,2,3,1,8,4,7,5]=>[3,2,1,1,1]=>1120
[8,2,1,7,3,4,5,6]=>[7,1]=>5760
[7,1,6,2,3,4,5,8]=>[7,1]=>5760
[8,1,6,2,3,4,5,7]=>[8]=>5040
[8,1,7,3,4,5,6,2]=>[5,3]=>2688
[8,6,1,7,2,4,5,3]=>[5,3]=>2688
[8,1,5,7,2,3,6,4]=>[8]=>5040
[7,3,8,2,4,5,6,1]=>[8]=>5040
[7,2,8,3,4,5,6,1]=>[7,1]=>5760
[1,7,8,3,4,5,6,2]=>[7,1]=>5760
[1,4,5,8,3,6,7,2]=>[3,2,1,1,1]=>1120
[6,2,7,1,8,4,5,3]=>[4,3,1]=>3360
[4,7,1,3,8,5,6,2]=>[5,3]=>2688
[3,2,8,7,1,4,6,5]=>[4,3,1]=>3360
[3,1,8,7,2,4,6,5]=>[5,3]=>2688
[5,3,7,6,1,2,4,8]=>[5,2,1]=>4032
[1,8,3,7,2,4,5,6]=>[6,1,1]=>3360
[3,8,1,7,2,4,5,6]=>[6,2]=>3360
[6,8,2,3,5,1,4,7]=>[5,2,1]=>4032
[4,7,8,2,6,1,3,5]=>[8]=>5040
[1,7,6,2,3,4,5,8]=>[6,1,1]=>3360
[1,8,6,2,3,4,5,7]=>[7,1]=>5760
[2,8,7,3,4,5,6,1]=>[5,3]=>2688
[7,8,3,6,2,4,5,1]=>[5,2,1]=>4032
[8,7,6,1,3,4,5,2]=>[8]=>5040
[3,4,7,2,5,1,8,6]=>[5,2,1]=>4032
[1,2,8,3,7,5,4,6]=>[6,1,1]=>3360
[1,6,3,8,7,4,2,5]=>[6,1,1]=>3360
[4,3,8,1,2,6,7,5]=>[4,2,1,1]=>2520
[7,8,10,9,5,6,3,4,1,2]=>[8,1,1]=>226800
[9,10,5,6,8,7,3,4,1,2]=>[6,2,2]=>75600
[5,8,10,6,9,7,3,4,1,2]=>[7,3]=>172800
[5,6,7,10,9,8,3,4,1,2]=>[5,3,2]=>120960
[9,10,7,8,3,4,6,5,1,2]=>[6,2,2]=>75600
[7,8,10,9,3,4,6,5,1,2]=>[5,5]=>72576
[9,10,3,6,8,4,7,5,1,2]=>[2,2,2,2,1,1]=>4725
[3,8,10,6,9,4,7,5,1,2]=>[7,2,1]=>259200
[3,6,7,10,9,4,8,5,1,2]=>[6,4]=>151200
[9,10,3,4,5,8,7,6,1,2]=>[2,2,2,1,1,1,1]=>3150
[3,8,10,4,5,9,7,6,1,2]=>[7,1,1,1]=>86400
[3,4,7,10,5,9,8,6,1,2]=>[6,3,1]=>201600
[3,4,5,6,10,9,8,7,1,2]=>[8,2]=>226800
[9,10,7,8,5,6,1,2,4,3]=>[8,1,1]=>226800
[7,8,10,9,5,6,1,2,4,3]=>[2,2,2,2,1,1]=>4725
[9,10,5,6,8,7,1,2,4,3]=>[5,5]=>72576
[5,8,10,6,9,7,1,2,4,3]=>[6,2,2]=>75600
[5,6,7,10,9,8,1,2,4,3]=>[7,3]=>172800
[9,10,7,8,1,4,6,2,5,3]=>[7,3]=>172800
[7,8,10,9,1,4,6,2,5,3]=>[6,2,2]=>75600
[9,10,1,6,8,4,7,2,5,3]=>[7,2,1]=>259200
[1,8,10,6,9,4,7,2,5,3]=>[2,2,2,2,1,1]=>4725
[1,6,7,10,9,4,8,2,5,3]=>[7,2,1]=>259200
[9,10,1,4,5,8,7,2,6,3]=>[7,1,1,1]=>86400
[1,8,10,4,5,9,7,2,6,3]=>[2,2,2,1,1,1,1]=>3150
[1,4,7,10,5,9,8,2,6,3]=>[6,2,1,1]=>151200
[1,4,5,6,10,9,8,2,7,3]=>[6,3,1]=>201600
[9,10,7,8,1,2,3,6,5,4]=>[5,3,2]=>120960
[7,8,10,9,1,2,3,6,5,4]=>[7,3]=>172800
[9,10,1,6,8,2,3,7,5,4]=>[6,4]=>151200
[1,8,10,6,9,2,3,7,5,4]=>[7,2,1]=>259200
[1,6,7,10,9,2,3,8,5,4]=>[2,2,2,2,1,1]=>4725
[9,10,1,2,5,8,3,7,6,4]=>[6,3,1]=>201600
[1,8,10,2,5,9,3,7,6,4]=>[6,2,1,1]=>151200
[1,2,7,10,5,9,3,8,6,4]=>[2,2,2,1,1,1,1]=>3150
[1,2,5,6,10,9,3,8,7,4]=>[7,1,1,1]=>86400
[9,10,1,2,3,4,8,7,6,5]=>[8,2]=>226800
[1,8,10,2,3,4,9,7,6,5]=>[6,3,1]=>201600
[1,2,7,10,3,4,9,8,6,5]=>[7,1,1,1]=>86400
[1,2,3,6,10,4,9,8,7,5]=>[2,2,2,1,1,1,1]=>3150
[1,2,3,4,5,10,9,8,7,6]=>[2,2,1,1,1,1,1,1]=>630
[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2,2]=>10395
[7,8,9,12,11,10,5,6,3,4,1,2]=>[6,4,2]=>9979200
[11,12,5,6,7,10,9,8,3,4,1,2]=>[4,3,2,2,1]=>4989600
[5,10,12,6,7,11,9,8,3,4,1,2]=>[11,1]=>43545600
[5,6,7,8,12,11,10,9,3,4,1,2]=>[6,6]=>6652800
[9,10,12,11,7,8,3,4,6,5,1,2]=>[6,6]=>6652800
[11,12,7,8,10,9,3,4,6,5,1,2]=>[2,2,2,2,2,2]=>10395
[3,8,9,12,11,6,10,4,7,5,1,2]=>[7,4,1]=>17107200
[3,10,12,6,7,11,9,4,8,5,1,2]=>[12]=>39916800
[3,6,9,12,7,11,10,4,8,5,1,2]=>[9,3]=>17740800
[11,12,9,10,3,4,5,8,7,6,1,2]=>[4,3,2,2,1]=>4989600
[9,10,12,11,3,4,5,8,7,6,1,2]=>[11,1]=>43545600
[3,10,12,8,11,4,5,9,7,6,1,2]=>[12]=>39916800
[3,8,9,12,11,4,5,10,7,6,1,2]=>[6,6]=>6652800
[3,4,7,8,12,11,5,10,9,6,1,2]=>[11,1]=>43545600
[3,4,5,8,12,6,11,10,9,7,1,2]=>[10,1,1]=>23950080
[3,4,5,6,7,12,11,10,9,8,1,2]=>[5,4,2,1]=>11975040
[9,10,12,11,7,8,5,6,1,2,4,3]=>[2,2,2,2,2,2]=>10395
[11,12,7,8,10,9,5,6,1,2,4,3]=>[6,6]=>6652800
[5,8,9,12,11,6,10,7,1,2,4,3]=>[7,4,1]=>17107200
[11,12,5,6,7,10,9,8,1,2,4,3]=>[11,1]=>43545600
[5,10,12,6,7,11,9,8,1,2,4,3]=>[4,3,2,2,1]=>4989600
[5,6,9,12,7,11,10,8,1,2,4,3]=>[11,1]=>43545600
[5,6,7,8,12,11,10,9,1,2,4,3]=>[12]=>39916800
[7,10,12,8,11,9,1,4,6,2,5,3]=>[2,2,2,2,2,2]=>10395
[11,12,1,6,7,10,9,4,8,2,5,3]=>[12]=>39916800
[11,12,9,10,1,4,5,8,7,2,6,3]=>[11,1]=>43545600
[9,10,12,11,1,4,5,8,7,2,6,3]=>[4,3,2,2,1]=>4989600
[11,12,1,8,10,4,5,9,7,2,6,3]=>[12]=>39916800
[1,4,7,8,12,11,5,10,9,2,6,3]=>[4,4,2,1,1]=>3742200
[1,4,5,6,7,12,11,10,9,2,8,3]=>[10,1,1]=>23950080
[11,12,9,10,7,8,1,2,3,6,5,4]=>[6,4,2]=>9979200
[7,8,9,12,11,10,1,2,3,6,5,4]=>[2,2,2,2,2,2]=>10395
[9,10,12,11,1,6,8,2,3,7,5,4]=>[7,4,1]=>17107200
[11,12,1,8,10,6,9,2,3,7,5,4]=>[7,4,1]=>17107200
[11,12,1,6,7,10,9,2,3,8,5,4]=>[6,6]=>6652800
[1,6,7,8,12,11,10,2,3,9,5,4]=>[7,4,1]=>17107200
[9,10,12,11,1,2,5,8,3,7,6,4]=>[11,1]=>43545600
[11,12,1,8,10,2,5,9,3,7,6,4]=>[9,3]=>17740800
[11,12,9,10,1,2,3,4,8,7,6,5]=>[6,6]=>6652800
[9,10,12,11,1,2,3,4,8,7,6,5]=>[12]=>39916800
[1,8,9,12,11,2,3,4,10,7,6,5]=>[7,4,1]=>17107200
[11,12,1,2,7,10,3,4,9,8,6,5]=>[11,1]=>43545600
[1,10,12,2,7,11,3,4,9,8,6,5]=>[4,4,2,1,1]=>3742200
[11,12,1,2,3,6,10,4,9,8,7,5]=>[10,1,1]=>23950080
[11,12,1,2,3,4,5,10,9,8,7,6]=>[5,4,2,1]=>11975040
[1,10,12,2,3,4,5,11,9,8,7,6]=>[10,1,1]=>23950080
[3,1,2,4,5,6,7,8,9]=>[3,1,1,1,1,1,1]=>168
[2,4,1,3,5,6,7,8,9]=>[4,1,1,1,1,1]=>756
[2,3,5,1,4,6,7,8,9]=>[5,1,1,1,1]=>3024
[2,3,4,6,1,5,7,8,9]=>[6,1,1,1]=>10080
[2,3,4,5,7,1,6,8,9]=>[7,1,1]=>25920
[2,3,4,5,6,8,1,7,9]=>[8,1]=>45360
[3,6,8,7,1,2,5,4]=>[6,2]=>3360
[6,5,7,2,4,8,1,3]=>[5,3]=>2688
[3,7,5,2,1,4,6,8]=>[4,3,1]=>3360
[5,2,8,4,7,3,1,6]=>[3,3,1,1]=>1120
[5,2,7,4,1,3,6,8]=>[3,2,1,1,1]=>1120
[3,1,4,6,2,8,7,5]=>[7,1]=>5760
[1,4,6,5,2,8,7,3]=>[3,3,1,1]=>1120
[3,4,5,6,1,8,7,2]=>[4,3,1]=>3360
[1,4,7,2,6,3,5,8]=>[4,2,1,1]=>2520
[8,1,4,7,2,3,6,5]=>[4,4]=>1260
[6,3,5,1,7,4,2,8]=>[4,3,1]=>3360
[5,4,7,6,3,8,1,2]=>[4,4]=>1260
[4,6,3,7,5,8,1,2]=>[3,3,1,1]=>1120
[4,1,3,5,8,6,2,7]=>[6,1,1]=>3360
[5,7,4,3,8,1,2,6]=>[4,2,2]=>1260
[4,3,8,2,1,6,5,7]=>[7,1]=>5760
[1,8,2,7,6,5,4,3]=>[3,2,2,1]=>1680
[3,8,1,6,7,5,4,2]=>[4,2,2]=>1260
[3,7,2,6,8,5,1,4]=>[4,4]=>1260
[7,2,3,8,5,6,1,4]=>[2,2,1,1,1,1]=>210
[8,2,4,3,6,1,5,7]=>[5,2,1]=>4032
[1,7,8,5,4,3,6,2]=>[5,2,1]=>4032
[1,8,4,5,3,2,6,7]=>[4,3,1]=>3360
[7,1,6,3,4,2,5,8]=>[7,1]=>5760
[8,1,7,6,2,4,3,5]=>[4,2,2]=>1260
[8,5,6,1,4,2,3,7]=>[8]=>5040
[1,6,4,5,7,2,3,8]=>[4,2,1,1]=>2520
[8,3,6,1,7,2,4,5]=>[5,3]=>2688
[7,4,1,6,5,8,3,2]=>[4,3,1]=>3360
[1,5,3,6,8,7,4,2]=>[3,3,1,1]=>1120
[3,5,4,6,1,8,2,7]=>[8]=>5040
[3,1,5,7,6,8,2,4]=>[8]=>5040
[1,4,6,3,7,2,8,5]=>[4,3,1]=>3360
[8,6,2,5,4,1,7,3]=>[5,2,1]=>4032
[3,7,2,6,5,4,1,8]=>[4,2,1,1]=>2520
[7,6,2,5,4,3,1,8]=>[3,2,2,1]=>1680
[3,2,6,4,7,5,1,8]=>[5,1,1,1]=>1344
[1,3,4,7,6,2,8,5]=>[7,1]=>5760
[8,7,2,5,1,6,4,3]=>[7,1]=>5760
[7,8,2,5,4,1,6,3]=>[3,3,2]=>1120
[8,1,3,6,2,7,5,4]=>[7,1]=>5760
[1,2,4,7,3,8,6,5]=>[6,1,1]=>3360
[3,1,8,6,2,7,5,4]=>[8]=>5040
[5,6,1,8,2,7,4,3]=>[8]=>5040
[4,2,7,8,1,6,5,3]=>[6,1,1]=>3360
[3,2,8,6,1,7,5,4]=>[7,1]=>5760
[7,2,8,1,6,5,4,3]=>[3,2,2,1]=>1680
[2,8,7,1,6,5,4,3]=>[6,2]=>3360
[3,8,7,1,6,5,4,2]=>[4,2,2]=>1260
[4,8,7,5,1,6,3,2]=>[3,2,2,1]=>1680
[6,7,8,5,1,4,3,2]=>[4,4]=>1260
[5,6,3,8,4,1,7,2]=>[6,1,1]=>3360
[7,3,8,5,4,1,6,2]=>[3,3,2]=>1120
[3,4,8,6,5,1,7,2]=>[6,1,1]=>3360
[1,4,6,2,3,8,7,5]=>[4,2,1,1]=>2520
[5,6,7,1,2,8,4,3]=>[8]=>5040
[4,7,5,1,2,8,6,3]=>[6,2]=>3360
[2,7,1,3,8,6,5,4]=>[7,1]=>5760
[5,6,8,1,2,7,4,3]=>[6,2]=>3360
[2,1,3,7,4,8,6,5]=>[5,2,1]=>4032
[5,3,6,4,2,8,1,7]=>[7,1]=>5760
[4,1,5,3,8,2,7,6]=>[7,1]=>5760
[5,2,6,4,7,3,1,8]=>[3,2,1,1,1]=>1120
[2,6,3,5,4,8,1,7]=>[5,2,1]=>4032
[7,6,4,5,2,8,1,3]=>[6,2]=>3360
[5,4,3,1,8,2,7,6]=>[6,1,1]=>3360
[5,4,1,8,3,2,6,7]=>[5,3]=>2688
[6,1,5,3,8,2,7,4]=>[4,3,1]=>3360
[5,8,4,2,7,3,1,6]=>[5,3]=>2688
[8,2,6,4,7,3,1,5]=>[4,2,1,1]=>2520
[8,6,1,7,4,5,2,3]=>[5,3]=>2688
[6,1,8,4,3,2,5,7]=>[4,3,1]=>3360
[1,7,8,4,3,5,6,2]=>[6,1,1]=>3360
[4,3,1,6,8,2,7,5]=>[5,2,1]=>4032
[5,8,3,2,6,4,1,7]=>[7,1]=>5760
[7,3,8,2,6,4,1,5]=>[6,2]=>3360
[3,8,7,4,5,6,1,2]=>[3,2,1,1,1]=>1120
[2,7,6,3,5,4,1,8]=>[3,3,1,1]=>1120
[1,8,6,5,3,2,4,7]=>[7,1]=>5760
[3,8,7,4,6,2,5,1]=>[7,1]=>5760
[5,8,3,7,6,2,4,1]=>[5,2,1]=>4032
[8,7,2,5,4,3,1,6]=>[6,2]=>3360
[6,8,3,2,5,4,7,1]=>[5,1,1,1]=>1344
[1,5,7,8,4,3,6,2]=>[4,3,1]=>3360
[6,3,8,1,5,4,7,2]=>[3,3,1,1]=>1120
[2,5,6,8,4,3,7,1]=>[5,2,1]=>4032
[2,5,4,7,1,8,6,3]=>[5,3]=>2688
[5,2,1,8,7,6,4,3]=>[6,1,1]=>3360
[4,8,6,7,5,3,1,2]=>[3,2,2,1]=>1680
[6,5,4,8,2,1,7,3]=>[3,2,2,1]=>1680
[5,8,4,7,2,6,3,1]=>[4,3,1]=>3360
[5,8,3,2,7,6,4,1]=>[6,1,1]=>3360
[5,2,1,4,3,6,7,8]=>[3,1,1,1,1,1]=>112
[3,5,7,4,2,6,1,8]=>[3,2,1,1,1]=>1120
[4,2,1,5,7,6,3,8]=>[5,1,1,1]=>1344
[3,5,4,7,1,6,2,8]=>[6,1,1]=>3360
[4,3,5,1,6,8,7,2]=>[5,2,1]=>4032
[4,3,2,1,7,6,5,9,8,10]=>[2,2,2,2,1,1]=>4725
[7,3,2,1,6,5,4,9,8,10]=>[3,2,2,2,1]=>25200
[4,3,2,1,9,6,5,8,7,10]=>[3,2,2,1,1,1]=>25200
[6,3,2,1,9,5,4,8,7,10]=>[6,2,1,1]=>151200
[9,3,2,1,8,5,4,7,6,10]=>[7,2,1]=>259200
[6,5,2,1,9,4,3,8,7,10]=>[5,3,1,1]=>120960
[9,5,2,1,8,4,3,7,6,10]=>[5,4,1]=>181440
[4,3,2,1,7,6,5,10,8,9]=>[3,2,2,2,1]=>25200
[7,3,2,1,6,5,4,10,8,9]=>[3,3,2,2]=>25200
[4,3,2,1,8,6,5,10,7,9]=>[5,2,2,1]=>90720
[6,3,2,1,8,5,4,10,7,9]=>[8,2]=>226800
[8,3,2,1,7,5,4,10,6,9]=>[8,2]=>226800
[6,5,2,1,8,4,3,10,7,9]=>[7,3]=>172800
[8,5,2,1,7,4,3,10,6,9]=>[6,4]=>151200
[4,3,2,1,10,6,5,9,7,8]=>[5,2,2,1]=>90720
[6,3,2,1,10,5,4,9,7,8]=>[8,2]=>226800
[7,3,2,1,10,5,4,9,6,8]=>[5,3,2]=>120960
[10,3,2,1,9,5,4,8,6,7]=>[4,3,2,1]=>151200
[6,5,2,1,10,4,3,9,7,8]=>[7,3]=>172800
[7,5,2,1,10,4,3,9,6,8]=>[10]=>362880
[10,5,2,1,9,4,3,8,6,7]=>[9,1]=>403200
[4,3,2,1,8,7,5,10,6,9]=>[6,2,2]=>75600
[5,3,2,1,8,7,4,10,6,9]=>[8,2]=>226800
[8,3,2,1,7,6,4,10,5,9]=>[7,2,1]=>259200
[5,4,2,1,8,7,3,10,6,9]=>[10]=>362880
[8,4,2,1,7,6,3,10,5,9]=>[9,1]=>403200
[4,3,2,1,10,7,5,9,6,8]=>[6,2,2]=>75600
[5,3,2,1,10,7,4,9,6,8]=>[8,2]=>226800
[7,3,2,1,10,6,4,9,5,8]=>[4,3,2,1]=>151200
[10,3,2,1,9,6,4,8,5,7]=>[4,2,2,1,1]=>56700
[5,4,2,1,10,7,3,9,6,8]=>[10]=>362880
[7,4,2,1,10,6,3,9,5,8]=>[5,4,1]=>181440
[10,4,2,1,9,6,3,8,5,7]=>[6,2,1,1]=>151200
[7,6,2,1,10,5,3,9,4,8]=>[10]=>362880
[10,6,2,1,9,5,3,8,4,7]=>[9,1]=>403200
[5,4,3,1,8,7,2,10,6,9]=>[9,1]=>403200
[8,4,3,1,7,6,2,10,5,9]=>[8,1,1]=>226800
[5,4,3,1,10,7,2,9,6,8]=>[9,1]=>403200
[7,4,3,1,10,6,2,9,5,8]=>[4,4,1,1]=>56700
[10,4,3,1,9,6,2,8,5,7]=>[5,2,1,1,1]=>60480
[7,6,3,1,10,5,2,9,4,8]=>[9,1]=>403200
[10,6,3,1,9,5,2,8,4,7]=>[8,1,1]=>226800
[4,3,1,2,6,5,8,7,10,9]=>[4,2,2,2]=>18900
[10,3,1,5,2,7,4,9,6,8]=>[10]=>362880
[10,9,4,1,6,2,8,3,5,7]=>[6,4]=>151200
[10,9,8,5,1,7,2,3,4,6]=>[8,2]=>226800
[7,6,5,4,3,2,9,1,8]=>[4,2,2,1]=>11340
[6,5,4,3,9,2,8,1,7]=>[7,2]=>25920
[6,5,4,3,2,8,1,7,9]=>[4,2,2,1]=>11340
[5,4,9,3,8,2,7,1,6]=>[5,3,1]=>24192
[5,4,3,8,2,7,1,6,9]=>[7,1,1]=>25920
[5,4,3,2,7,9,1,6,8]=>[3,3,2,1]=>10080
[5,4,3,2,7,1,6,8,9]=>[4,2,1,1,1]=>7560
[4,8,3,7,2,6,1,5,9]=>[3,3,1,1,1]=>3360
[4,3,7,2,6,9,1,5,8]=>[5,4]=>18144
[4,3,7,2,6,1,5,8,9]=>[7,1,1]=>25920
[4,3,2,6,8,1,5,7,9]=>[3,3,2,1]=>10080
[4,3,2,6,1,5,7,8,9]=>[4,2,1,1,1]=>7560
[3,6,9,2,5,8,1,4,7]=>[4,4,1]=>11340
[3,6,2,5,8,1,4,7,9]=>[4,4,1]=>11340
[3,6,2,5,1,4,7,8,9]=>[6,1,1,1]=>10080
[3,2,5,7,9,1,4,6,8]=>[6,2,1]=>30240
[3,2,5,7,1,4,6,8,9]=>[3,3,1,1,1]=>3360
[3,2,5,1,4,6,7,8,9]=>[4,1,1,1,1,1]=>756
[2,4,6,8,1,3,5,7,9]=>[6,2,1]=>30240
[2,4,6,1,3,5,7,8,9]=>[3,3,1,1,1]=>3360
[8,7,6,5,4,3,2,10,1,9]=>[4,2,2,2]=>18900
[7,6,5,4,3,10,2,9,1,8]=>[7,2,1]=>259200
[7,6,5,4,3,2,9,1,8,10]=>[4,2,2,1,1]=>56700
[6,5,4,10,3,9,2,8,1,7]=>[6,3,1]=>201600
[6,5,4,3,9,2,8,1,7,10]=>[7,2,1]=>259200
[6,5,4,3,2,8,10,1,7,9]=>[3,3,2,2]=>25200
[6,5,4,3,2,8,1,7,9,10]=>[4,2,2,1,1]=>56700
[5,10,4,9,3,8,2,7,1,6]=>[5,5]=>72576
[5,4,9,3,8,2,7,1,6,10]=>[5,3,1,1]=>120960
[5,4,3,8,2,7,10,1,6,9]=>[5,4,1]=>181440
[5,4,3,8,2,7,1,6,9,10]=>[7,1,1,1]=>86400
[5,4,3,2,7,9,1,6,8,10]=>[3,3,2,1,1]=>50400
[5,4,3,2,7,1,6,8,9,10]=>[4,2,1,1,1,1]=>18900
[4,8,3,7,2,6,10,1,5,9]=>[8,1,1]=>226800
[4,8,3,7,2,6,1,5,9,10]=>[3,3,1,1,1,1]=>8400
[4,3,7,10,2,6,9,1,5,8]=>[5,4,1]=>181440
[4,3,7,2,6,9,1,5,8,10]=>[5,4,1]=>181440
[4,3,7,2,6,1,5,8,9,10]=>[7,1,1,1]=>86400
[4,3,2,6,8,10,1,5,7,9]=>[6,2,2]=>75600
[4,3,2,6,8,1,5,7,9,10]=>[3,3,2,1,1]=>50400
[4,3,2,6,1,5,7,8,9,10]=>[4,2,1,1,1,1]=>18900
[3,6,9,2,5,8,1,4,7,10]=>[4,4,1,1]=>56700
[3,6,2,5,8,10,1,4,7,9]=>[7,3]=>172800
[3,6,2,5,8,1,4,7,9,10]=>[4,4,1,1]=>56700
[3,6,2,5,1,4,7,8,9,10]=>[6,1,1,1,1]=>25200
[3,2,5,7,9,1,4,6,8,10]=>[6,2,1,1]=>151200
[3,2,5,7,1,4,6,8,9,10]=>[3,3,1,1,1,1]=>8400
[3,2,5,1,4,6,7,8,9,10]=>[4,1,1,1,1,1,1]=>1260
[2,4,6,8,1,3,5,7,9,10]=>[6,2,1,1]=>151200
[2,4,6,1,3,5,7,8,9,10]=>[3,3,1,1,1,1]=>8400
[2,4,1,3,5,6,7,8,9,10]=>[4,1,1,1,1,1,1]=>1260
[2,1,7,3,8,4,6,5]=>[4,2,2]=>1260
[4,1,8,2,7,3,6,5]=>[5,3]=>2688
[4,1,7,2,8,3,6,5]=>[3,3,2]=>1120
[7,1,3,2,8,4,6,5]=>[5,2,1]=>4032
[7,1,8,2,4,3,6,5]=>[8]=>5040
[8,1,7,2,5,3,6,4]=>[4,3,1]=>3360
[7,1,5,2,8,3,6,4]=>[8]=>5040
[5,1,7,2,8,3,6,4]=>[5,3]=>2688
[5,1,8,2,7,3,6,4]=>[8]=>5040
[5,1,8,2,4,3,7,6]=>[4,3,1]=>3360
[8,1,6,2,4,3,7,5]=>[5,2,1]=>4032
[6,1,8,2,4,3,7,5]=>[7,1]=>5760
[6,1,8,2,5,3,7,4]=>[6,1,1]=>3360
[8,1,6,2,5,3,7,4]=>[4,2,1,1]=>2520
[8,1,6,2,7,3,5,4]=>[4,2,2]=>1260
[6,1,8,2,7,3,5,4]=>[6,2]=>3360
[6,1,7,2,8,3,5,4]=>[8]=>5040
[6,1,7,2,5,3,8,4]=>[7,1]=>5760
[6,1,7,2,4,3,8,5]=>[8]=>5040
[5,1,6,2,4,3,8,7]=>[4,2,2]=>1260
[7,1,5,2,4,3,8,6]=>[8]=>5040
[7,1,6,2,4,3,8,5]=>[6,2]=>3360
[7,1,6,2,5,3,8,4]=>[5,2,1]=>4032
[7,1,6,2,8,3,5,4]=>[6,2]=>3360
[7,1,8,2,6,3,5,4]=>[8]=>5040
[1,8,2,7,5,4,6,3]=>[3,3,1,1]=>1120
[1,8,2,7,4,3,5,6]=>[4,3,1]=>3360
[1,8,6,4,7,2,3,5]=>[6,1,1]=>3360
[1,8,4,2,6,3,5,7]=>[7,1]=>5760
[7,4,8,1,5,2,3,6]=>[7,1]=>5760
[4,1,7,2,6,3,5,8]=>[4,3,1]=>3360
[5,1,7,4,3,6,2,8]=>[5,1,1,1]=>1344
[7,5,8,3,2,4,1,6]=>[4,2,2]=>1260
[1,8,5,4,3,6,2,7]=>[3,2,1,1,1]=>1120
[1,8,5,4,3,7,2,6]=>[4,2,1,1]=>2520
[1,8,4,2,5,3,7,6]=>[5,1,1,1]=>1344
[1,8,5,4,2,6,7,3]=>[4,1,1,1,1]=>420
[7,4,8,2,1,3,5,6]=>[3,3,2]=>1120
[4,1,7,3,2,5,6,8]=>[7,1]=>5760
[7,5,4,8,2,3,6,1]=>[6,2]=>3360
[3,1,7,2,6,8,4,5]=>[5,3]=>2688
[5,1,7,4,2,6,8,3]=>[3,3,1,1]=>1120
[4,1,6,3,2,5,8,7]=>[6,2]=>3360
[4,3,1,6,2,5,7,8]=>[6,1,1]=>3360
[6,5,4,3,7,1,8,2]=>[4,2,2]=>1260
[6,5,1,7,3,8,2,4]=>[8]=>5040
[6,3,2,8,5,7,1,4]=>[3,2,2,1]=>1680
[6,5,4,3,8,2,7,1]=>[5,2,1]=>4032
[6,5,4,3,8,7,1,2]=>[3,3,2]=>1120
[7,6,3,8,5,4,1,2]=>[4,2,1,1]=>2520
[5,4,8,2,1,7,3,6]=>[4,2,2]=>1260
[6,4,2,8,5,1,3,7]=>[5,2,1]=>4032
[7,6,4,8,5,1,2,3]=>[4,3,1]=>3360
[7,2,8,6,3,1,4,5]=>[4,3,1]=>3360
[7,2,8,6,1,5,3,4]=>[7,1]=>5760
[2,1,7,8,3,6,4,5]=>[5,2,1]=>4032
[6,4,1,7,8,2,3,5]=>[6,2]=>3360
[4,2,1,6,7,3,5,8]=>[4,2,1,1]=>2520
[4,3,1,5,2,7,6,8]=>[5,2,1]=>4032
[5,4,2,7,3,8,1,6]=>[6,2]=>3360
[4,1,5,3,2,8,6,7]=>[5,3]=>2688
[3,1,6,2,8,7,4,5]=>[6,2]=>3360
[6,3,1,7,8,5,2,4]=>[8]=>5040
[6,5,4,1,7,8,3,2]=>[8]=>5040
[5,4,3,1,6,7,2,8]=>[6,1,1]=>3360
[6,5,4,2,7,8,3,1]=>[5,3]=>2688
[5,4,2,6,3,8,7,1]=>[7,1]=>5760
[4,3,1,5,2,6,8,7]=>[5,2,1]=>4032
[5,4,2,1,6,7,8,3]=>[8]=>5040
[5,4,3,1,6,7,8,2]=>[7,1]=>5760
[6,3,8,1,2,5,7,4]=>[7,1]=>5760
[3,6,7,1,2,5,8,4]=>[5,3]=>2688
[7,8,3,1,2,5,6,4]=>[7,1]=>5760
[7,8,1,3,2,4,6,5]=>[5,3]=>2688
[7,8,2,1,3,5,4,6]=>[5,3]=>2688
[5,2,3,7,1,8,6,4]=>[4,2,1,1]=>2520
[2,5,3,6,1,8,7,4]=>[3,3,1,1]=>1120
[2,6,7,3,1,8,4,5]=>[5,3]=>2688
[2,6,7,1,3,5,4,8]=>[7,1]=>5760
[6,2,8,3,1,7,4,5]=>[7,1]=>5760
[3,2,5,7,1,8,4,6]=>[3,2,2,1]=>1680
[4,3,1,2,7,8,6,5]=>[4,4]=>1260
[5,1,2,7,3,6,4,8]=>[4,2,1,1]=>2520
[5,1,4,7,8,2,3,6]=>[5,3]=>2688
[5,3,4,7,8,6,1,2]=>[7,1]=>5760
[3,5,4,6,8,7,1,2]=>[5,3]=>2688
[1,5,4,6,8,2,3,7]=>[7,1]=>5760
[1,6,7,3,2,4,8,5]=>[7,1]=>5760
[1,5,3,6,2,7,8,4]=>[4,2,1,1]=>2520
[5,1,3,7,2,6,8,4]=>[3,3,1,1]=>1120
[5,2,4,7,8,1,6,3]=>[7,1]=>5760
[4,2,5,7,6,1,8,3]=>[7,1]=>5760
[4,5,2,8,6,1,7,3]=>[7,1]=>5760
[5,3,1,8,2,6,7,4]=>[4,2,1,1]=>2520
[6,1,8,3,2,4,7,5]=>[7,1]=>5760
[4,3,5,7,6,8,1,2]=>[5,3]=>2688
[4,1,5,7,6,2,3,8]=>[7,1]=>5760
[4,5,1,8,6,2,3,7]=>[5,3]=>2688
[5,2,1,8,3,6,4,7]=>[3,3,1,1]=>1120
[3,4,2,1,8,7,5,6]=>[4,4]=>1260
[7,6,5,8,2,1,4,3]=>[8]=>5040
[8,5,4,3,2,1,7,6]=>[3,2,2,1]=>1680
[8,6,5,4,3,2,1,9,7]=>[4,2,2,1]=>11340
[7,6,5,4,3,2,1,9,8]=>[2,2,2,2,1]=>945
[7,6,5,4,1,8,3,2]=>[4,3,1]=>3360
[7,6,5,8,4,1,3,2]=>[8]=>5040
[7,6,8,5,2,1,4,3]=>[6,2]=>3360
[9,6,5,4,3,2,1,8,7]=>[3,2,2,1,1]=>7560
[9,7,6,5,4,3,2,1,10,8]=>[4,2,2,2]=>18900
[7,8,4,5,9,2,3,6,10,1]=>[7,3]=>172800
[7,8,2,4,5,1,3,6]=>[6,1,1]=>3360
[4,6,7,2,5,1,3,8]=>[4,2,1,1]=>2520
[7,8,1,3,2,4,5,6]=>[8]=>5040
[7,8,4,1,5,2,3,6]=>[4,3,1]=>3360
[3,6,7,2,1,4,5,8]=>[4,3,1]=>3360
[5,2,3,6,1,4,7,8]=>[2,2,1,1,1,1]=>210
[2,5,3,6,1,4,7,8]=>[3,2,1,1,1]=>1120
[2,6,7,3,1,4,5,8]=>[7,1]=>5760
[4,6,7,1,5,2,3,8]=>[2,2,2,1,1]=>420
[4,6,7,3,5,8,1,2]=>[4,3,1]=>3360
[6,4,7,1,5,2,3,8]=>[4,2,1,1]=>2520
[6,2,7,3,1,4,5,8]=>[6,1,1]=>3360
[3,2,5,6,1,4,7,8]=>[3,2,1,1,1]=>1120
[3,5,2,6,1,4,7,8]=>[4,2,1,1]=>2520
[5,1,4,6,7,2,3,8]=>[7,1]=>5760
[3,5,4,6,7,8,1,2]=>[8]=>5040
[1,5,4,6,7,2,3,8]=>[6,1,1]=>3360
[1,6,7,3,2,4,5,8]=>[6,1,1]=>3360
[1,5,3,6,2,4,7,8]=>[2,2,1,1,1,1]=>210
[5,1,3,6,2,4,7,8]=>[3,2,1,1,1]=>1120
[5,2,4,6,7,1,3,8]=>[6,1,1]=>3360
[2,5,4,6,7,1,3,8]=>[7,1]=>5760
[2,6,7,4,5,1,3,8]=>[3,2,1,1,1]=>1120
[6,2,7,4,5,1,3,8]=>[2,2,1,1,1,1]=>210
[4,2,5,6,7,1,3,8]=>[3,3,1,1]=>1120
[4,5,2,6,7,1,3,8]=>[4,3,1]=>3360
[5,3,1,6,2,4,7,8]=>[4,2,1,1]=>2520
[6,1,7,3,2,4,5,8]=>[7,1]=>5760
[6,1,7,4,5,2,3,8]=>[3,2,1,1,1]=>1120
[6,3,7,4,5,8,1,2]=>[6,1,1]=>3360
[5,4,1,6,7,2,3,8]=>[4,3,1]=>3360
[5,2,1,6,3,4,7,8]=>[3,2,1,1,1]=>1120
[7,3,2,5,4,1,6,8]=>[3,2,2,1]=>1680
[7,3,5,4,2,1,6,8]=>[3,3,1,1]=>1120
[7,3,5,2,4,1,6,8]=>[4,3,1]=>3360
[7,6,5,2,1,4,3,8]=>[4,3,1]=>3360
[1,3,6,7,5,2,8,4]=>[3,3,1,1]=>1120
[7,3,4,1,6,2,5,8]=>[7,1]=>5760
[7,3,4,1,6,5,2,8]=>[5,2,1]=>4032
[7,3,4,1,5,6,2,8]=>[5,1,1,1]=>1344
[7,3,2,5,1,6,4,8]=>[4,2,1,1]=>2520
[7,6,5,4,1,3,2,8]=>[6,1,1]=>3360
[7,3,4,1,5,2,6,8]=>[6,1,1]=>3360
[1,3,6,7,2,5,8,4]=>[4,3,1]=>3360
[1,7,4,6,2,8,5,3]=>[4,3,1]=>3360
[4,3,1,7,2,6,8,5]=>[7,1]=>5760
[5,6,1,4,7,3,8,2]=>[7,1]=>5760
[5,3,2,1,7,4,8,6]=>[6,2]=>3360
[1,3,4,5,8,7,2,6]=>[7,1]=>5760
[6,3,4,5,8,1,7,2]=>[5,2,1]=>4032
[2,4,5,1,6,8,7,3]=>[4,3,1]=>3360
[3,1,2,5,6,8,7,4]=>[4,3,1]=>3360
[4,3,2,5,6,8,1,7]=>[6,2]=>3360
[3,7,5,4,6,8,1,2]=>[7,1]=>5760
[3,1,4,6,5,8,2,7]=>[7,1]=>5760
[2,3,4,5,8,6,1,7]=>[7,1]=>5760
[2,3,4,5,8,1,7,6]=>[7,1]=>5760
[3,1,4,6,5,8,7,2]=>[6,1,1]=>3360
[3,7,5,4,6,8,2,1]=>[5,2,1]=>4032
[5,6,1,4,7,2,8,3]=>[5,2,1]=>4032
[4,3,1,7,5,6,8,2]=>[6,1,1]=>3360
[4,3,1,7,6,5,8,2]=>[6,2]=>3360
[3,1,4,6,7,8,5,2]=>[6,2]=>3360
[1,4,5,2,6,8,7,3]=>[4,2,1,1]=>2520
[3,7,5,2,6,8,1,4]=>[8]=>5040
[3,7,5,2,6,8,4,1]=>[5,3]=>2688
[5,6,1,2,7,4,8,3]=>[5,3]=>2688
[6,3,5,2,4,7,8,1]=>[4,4]=>1260
[5,3,2,1,4,7,8,6]=>[3,3,2]=>1120
[5,3,1,4,2,7,8,6]=>[4,3,1]=>3360
[5,3,1,2,4,7,8,6]=>[5,3]=>2688
[7,1,5,2,6,8,4,3]=>[4,4]=>1260
[7,1,5,2,6,8,3,4]=>[8]=>5040
[1,7,4,6,5,8,3,2]=>[6,1,1]=>3360
[2,7,4,6,1,8,3,5]=>[8]=>5040
[2,7,4,6,1,8,5,3]=>[4,4]=>1260
[2,3,6,7,1,5,8,4]=>[5,3]=>2688
[2,3,6,7,5,1,8,4]=>[4,3,1]=>3360
[4,3,2,6,7,1,8,5]=>[3,3,2]=>1120
[7,3,2,5,6,8,1,4]=>[4,2,2]=>1260
[7,1,5,4,6,8,2,3]=>[4,3,1]=>3360
[2,7,4,6,5,8,1,3]=>[4,3,1]=>3360
[7,3,4,5,8,6,1,2]=>[5,2,1]=>4032
[7,3,4,5,8,1,6,2]=>[5,3]=>2688
[7,3,4,5,8,1,2,6]=>[8]=>5040
[1,3,4,5,8,6,2,7]=>[6,1,1]=>3360
[1,3,4,5,8,2,7,6]=>[6,1,1]=>3360
[6,3,4,5,8,2,1,7]=>[8]=>5040
[6,3,4,5,8,2,7,1]=>[7,1]=>5760
[7,3,4,5,8,6,2,1]=>[7,1]=>5760
[2,7,4,6,5,8,3,1]=>[7,1]=>5760
[7,1,5,4,6,8,3,2]=>[7,1]=>5760
[7,3,2,5,6,8,4,1]=>[6,2]=>3360
[5,7,4,6,1,8,3,2]=>[6,2]=>3360
[6,3,4,5,8,1,2,7]=>[6,2]=>3360
[7,3,4,5,8,2,1,6]=>[6,2]=>3360
[7,3,4,5,8,2,6,1]=>[8]=>5040
[4,8,6,1,7,5,2,3]=>[6,2]=>3360
[4,7,8,2,6,1,5,3]=>[6,2]=>3360
[7,6,4,2,8,3,5,1]=>[4,4]=>1260
[8,6,4,2,7,5,3,1]=>[6,2]=>3360
[8,4,7,3,6,5,1,2]=>[6,2]=>3360
[8,4,6,1,7,5,3,2]=>[4,4]=>1260
[6,4,7,1,8,3,2,5]=>[6,2]=>3360
[7,4,8,3,6,1,5,2]=>[4,4]=>1260
[8,10,7,9,5,6,3,4,1,2]=>[4,2,2,1,1]=>56700
[9,10,6,8,5,7,3,4,1,2]=>[3,2,2,2,1]=>25200
[8,10,6,9,5,7,3,4,1,2]=>[4,3,2,1]=>151200
[7,10,6,9,5,8,3,4,1,2]=>[7,2,1]=>259200
[9,10,7,8,4,6,3,5,1,2]=>[3,2,2,2,1]=>25200
[8,10,7,9,4,6,3,5,1,2]=>[5,2,2,1]=>90720
[9,10,6,8,4,7,3,5,1,2]=>[3,3,2,2]=>25200
[8,10,6,9,4,7,3,5,1,2]=>[5,3,2]=>120960
[7,10,6,9,4,8,3,5,1,2]=>[8,2]=>226800
[9,10,5,8,4,7,3,6,1,2]=>[6,2,2]=>75600
[8,10,5,9,4,7,3,6,1,2]=>[8,2]=>226800
[7,10,5,9,4,8,3,6,1,2]=>[6,2,2]=>75600
[6,10,5,9,4,8,3,7,1,2]=>[8,2]=>226800
[9,10,7,8,5,6,2,4,1,3]=>[4,2,2,1,1]=>56700
[8,10,7,9,5,6,2,4,1,3]=>[4,4,1,1]=>56700
[9,10,6,8,5,7,2,4,1,3]=>[5,2,2,1]=>90720
[8,10,6,9,5,7,2,4,1,3]=>[5,4,1]=>181440
[7,10,6,9,5,8,2,4,1,3]=>[9,1]=>403200
[9,10,7,8,4,6,2,5,1,3]=>[4,3,2,1]=>151200
[8,10,7,9,4,6,2,5,1,3]=>[5,4,1]=>181440
[9,10,6,8,4,7,2,5,1,3]=>[5,3,2]=>120960
[8,10,6,9,4,7,2,5,1,3]=>[5,5]=>72576
[7,10,6,9,4,8,2,5,1,3]=>[10]=>362880
[9,10,5,8,4,7,2,6,1,3]=>[8,2]=>226800
[8,10,5,9,4,7,2,6,1,3]=>[10]=>362880
[7,10,5,9,4,8,2,6,1,3]=>[8,2]=>226800
[6,10,5,9,4,8,2,7,1,3]=>[10]=>362880
[9,10,7,8,3,6,2,5,1,4]=>[7,2,1]=>259200
[8,10,7,9,3,6,2,5,1,4]=>[9,1]=>403200
[9,10,6,8,3,7,2,5,1,4]=>[8,2]=>226800
[8,10,6,9,3,7,2,5,1,4]=>[10]=>362880
[7,10,6,9,3,8,2,5,1,4]=>[6,4]=>151200
[9,10,5,8,3,7,2,6,1,4]=>[6,2,2]=>75600
[8,10,5,9,3,7,2,6,1,4]=>[8,2]=>226800
[7,10,5,9,3,8,2,6,1,4]=>[6,2,2]=>75600
[6,10,5,9,3,8,2,7,1,4]=>[8,2]=>226800
[9,10,4,8,3,7,2,6,1,5]=>[8,2]=>226800
[8,10,4,9,3,7,2,6,1,5]=>[10]=>362880
[7,10,4,9,3,8,2,6,1,5]=>[8,2]=>226800
[6,10,4,9,3,8,2,7,1,5]=>[10]=>362880
[10,12,8,11,7,9,5,6,3,4,1,2]=>[4,4,2,2]=>1871100
[10,12,9,11,6,8,5,7,3,4,1,2]=>[4,4,2,2]=>1871100
[10,12,8,11,6,9,5,7,3,4,1,2]=>[6,4,2]=>9979200
[11,12,7,10,6,9,5,8,3,4,1,2]=>[5,2,2,2,1]=>1995840
[10,12,7,11,6,9,5,8,3,4,1,2]=>[5,4,2,1]=>11975040
[11,12,8,10,7,9,4,6,3,5,1,2]=>[4,4,2,2]=>1871100
[10,12,8,11,7,9,4,6,3,5,1,2]=>[6,4,2]=>9979200
[11,12,9,10,5,8,4,7,3,6,1,2]=>[5,2,2,2,1]=>1995840
[11,12,6,10,5,9,4,8,3,7,1,2]=>[3,3,2,2,1,1]=>1663200
[10,12,6,11,5,9,4,8,3,7,1,2]=>[5,3,2,1,1]=>7983360
[7,12,6,11,5,10,4,9,3,8,1,2]=>[5,4,2,1]=>11975040
[10,12,9,11,7,8,5,6,2,4,1,3]=>[4,4,2,2]=>1871100
[10,12,8,11,7,9,5,6,2,4,1,3]=>[6,4,2]=>9979200
[11,12,9,10,6,8,5,7,2,4,1,3]=>[4,4,2,2]=>1871100
[10,12,9,11,6,8,5,7,2,4,1,3]=>[4,4,4]=>1247400
[9,12,8,11,6,10,5,7,2,4,1,3]=>[12]=>39916800
[10,12,7,11,6,9,5,8,2,4,1,3]=>[7,4,1]=>17107200
[9,12,7,11,6,10,5,8,2,4,1,3]=>[11,1]=>43545600
[8,12,7,11,6,10,5,9,2,4,1,3]=>[12]=>39916800
[11,12,9,10,7,8,4,6,2,5,1,3]=>[4,4,2,2]=>1871100
[10,12,9,11,7,8,4,6,2,5,1,3]=>[6,4,2]=>9979200
[11,12,8,10,7,9,4,6,2,5,1,3]=>[6,4,2]=>9979200
[10,12,8,11,7,9,4,6,2,5,1,3]=>[6,6]=>6652800
[9,12,8,11,7,10,4,6,2,5,1,3]=>[12]=>39916800
[11,12,9,10,6,8,4,7,2,5,1,3]=>[6,4,2]=>9979200
[10,12,8,11,6,9,4,7,2,5,1,3]=>[12]=>39916800
[9,12,8,11,6,10,4,7,2,5,1,3]=>[9,3]=>17740800
[10,12,7,11,6,9,4,8,2,5,1,3]=>[11,1]=>43545600
[8,12,7,11,6,10,4,9,2,5,1,3]=>[9,3]=>17740800
[11,12,9,10,5,8,4,7,2,6,1,3]=>[5,4,2,1]=>11975040
[10,12,9,11,5,8,4,7,2,6,1,3]=>[7,4,1]=>17107200
[10,12,8,11,5,9,4,7,2,6,1,3]=>[11,1]=>43545600
[10,12,7,11,5,9,4,8,2,6,1,3]=>[10,1,1]=>23950080
[11,12,6,10,5,9,4,8,2,7,1,3]=>[5,3,2,1,1]=>7983360
[9,12,6,11,5,10,4,8,2,7,1,3]=>[10,1,1]=>23950080
[8,12,6,11,5,10,4,9,2,7,1,3]=>[11,1]=>43545600
[7,12,6,11,5,10,4,9,2,8,1,3]=>[7,4,1]=>17107200
[10,12,8,11,7,9,3,6,2,5,1,4]=>[12]=>39916800
[9,12,8,11,7,10,3,6,2,5,1,4]=>[6,6]=>6652800
[10,12,9,11,6,8,3,7,2,5,1,4]=>[12]=>39916800
[10,12,8,11,6,9,3,7,2,5,1,4]=>[9,3]=>17740800
[10,12,9,11,5,8,3,7,2,6,1,4]=>[11,1]=>43545600
[10,12,6,11,5,9,3,8,2,7,1,4]=>[10,1,1]=>23950080
[8,12,6,11,5,10,3,9,2,7,1,4]=>[7,4,1]=>17107200
[7,12,6,11,5,10,3,9,2,8,1,4]=>[11,1]=>43545600
[10,12,9,11,4,8,3,7,2,6,1,5]=>[12]=>39916800
[10,12,8,11,4,9,3,7,2,6,1,5]=>[9,3]=>17740800
[10,12,6,11,4,9,3,8,2,7,1,5]=>[11,1]=>43545600
[9,12,6,11,4,10,3,8,2,7,1,5]=>[7,4,1]=>17107200
[7,12,6,11,4,10,3,9,2,8,1,5]=>[12]=>39916800
[11,12,5,10,4,9,3,8,2,7,1,6]=>[5,4,2,1]=>11975040
[10,12,5,11,4,9,3,8,2,7,1,6]=>[7,4,1]=>17107200
[9,12,5,11,4,10,3,8,2,7,1,6]=>[11,1]=>43545600
[8,12,5,11,4,10,3,9,2,7,1,6]=>[12]=>39916800
[7,12,5,11,4,10,3,9,2,8,1,6]=>[6,6]=>6652800
[6,12,5,11,4,10,3,9,2,8,1,7]=>[12]=>39916800
[6,2,1,7,3,5,4,8]=>[4,2,1,1]=>2520
[2,1,8,6,3,5,4,7]=>[6,2]=>3360
[2,1,7,3,5,8,6,4]=>[5,2,1]=>4032
[2,7,3,1,5,4,6,8]=>[5,1,1,1]=>1344
[2,6,3,1,4,8,5,7]=>[7,1]=>5760
[4,2,1,8,3,6,7,5]=>[5,1,1,1]=>1344
[2,1,8,6,3,5,7,4]=>[5,2,1]=>4032
[6,2,1,7,3,5,8,4]=>[4,3,1]=>3360
[2,7,3,1,4,8,5,6]=>[5,2,1]=>4032
[3,2,1,6,4,5,7,8]=>[3,2,1,1,1]=>1120
[3,2,1,5,7,8,4,6]=>[3,2,2,1]=>1680
[2,1,7,3,6,8,4,5]=>[3,3,2]=>1120
[2,7,3,1,5,6,8,4]=>[5,1,1,1]=>1344
[2,4,7,5,1,6,8,3]=>[4,3,1]=>3360
[4,3,7,5,6,1,8,2]=>[4,4]=>1260
[4,3,6,8,5,1,7,2]=>[6,1,1]=>3360
[2,6,1,8,3,5,7,4]=>[5,2,1]=>4032
[2,1,6,8,3,7,4,5]=>[6,2]=>3360
[2,1,8,3,5,7,4,6]=>[5,2,1]=>4032
[3,2,1,5,6,8,4,7]=>[5,2,1]=>4032
[3,2,1,5,7,4,6,8]=>[4,2,1,1]=>2520
[2,1,7,3,6,4,5,8]=>[5,2,1]=>4032
[2,1,6,3,5,8,4,7]=>[5,2,1]=>4032
[8,2,4,1,7,5,6,3]=>[4,3,1]=>3360
[3,8,4,7,5,1,6,2]=>[5,2,1]=>4032
[8,4,3,6,1,7,5,2]=>[7,1]=>5760
[8,2,1,7,3,5,4,6]=>[5,2,1]=>4032
[2,6,1,8,3,5,4,7]=>[5,3]=>2688
[2,7,3,1,5,6,4,8]=>[4,1,1,1,1]=>420
[2,4,7,5,1,6,3,8]=>[4,2,1,1]=>2520
[8,2,4,1,7,5,3,6]=>[7,1]=>5760
[5,8,6,3,1,7,4,2]=>[4,2,2]=>1260
[2,4,7,1,8,5,3,6]=>[3,3,2]=>1120
[2,4,8,5,1,6,3,7]=>[4,3,1]=>3360
[6,2,1,7,3,4,8,5]=>[7,1]=>5760
[6,2,1,7,8,3,5,4]=>[4,3,1]=>3360
[2,7,1,8,3,5,6,4]=>[6,2]=>3360
[2,1,8,3,6,4,5,7]=>[6,2]=>3360
[3,2,1,6,7,4,5,8]=>[2,2,2,1,1]=>420
[3,2,1,7,4,5,6,8]=>[4,2,1,1]=>2520
[3,2,1,6,8,4,5,7]=>[3,2,2,1]=>1680
[2,1,8,3,7,4,5,6]=>[4,2,2]=>1260
[2,1,8,3,6,7,4,5]=>[6,2]=>3360
[2,4,8,5,1,6,7,3]=>[4,2,1,1]=>2520
[4,3,8,5,6,1,7,2]=>[4,3,1]=>3360
[3,2,1,8,4,5,6,7]=>[5,2,1]=>4032
[1,6,8,3,7,2,4,5]=>[5,2,1]=>4032
[3,8,1,5,7,2,4,6]=>[3,3,2]=>1120
[1,2,6,8,4,7,3,5]=>[3,3,1,1]=>1120
[6,1,5,8,2,4,7,3]=>[7,1]=>5760
[1,2,4,8,3,6,7,5]=>[4,1,1,1,1]=>420
[4,1,2,7,8,3,6,5]=>[6,2]=>3360
[3,5,7,4,8,6,1,2]=>[3,3,1,1]=>1120
[5,3,8,4,7,6,1,2]=>[3,3,1,1]=>1120
[8,7,1,2,5,4,6,3]=>[4,3,1]=>3360
[5,8,1,2,3,7,6,4]=>[3,3,2]=>1120
[1,2,8,4,3,5,7,6]=>[4,1,1,1,1]=>420
[1,2,5,3,7,6,4,8]=>[4,1,1,1,1]=>420
[6,1,2,8,7,4,5,3]=>[6,2]=>3360
[7,1,6,2,8,4,5,3]=>[8]=>5040
[1,2,6,3,8,5,4,7]=>[6,1,1]=>3360
[1,2,8,5,3,6,4,7]=>[5,1,1,1]=>1344
[1,2,7,3,8,5,4,6]=>[3,3,1,1]=>1120
[4,1,2,7,8,6,3,5]=>[5,2,1]=>4032
[1,6,2,8,4,3,5,7]=>[4,3,1]=>3360
[1,6,4,2,7,3,5,8]=>[4,2,1,1]=>2520
[1,8,6,3,2,4,5,7]=>[4,3,1]=>3360
[1,7,3,2,8,4,5,6]=>[6,1,1]=>3360
[3,1,7,8,6,2,4,5]=>[8]=>5040
[1,8,7,2,4,5,6,3]=>[7,1]=>5760
[1,8,7,3,5,6,2,4]=>[5,1,1,1]=>1344
[1,3,2,8,7,4,5,6]=>[3,2,2,1]=>1680
[1,8,3,2,6,4,5,7]=>[6,1,1]=>3360
[1,7,6,3,2,4,5,8]=>[3,3,1,1]=>1120
[1,2,8,4,3,7,5,6]=>[5,1,1,1]=>1344
[8,5,1,7,2,4,6,3]=>[3,3,2]=>1120
[5,3,8,7,4,6,1,2]=>[4,3,1]=>3360
[3,8,6,4,7,5,1,2]=>[5,2,1]=>4032
[6,1,8,2,7,4,5,3]=>[4,2,2]=>1260
[1,2,5,3,8,6,4,7]=>[5,1,1,1]=>1344
[1,2,7,5,3,6,4,8]=>[4,1,1,1,1]=>420
[1,2,6,3,7,5,4,8]=>[5,1,1,1]=>1344
[1,2,3,7,5,4,8,6]=>[4,1,1,1,1]=>420
[3,7,4,8,6,5,1,2]=>[6,2]=>3360
[1,8,2,7,6,4,5,3]=>[4,3,1]=>3360
[2,9,8,7,6,5,4,1,3]=>[5,2,2]=>9072
[2,8,7,6,5,1,4,3]=>[7,1]=>5760
[7,1,6,3,2,5,4,8]=>[7,1]=>5760
[2,7,6,3,1,5,8,4]=>[8]=>5040
[1,8,4,3,6,5,2,7]=>[3,2,2,1]=>1680
[1,8,4,6,5,3,2,7]=>[3,3,1,1]=>1120
[7,4,2,1,6,5,3,8]=>[5,2,1]=>4032
[7,6,1,4,3,5,2,8]=>[6,1,1]=>3360
[7,4,1,3,5,2,6,8]=>[6,1,1]=>3360
[7,3,1,2,4,6,5,8]=>[6,1,1]=>3360
[1,8,6,3,4,5,2,7]=>[4,3,1]=>3360
[1,8,6,7,4,2,5,3]=>[4,3,1]=>3360
[3,6,2,1,4,8,5,7]=>[8]=>5040
[3,1,7,2,4,6,8,5]=>[7,1]=>5760
[3,4,7,1,5,2,8,6]=>[7,1]=>5760
[3,6,7,4,1,5,8,2]=>[7,1]=>5760
[4,3,2,7,1,5,8,6]=>[6,2]=>3360
[3,1,2,8,6,5,4,7]=>[3,3,2]=>1120
[5,4,8,6,1,2,3,7]=>[3,3,2]=>1120
[5,6,8,7,4,3,1,2]=>[4,4]=>1260
[1,8,2,7,4,3,6,5]=>[7,1]=>5760
[6,5,8,2,3,7,1,4]=>[5,3]=>2688
[6,4,8,5,3,1,7,2]=>[5,2,1]=>4032
[5,7,8,6,1,3,2,4]=>[4,2,2]=>1260
[2,4,8,1,6,3,7,5]=>[4,3,1]=>3360
[3,1,2,8,6,4,7,5]=>[4,3,1]=>3360
[5,3,2,6,4,8,1,7]=>[6,2]=>3360
[4,1,6,3,5,8,2,7]=>[7,1]=>5760
[2,4,5,3,8,6,1,7]=>[7,1]=>5760
[1,8,5,3,2,7,6,4]=>[5,2,1]=>4032
[1,8,4,5,2,6,7,3]=>[5,1,1,1]=>1344
[4,1,2,7,6,5,8,3]=>[6,2]=>3360
[2,4,1,6,7,8,5,3]=>[6,2]=>3360
[1,8,4,3,6,2,7,5]=>[4,2,1,1]=>2520
[5,6,7,3,2,8,1,4]=>[8]=>5040
[2,5,7,3,6,8,4,1]=>[5,3]=>2688
[5,3,2,1,4,8,6,7]=>[3,3,2]=>1120
[5,3,1,4,2,8,6,7]=>[4,3,1]=>3360
[7,6,1,3,8,5,4,2]=>[4,4]=>1260
[3,4,7,8,1,2,6,5]=>[8]=>5040
[3,6,7,8,1,4,5,2]=>[4,4]=>1260
[3,6,2,8,1,5,4,7]=>[5,3]=>2688
[2,3,6,8,5,1,4,7]=>[4,3,1]=>3360
[3,1,6,4,8,2,5,7]=>[4,3,1]=>3360
[7,3,2,6,8,5,1,4]=>[4,2,2]=>1260
[7,3,5,8,4,6,1,2]=>[5,2,1]=>4032
[7,5,2,8,4,1,6,3]=>[5,3]=>2688
[7,4,5,8,2,1,3,6]=>[8]=>5040
[1,8,5,2,4,6,3,7]=>[6,1,1]=>3360
[1,8,4,2,3,5,7,6]=>[6,1,1]=>3360
[6,4,2,8,3,5,1,7]=>[8]=>5040
[6,3,4,8,2,5,7,1]=>[7,1]=>5760
[7,5,4,8,3,6,2,1]=>[7,1]=>5760
[2,7,4,8,5,3,6,1]=>[7,1]=>5760
[7,1,5,4,8,3,6,2]=>[7,1]=>5760
[7,3,2,5,8,4,6,1]=>[6,2]=>3360
[8,4,6,3,7,2,5,1]=>[4,2,2]=>1260
[7,4,6,3,8,5,1,2]=>[6,2]=>3360
[2,5,6,8,3,4,1,7]=>[8]=>5040
[8,4,6,2,7,5,3,1]=>[4,2,2]=>1260
[2,5,7,8,4,1,3,6]=>[6,2]=>3360
[3,5,6,8,4,2,1,7]=>[8]=>5040
[3,6,7,8,1,4,2,5]=>[8]=>5040
[6,5,7,8,3,1,4,2]=>[6,2]=>3360
[2,5,7,8,3,1,4,6]=>[8]=>5040
[6,4,7,3,8,1,5,2]=>[6,2]=>3360
[7,4,6,3,8,2,1,5]=>[4,2,2]=>1260
[6,3,2,5,4,8,1,7]=>[4,2,2]=>1260
[6,4,5,2,3,8,1,7]=>[4,2,2]=>1260
[6,4,5,3,2,8,1,7]=>[4,4]=>1260
[5,4,6,3,8,2,1,7]=>[4,4]=>1260
[5,4,7,3,8,1,6,2]=>[8]=>5040
[2,5,7,8,3,1,6,4]=>[6,2]=>3360
[4,5,6,8,2,3,1,7]=>[4,2,2]=>1260
[5,4,6,2,8,3,1,7]=>[4,2,2]=>1260
[4,6,7,8,1,3,2,5]=>[4,4]=>1260
[4,6,7,8,1,3,5,2]=>[8]=>5040
[4,6,7,8,1,5,2,3]=>[8]=>5040
[4,6,7,8,1,2,5,3]=>[6,2]=>3360
[4,5,7,8,2,1,6,3]=>[6,2]=>3360
[5,4,7,2,8,1,6,3]=>[6,2]=>3360
[4,3,2,7,8,1,6,5]=>[4,2,2]=>1260
[3,6,7,8,1,2,5,4]=>[4,2,2]=>1260
[3,6,7,8,1,5,2,4]=>[6,2]=>3360
[3,6,7,8,1,5,4,2]=>[8]=>5040
[2,6,7,8,1,5,4,3]=>[4,4]=>1260
[2,3,4,5,6,7,8,9,10,1,11]=>[10,1]=>3991680
[3,4,5,6,7,8,9,1,2,10]=>[9,1]=>403200
[2,4,5,6,7,8,1,3,9]=>[8,1]=>45360
[1,4,5,6,7,8,2,9,3]=>[8,1]=>45360
[1,4,5,6,7,8,9,10,2,3]=>[9,1]=>403200
[1,3,4,5,6,7,8,9,10,11,2]=>[10,1]=>3991680
[4,2,7,1,5,3,8,6]=>[4,2,1,1]=>2520
[4,2,8,6,1,5,3,7]=>[4,3,1]=>3360
[3,2,6,7,5,1,4,8]=>[3,2,1,1,1]=>1120
[2,7,1,3,5,4,8,6]=>[7,1]=>5760
[4,7,2,1,5,8,6,3]=>[5,2,1]=>4032
[7,2,1,3,5,8,6,4]=>[6,1,1]=>3360
[2,3,6,4,7,1,5,8]=>[4,2,1,1]=>2520
[1,3,4,8,2,7,5,6]=>[7,1]=>5760
[3,1,4,8,2,6,7,5]=>[6,1,1]=>3360
[8,3,1,6,2,5,7,4]=>[7,1]=>5760
[4,8,6,2,1,5,7,3]=>[7,1]=>5760
[4,8,3,6,5,1,7,2]=>[3,2,1,1,1]=>1120
[6,4,7,3,5,1,8,2]=>[5,2,1]=>4032
[6,4,7,5,1,8,2,3]=>[8]=>5040
[3,6,1,7,5,8,2,4]=>[5,2,1]=>4032
[7,3,5,1,6,8,2,4]=>[8]=>5040
[4,7,3,5,6,1,8,2]=>[4,3,1]=>3360
[3,4,6,8,5,1,7,2]=>[3,3,1,1]=>1120
[4,6,8,2,1,5,7,3]=>[5,2,1]=>4032
[6,8,2,1,3,5,7,4]=>[7,1]=>5760
[1,8,2,3,5,7,4,6]=>[6,1,1]=>3360
[2,7,3,6,1,4,5,8]=>[4,2,1,1]=>2520
[2,6,1,3,5,8,4,7]=>[7,1]=>5760
[7,3,2,5,6,1,4,8]=>[5,2,1]=>4032
[4,7,5,2,6,1,3,8]=>[7,1]=>5760
[4,6,2,8,1,5,3,7]=>[8]=>5040
[8,4,1,2,7,5,3,6]=>[6,2]=>3360
[4,5,6,2,7,1,3,8]=>[7,1]=>5760
[8,5,1,2,6,3,4,7]=>[8]=>5040
[1,6,2,7,4,8,3,5]=>[7,1]=>5760
[6,2,1,7,8,5,3,4]=>[7,1]=>5760
[6,7,3,8,4,1,5,2]=>[5,2,1]=>4032
[2,7,8,4,1,5,6,3]=>[5,2,1]=>4032
[2,7,1,8,5,6,3,4]=>[4,2,1,1]=>2520
[8,2,5,1,6,7,3,4]=>[4,3,1]=>3360
[8,2,4,5,1,6,7,3]=>[5,1,1,1]=>1344
[3,8,4,5,6,1,7,2]=>[5,2,1]=>4032
[4,5,8,3,6,7,1,2]=>[8]=>5040
[4,5,8,3,7,6,1,2]=>[7,1]=>5760
[4,2,8,3,7,1,6,5]=>[7,1]=>5760
[7,2,3,4,8,1,6,5]=>[3,2,1,1,1]=>1120
[7,2,3,8,5,1,4,6]=>[5,1,1,1]=>1344
[7,2,3,8,5,1,6,4]=>[3,2,1,1,1]=>1120
[7,2,3,5,8,1,4,6]=>[6,1,1]=>3360
[7,8,2,3,6,1,4,5]=>[8]=>5040
[2,6,4,8,1,3,7,5]=>[7,1]=>5760
[7,6,5,1,2,3,8,4]=>[4,4]=>1260
[7,8,5,4,1,2,6,3]=>[7,1]=>5760
[7,6,5,1,2,4,8,3]=>[8]=>5040
[7,6,5,1,3,2,8,4]=>[4,2,2]=>1260
[7,2,3,4,5,1,8,6]=>[4,1,1,1,1]=>420
[2,6,4,3,1,5,8,7]=>[4,2,2]=>1260
[3,5,8,4,1,2,7,6]=>[6,1,1]=>3360
[4,2,8,3,6,1,7,5]=>[6,1,1]=>3360
[3,5,8,4,1,6,7,2]=>[5,1,1,1]=>1344
[2,5,8,4,1,7,3,6]=>[4,3,1]=>3360
[3,6,4,2,1,7,8,5]=>[8]=>5040
[7,6,5,1,8,3,2,4]=>[8]=>5040
[7,6,5,1,4,8,2,3]=>[8]=>5040
[3,6,4,5,1,7,2,8]=>[4,3,1]=>3360
[2,5,6,4,1,7,8,3]=>[4,3,1]=>3360
[7,8,5,4,1,6,3,2]=>[4,2,1,1]=>2520
[2,5,6,4,1,7,3,8]=>[3,3,1,1]=>1120
[7,6,5,1,8,3,4,2]=>[5,3]=>2688
[7,6,5,1,8,4,2,3]=>[5,3]=>2688
[4,1,7,6,2,8,5,3]=>[8]=>5040
[7,8,6,2,1,3,5,4]=>[3,3,2]=>1120
[3,7,6,1,2,8,4,5]=>[8]=>5040
[2,6,5,3,1,4,8,7]=>[6,2]=>3360
[4,6,1,5,3,2,8,7]=>[4,2,2]=>1260
[3,6,1,4,2,5,8,7]=>[3,2,2,1]=>1680
[2,6,4,5,7,8,1,3]=>[8]=>5040
[8,7,1,6,5,2,4,3]=>[4,3,1]=>3360
[7,2,5,6,8,1,3,4]=>[7,1]=>5760
[6,1,3,4,2,8,7,5]=>[5,1,1,1]=>1344
[2,4,5,6,1,8,7,3]=>[7,1]=>5760
[8,4,1,6,5,7,3,2]=>[7,1]=>5760
[2,8,3,4,7,5,1,6]=>[6,1,1]=>3360
[6,8,2,7,4,3,5,1]=>[5,3]=>2688
[4,7,8,5,1,6,3,2]=>[4,3,1]=>3360
[8,2,6,4,7,3,5,1]=>[2,2,2,1,1]=>420
[4,8,6,1,7,3,2,5]=>[4,2,2]=>1260
[8,7,3,2,1,5,4,6]=>[4,3,1]=>3360
[3,8,5,1,7,2,4,6]=>[5,3]=>2688
[6,8,7,1,3,2,4,5]=>[8]=>5040
[2,5,1,8,7,4,6,3]=>[8]=>5040
[3,7,1,8,4,5,6,2]=>[6,2]=>3360
[6,2,3,8,4,7,5,1]=>[6,1,1]=>3360
[8,6,4,3,1,7,2,5]=>[3,3,2]=>1120
[8,3,7,4,6,1,2,5]=>[4,3,1]=>3360
[7,1,3,8,6,4,5,2]=>[7,1]=>5760
[2,3,5,8,6,7,4,1]=>[8]=>5040
[7,4,2,1,8,6,5,3]=>[7,1]=>5760
[4,6,7,2,5,8,3,1]=>[5,2,1]=>4032
[7,6,2,5,3,8,1,4]=>[6,2]=>3360
[6,2,1,3,4,8,7,5]=>[6,1,1]=>3360
[6,5,4,2,8,3,1,7]=>[8]=>5040
[5,4,3,1,8,7,2,6]=>[7,1]=>5760
[6,1,4,3,8,5,2,7]=>[6,2]=>3360
[4,7,6,2,8,1,5,3]=>[8]=>5040
[6,4,5,1,7,8,3,2]=>[5,3]=>2688
[4,2,3,1,7,8,6,5]=>[4,2,1,1]=>2520
[3,4,2,1,8,6,7,5]=>[4,2,1,1]=>2520
[2,7,6,8,1,5,3,4]=>[6,2]=>3360
[6,4,5,8,3,1,2,7]=>[4,2,2]=>1260
[8,1,3,2,5,6,7,4]=>[4,1,1,1,1]=>420
[3,6,8,1,5,2,4,7]=>[5,2,1]=>4032
[3,2,8,7,4,5,1,6]=>[7,1]=>5760
[6,3,8,5,7,4,2,1]=>[8]=>5040
[7,4,6,8,5,1,2,3]=>[7,1]=>5760
[2,1,4,8,7,5,3,6]=>[6,2]=>3360
[2,1,6,8,3,7,5,4]=>[4,2,2]=>1260
[3,6,8,2,4,1,5,7]=>[8]=>5040
[6,2,8,1,7,5,4,3]=>[5,2,1]=>4032
[2,6,5,4,8,1,3,7]=>[4,3,1]=>3360
[6,5,3,4,8,1,7,2]=>[3,2,1,1,1]=>1120
[8,4,3,2,5,1,7,6]=>[3,2,1,1,1]=>1120
[4,2,8,1,5,3,6,7]=>[4,2,1,1]=>2520
[5,1,8,2,6,4,3,7]=>[5,3]=>2688
[7,4,8,6,2,1,3,5]=>[8]=>5040
[4,6,2,8,3,7,5,1]=>[5,3]=>2688
[2,1,5,8,3,6,4,7]=>[3,2,2,1]=>1680
[2,8,5,3,6,7,1,4]=>[8]=>5040
[7,8,5,6,4,1,3,2]=>[6,2]=>3360
[5,8,4,1,6,3,7,2]=>[5,2,1]=>4032
[4,8,1,3,5,7,6,2]=>[3,2,2,1]=>1680
[3,8,1,4,5,6,2,7]=>[3,2,1,1,1]=>1120
[9,7,8,5,6,3,1,4,2]=>[5,4]=>18144
[9,7,8,5,3,6,1,4,2]=>[4,4,1]=>11340
[9,7,5,8,3,6,1,4,2]=>[4,2,2,1]=>11340
[7,9,5,8,3,6,1,4,2]=>[2,2,2,2,1]=>945
[7,6,8,3,5,1,4,2]=>[7,1]=>5760
[8,9,5,7,3,6,1,4,2]=>[4,2,2,1]=>11340
[8,9,6,7,3,5,1,4,2]=>[4,3,2]=>15120
[8,9,6,7,4,5,1,3,2]=>[7,2]=>25920
[8,9,6,7,4,5,2,3,1]=>[9]=>40320
[9,10,7,8,5,6,3,1,4,2]=>[4,2,2,1,1]=>56700
[9,7,8,5,3,1,6,4,2]=>[5,4]=>18144
[9,10,7,8,5,3,6,1,4,2]=>[4,3,2,1]=>151200
[9,7,5,3,8,6,1,4,2]=>[4,4,1]=>11340
[9,10,7,5,8,3,6,1,4,2]=>[5,3,2]=>120960
[7,5,9,8,3,6,1,4,2]=>[4,2,2,1]=>11340
[9,7,10,5,8,3,6,1,4,2]=>[5,5]=>72576
[7,8,6,3,5,1,4,2]=>[5,2,1]=>4032
[5,3,8,7,6,1,4,2]=>[3,3,2]=>1120
[9,8,5,7,3,6,1,4,2]=>[6,2,1]=>30240
[10,7,9,5,8,3,6,1,4,2]=>[10]=>362880
[7,9,6,8,3,5,1,4,2]=>[3,2,2,2]=>2520
[10,8,9,5,7,3,6,1,4,2]=>[6,4]=>151200
[6,5,8,4,7,1,3,2]=>[5,2,1]=>4032
[8,9,5,7,4,6,1,3,2]=>[6,2,1]=>30240
[10,8,9,6,7,3,5,1,4,2]=>[4,4,2]=>56700
[8,9,6,7,3,5,2,4,1]=>[6,3]=>20160
[10,8,9,6,7,4,5,1,3,2]=>[4,2,2,2]=>18900
[6,7,4,2,5,3,1,8]=>[6,1,1]=>3360
[7,6,4,8,3,1,5,2]=>[8]=>5040
[7,4,8,5,6,1,3,2]=>[8]=>5040
[7,4,2,5,6,3,1,8]=>[5,2,1]=>4032
[4,2,7,5,6,3,1,8]=>[6,1,1]=>3360
[3,4,7,5,6,2,1,8]=>[4,3,1]=>3360
[4,7,3,5,6,2,1,8]=>[6,1,1]=>3360
[3,7,2,5,6,4,1,8]=>[4,3,1]=>3360
[7,8,3,5,6,1,4,2]=>[5,2,1]=>4032
[1,6,8,5,2,7,4,3]=>[5,2,1]=>4032
[6,2,8,5,1,7,4,3]=>[5,2,1]=>4032
[6,7,4,8,2,1,5,3]=>[3,3,2]=>1120
[3,2,7,8,6,1,5,4]=>[5,2,1]=>4032
[6,8,4,1,2,3,7,5]=>[4,3,1]=>3360
[4,1,8,5,6,3,2,7]=>[8]=>5040
[1,8,2,5,6,4,3,7]=>[4,3,1]=>3360
[6,1,8,5,3,7,4,2]=>[8]=>5040
[3,8,1,5,2,7,6,4]=>[4,2,2]=>1260
[8,2,1,5,3,7,6,4]=>[5,2,1]=>4032
[1,5,2,4,6,7,8,3]=>[6,1,1]=>3360
[4,1,5,3,6,7,8,2]=>[8]=>5040
[8,1,6,5,3,7,2,4]=>[8]=>5040
[7,1,4,6,3,2,8,5]=>[8]=>5040
[3,2,6,4,1,7,8,5]=>[6,1,1]=>3360
[7,6,4,3,1,2,8,5]=>[4,2,2]=>1260
[8,6,3,5,1,7,2,4]=>[4,3,1]=>3360
[4,5,3,1,6,7,8,2]=>[5,2,1]=>4032
[3,5,2,1,6,7,8,4]=>[8]=>5040
[5,2,3,1,6,7,8,4]=>[6,1,1]=>3360
[1,5,3,2,6,7,8,4]=>[6,1,1]=>3360
[8,4,6,5,1,7,2,3]=>[8]=>5040
[7,5,4,6,1,2,8,3]=>[8]=>5040
[3,2,5,6,1,7,8,4]=>[4,3,1]=>3360
[3,2,8,7,6,1,4,5]=>[5,2,1]=>4032
[6,8,4,7,2,1,3,5]=>[3,3,2]=>1120
[3,8,7,5,6,1,2,4]=>[8]=>5040
[8,2,7,5,6,1,3,4]=>[5,2,1]=>4032
[4,8,6,5,1,7,3,2]=>[3,3,2]=>1120
[1,7,4,6,2,3,8,5]=>[4,3,1]=>3360
[7,6,4,2,1,5,8,3]=>[8]=>5040
[5,7,4,6,1,3,8,2]=>[3,3,2]=>1120
[8,6,4,7,3,1,2,5]=>[8]=>5040
[5,2,4,3,7,1,8,6]=>[5,2,1]=>4032
[3,5,4,2,7,1,8,6]=>[8]=>5040
[8,6,4,1,3,5,2,7]=>[8]=>5040
[6,7,4,1,5,3,8,2]=>[4,3,1]=>3360
[7,5,4,1,2,6,8,3]=>[5,2,1]=>4032
[1,7,4,2,3,6,8,5]=>[6,1,1]=>3360
[1,8,2,5,3,7,6,4]=>[5,2,1]=>4032
[6,8,1,5,4,7,3,2]=>[4,2,2]=>1260
[8,2,1,5,6,4,3,7]=>[4,3,1]=>3360
[3,8,1,5,6,4,2,7]=>[3,3,2]=>1120
[6,8,4,1,2,5,3,7]=>[8]=>5040
[3,2,8,1,6,5,4,7]=>[5,2,1]=>4032
[3,2,6,1,5,7,8,4]=>[6,1,1]=>3360
[7,6,4,1,5,2,8,3]=>[5,2,1]=>4032
[8,6,1,5,4,7,2,3]=>[3,3,2]=>1120
[3,5,1,4,6,7,8,2]=>[5,2,1]=>4032
[5,2,1,4,6,7,8,3]=>[6,1,1]=>3360
[5,4,1,3,6,7,8,2]=>[8]=>5040
[8,4,1,5,3,7,2,6]=>[8]=>5040
[7,5,4,1,3,2,8,6]=>[8]=>5040
[3,2,5,1,4,7,8,6]=>[4,3,1]=>3360
[7,1,4,3,5,2,8,6]=>[5,2,1]=>4032
[8,1,3,5,4,7,2,6]=>[5,2,1]=>4032
[5,1,3,4,6,7,8,2]=>[6,1,1]=>3360
[8,3,2,6,1,4,7,5]=>[3,2,2,1]=>1680
[2,6,1,3,8,7,5,4]=>[8]=>5040
[2,6,8,1,5,7,4,3]=>[5,2,1]=>4032
[2,7,1,6,4,8,3,5]=>[4,4]=>1260
[2,7,1,6,5,3,8,4]=>[7,1]=>5760
[2,8,1,7,6,5,4,3]=>[4,2,2]=>1260
[8,3,2,7,1,6,5,4]=>[5,2,1]=>4032
[3,7,1,8,6,5,4,2]=>[4,2,2]=>1260
[3,6,8,5,1,4,7,2]=>[7,1]=>5760
[7,3,5,8,2,1,4,6]=>[5,3]=>2688
[7,3,6,2,1,4,5,8]=>[4,3,1]=>3360
[7,3,6,2,1,5,4,8]=>[7,1]=>5760
[7,4,2,8,1,6,5,3]=>[4,3,1]=>3360
[8,7,5,3,2,1,6,4]=>[8]=>5040
[7,5,2,6,3,1,4,8]=>[4,3,1]=>3360
[6,8,4,5,2,1,7,3]=>[5,2,1]=>4032
[4,6,8,5,1,7,3,2]=>[5,3]=>2688
[4,7,5,1,3,8,6,2]=>[4,2,2]=>1260
[5,1,7,6,3,8,2,4]=>[5,3]=>2688
[5,1,7,6,4,2,8,3]=>[5,3]=>2688
[5,1,8,7,6,4,3,2]=>[8]=>5040
[8,5,2,1,7,6,4,3]=>[7,1]=>5760
[8,5,2,1,6,3,7,4]=>[4,3,1]=>3360
[5,1,8,6,3,2,7,4]=>[7,1]=>5760
[8,4,2,5,7,3,1,6]=>[8]=>5040
[3,4,6,8,5,7,1,2]=>[4,3,1]=>3360
[5,4,8,2,7,3,6,1]=>[6,2]=>3360
[5,4,8,7,3,6,1,2]=>[7,1]=>5760
[8,5,4,7,3,6,2,1]=>[5,2,1]=>4032
[6,3,7,2,4,8,1,5]=>[8]=>5040
[5,7,4,2,8,1,3,6]=>[4,4]=>1260
[6,5,2,7,1,3,8,4]=>[5,3]=>2688
[8,6,5,4,2,1,7,3]=>[6,1,1]=>3360
[6,4,7,3,1,8,2,5]=>[4,4]=>1260
[7,5,8,4,6,3,2,1]=>[7,1]=>5760
[7,6,5,3,8,2,4,1]=>[6,2]=>3360
[6,5,4,3,2,1,9,8,7]=>[2,2,2,2,1]=>945
[6,5,4,3,2,1,8,7,9]=>[2,2,2,2,1]=>945
[5,4,3,2,1,9,8,7,6]=>[2,2,2,2,1]=>945
[5,4,3,2,1,8,7,6,9]=>[2,2,2,1,1,1]=>1260
[5,4,3,2,1,7,6,9,8]=>[2,2,2,2,1]=>945
[5,4,3,2,1,7,6,8,9]=>[2,2,2,1,1,1]=>1260
[4,3,2,1,8,7,6,5,9]=>[2,2,2,2,1]=>945
[4,3,2,1,7,6,5,9,8]=>[2,2,2,2,1]=>945
[4,3,2,1,7,6,5,8,9]=>[2,2,2,1,1,1]=>1260
[4,3,2,1,6,5,8,7,9]=>[2,2,2,2,1]=>945
[4,3,2,1,6,5,7,8,9]=>[2,2,2,1,1,1]=>1260
[3,2,1,6,5,4,8,7,9]=>[2,2,2,1,1,1]=>1260
[3,2,1,6,5,4,7,8,9]=>[2,2,1,1,1,1,1]=>378
[3,2,1,5,4,7,6,9,8]=>[2,2,2,2,1]=>945
[3,2,1,5,4,7,6,8,9]=>[2,2,2,1,1,1]=>1260
[3,2,1,5,4,6,7,8,9]=>[2,2,1,1,1,1,1]=>378
[2,1,4,3,6,5,7,8,9]=>[2,2,2,1,1,1]=>1260
[2,1,4,3,5,6,7,8,9]=>[2,2,1,1,1,1,1]=>378
[7,6,5,4,3,2,1,10,9,8]=>[2,2,2,2,1,1]=>4725
[7,6,5,4,3,2,1,9,8,10]=>[2,2,2,2,1,1]=>4725
[6,5,4,3,2,1,9,8,7,10]=>[2,2,2,2,1,1]=>4725
[6,5,4,3,2,1,8,7,9,10]=>[2,2,2,2,1,1]=>4725
[5,4,3,2,1,9,8,7,6,10]=>[2,2,2,2,1,1]=>4725
[5,4,3,2,1,8,7,6,10,9]=>[2,2,2,2,1,1]=>4725
[5,4,3,2,1,8,7,6,9,10]=>[2,2,2,1,1,1,1]=>3150
[5,4,3,2,1,7,6,9,8,10]=>[2,2,2,2,1,1]=>4725
[5,4,3,2,1,7,6,8,9,10]=>[2,2,2,1,1,1,1]=>3150
[4,3,2,1,8,7,6,5,9,10]=>[2,2,2,2,1,1]=>4725
[4,3,2,1,7,6,5,10,9,8]=>[2,2,2,2,1,1]=>4725
[4,3,2,1,7,6,5,8,9,10]=>[2,2,2,1,1,1,1]=>3150
[4,3,2,1,6,5,8,7,9,10]=>[2,2,2,2,1,1]=>4725
[4,3,2,1,6,5,7,8,9,10]=>[2,2,2,1,1,1,1]=>3150
[3,2,1,6,5,4,9,8,7,10]=>[2,2,2,1,1,1,1]=>3150
[3,2,1,6,5,4,8,7,10,9]=>[2,2,2,2,1,1]=>4725
[3,2,1,6,5,4,8,7,9,10]=>[2,2,2,1,1,1,1]=>3150
[3,2,1,6,5,4,7,8,9,10]=>[2,2,1,1,1,1,1,1]=>630
[3,2,1,5,4,7,6,9,8,10]=>[2,2,2,2,1,1]=>4725
[3,2,1,5,4,7,6,8,9,10]=>[2,2,2,1,1,1,1]=>3150
[3,2,1,5,4,6,7,8,9,10]=>[2,2,1,1,1,1,1,1]=>630
[2,1,4,3,6,5,8,7,9,10]=>[2,2,2,2,1,1]=>4725
[2,1,4,3,6,5,7,8,9,10]=>[2,2,2,1,1,1,1]=>3150
[2,1,4,3,5,6,7,8,9,10]=>[2,2,1,1,1,1,1,1]=>630
[5,6,3,7,4,2,1,8]=>[4,2,1,1]=>2520
[7,6,3,8,5,1,4,2]=>[6,1,1]=>3360
[6,4,8,1,3,2,5,7]=>[4,4]=>1260
[7,4,8,6,3,1,5,2]=>[8]=>5040
[4,2,7,6,5,3,1,8]=>[5,1,1,1]=>1344
[3,7,2,4,6,5,1,8]=>[4,2,1,1]=>2520
[8,1,3,4,5,2,6,7]=>[5,1,1,1]=>1344
[1,6,8,4,2,5,3,7]=>[3,3,1,1]=>1120
[6,2,8,4,1,5,7,3]=>[3,2,1,1,1]=>1120
[6,7,4,8,5,1,2,3]=>[3,2,2,1]=>1680
[3,2,7,8,5,1,6,4]=>[4,2,1,1]=>2520
[3,2,8,1,5,4,6,7]=>[6,1,1]=>3360
[6,1,4,8,5,3,7,2]=>[6,1,1]=>3360
[1,4,8,5,2,6,7,3]=>[3,2,1,1,1]=>1120
[6,1,8,4,3,7,2,5]=>[4,3,1]=>3360
[3,7,1,4,2,5,8,6]=>[5,2,1]=>4032
[7,2,1,4,3,5,6,8]=>[5,1,1,1]=>1344
[4,1,5,3,6,8,2,7]=>[8]=>5040
[6,1,8,5,3,2,7,4]=>[4,3,1]=>3360
[7,1,4,6,3,8,5,2]=>[8]=>5040
[3,2,6,4,1,8,7,5]=>[5,1,1,1]=>1344
[7,6,4,3,1,8,2,5]=>[6,2]=>3360
[3,5,2,1,8,7,6,4]=>[6,2]=>3360
[1,5,3,2,8,6,4,7]=>[5,1,1,1]=>1344
[5,4,2,1,7,8,6,3]=>[8]=>5040
[8,2,7,6,5,1,3,4]=>[4,2,1,1]=>2520
[8,6,2,7,1,4,5,3]=>[8]=>5040
[1,7,3,6,2,8,5,4]=>[3,3,1,1]=>1120
[7,6,3,2,1,8,5,4]=>[4,3,1]=>3360
[8,6,3,7,4,1,2,5]=>[7,1]=>5760
[5,2,3,4,7,1,8,6]=>[5,1,1,1]=>1344
[8,6,3,1,4,5,7,2]=>[6,1,1]=>3360
[6,7,3,1,5,4,2,8]=>[3,2,1,1,1]=>1120
[5,8,3,1,2,4,7,6]=>[6,1,1]=>3360
[8,1,3,2,4,5,6,7]=>[7,1]=>5760
[8,4,1,7,2,3,6,5]=>[8]=>5040
[8,2,1,6,5,4,7,3]=>[3,2,1,1,1]=>1120
[3,8,1,5,6,4,7,2]=>[3,2,2,1]=>1680
[6,8,4,1,2,5,7,3]=>[7,1]=>5760
[3,2,8,1,6,5,7,4]=>[4,2,1,1]=>2520
[7,6,4,1,5,2,3,8]=>[4,2,1,1]=>2520
[8,6,1,5,4,7,3,2]=>[6,2]=>3360
[3,5,1,4,6,7,2,8]=>[4,2,1,1]=>2520
[5,2,1,4,7,6,3,8]=>[4,1,1,1,1]=>420
[4,5,8,2,1,3,7,6]=>[4,3,1]=>3360
[5,8,2,3,1,4,6,7]=>[6,2]=>3360
[4,2,1,3,5,8,7,6]=>[3,2,1,1,1]=>1120
[5,4,1,3,6,2,8,7]=>[6,2]=>3360
[8,5,4,1,3,6,2,7]=>[7,1]=>5760
[3,2,5,1,4,6,8,7]=>[4,2,1,1]=>2520
[8,1,4,3,5,6,7,2]=>[3,2,1,1,1]=>1120
[7,1,3,5,4,6,2,8]=>[3,2,1,1,1]=>1120
[5,1,3,4,6,2,7,8]=>[4,1,1,1,1]=>420
[4,1,3,2,5,7,6,8]=>[3,2,1,1,1]=>1120
[3,1,4,2,6,5,8,7,9]=>[4,2,2,1]=>11340
[3,1,5,2,6,4,8,7,9]=>[6,2,1]=>30240
[3,1,5,2,4,7,6,9,8]=>[5,2,2]=>9072
[3,1,2,5,4,7,6,9,8]=>[3,2,2,2]=>2520
[3,1,4,2,6,5,8,7,10,9]=>[4,2,2,2]=>18900
[4,1,5,2,6,3,8,7,9]=>[3,3,2,1]=>10080
[3,1,5,2,6,4,8,7,10,9]=>[6,2,2]=>75600
[3,1,6,2,7,4,8,5,9]=>[5,3,1]=>24192
[3,1,5,2,7,4,8,6,10,9]=>[8,2]=>226800
[3,1,5,2,7,4,9,6,10,8]=>[10]=>362880
[1,3,5,2,4,7,6,9,8]=>[4,2,2,1]=>11340
[3,1,2,5,4,7,6,9,8,10]=>[3,2,2,2,1]=>25200
[4,6,7,3,1,5,2,8]=>[7,1]=>5760
[6,8,1,3,5,2,7,4]=>[6,1,1]=>3360
[6,8,3,1,4,5,7,2]=>[4,2,1,1]=>2520
[7,5,1,8,2,3,6,4]=>[4,2,2]=>1260
[5,3,8,4,2,6,7,1]=>[5,1,1,1]=>1344
[4,1,8,3,5,7,2,6]=>[7,1]=>5760
[4,5,7,2,3,6,8,1]=>[7,1]=>5760
[2,6,3,4,7,5,8,1]=>[6,1,1]=>3360
[3,4,1,6,5,8,2,7]=>[5,2,1]=>4032
[7,3,1,4,8,5,6,2]=>[7,1]=>5760
[6,4,2,8,7,1,5,3]=>[4,2,2]=>1260
[7,2,4,8,1,5,3,6]=>[7,1]=>5760
[4,6,3,1,7,8,5,2]=>[3,2,2,1]=>1680
[5,3,1,6,7,8,4,2]=>[8]=>5040
[4,1,6,2,7,8,5,3]=>[3,3,2]=>1120
[2,1,3,4,8,7,5,6]=>[4,2,1,1]=>2520
[4,5,6,7,8,9,1,2,3]=>[3,3,3]=>2240
[4,5,6,7,8,9,2,3,1]=>[9]=>40320
[5,6,7,8,9,1,2,3,4]=>[9]=>40320
[6,7,8,9,2,3,4,5,1]=>[9]=>40320
[8,9,6,7,5,4,3,2,1]=>[4,4,1]=>11340
[4,5,6,7,8,9,10,1,2,3]=>[10]=>362880
[4,5,6,7,8,9,10,2,3,1]=>[4,3,3]=>50400
[5,6,7,8,9,10,1,2,3,4]=>[5,5]=>72576
[5,6,7,8,9,10,3,4,1,2]=>[3,3,2,2]=>25200
[7,8,9,10,3,4,5,6,1,2]=>[5,5]=>72576
[7,8,9,10,5,6,3,4,1,2]=>[4,4,1,1]=>56700
[8,9,10,5,6,7,2,3,4,1]=>[6,4]=>151200
[4,8,3,7,6,5,1,2]=>[3,2,2,1]=>1680
[6,3,8,7,5,4,1,2]=>[4,3,1]=>3360
[5,3,8,7,6,4,1,2]=>[5,3]=>2688
[2,8,7,6,1,5,4,3]=>[8]=>5040
[5,2,8,7,6,1,4,3]=>[3,2,2,1]=>1680
[6,2,8,7,5,1,4,3]=>[2,2,2,1,1]=>420
[7,8,2,6,5,1,4,3]=>[4,3,1]=>3360
[6,1,8,7,5,4,3,2]=>[7,1]=>5760
[3,1,8,7,6,5,4,2]=>[4,2,2]=>1260
[7,8,2,6,1,5,4,3]=>[5,3]=>2688
[6,2,8,7,1,5,4,3]=>[3,2,2,1]=>1680
[4,2,8,1,7,6,5,3]=>[2,2,2,1,1]=>420
[4,8,2,7,6,1,5,3]=>[5,3]=>2688
[3,8,7,2,1,6,5,4]=>[4,3,1]=>3360
[6,5,8,7,1,4,3,2]=>[8]=>5040
[4,8,1,7,6,5,3,2]=>[4,2,2]=>1260
[5,4,1,8,7,6,3,2]=>[4,3,1]=>3360
[6,4,8,1,7,5,3,2]=>[8]=>5040
[7,8,4,1,6,5,3,2]=>[4,2,2]=>1260
[7,8,3,1,6,5,4,2]=>[3,2,2,1]=>1680
[6,3,8,1,7,5,4,2]=>[5,3]=>2688
[5,3,1,8,7,6,4,2]=>[7,1]=>5760
[7,8,2,1,6,5,4,3]=>[3,3,2]=>1120
[6,5,3,1,8,7,4,2]=>[4,3,1]=>3360
[6,4,3,1,8,7,5,2]=>[7,1]=>5760
[5,4,3,1,8,7,6,2]=>[5,2,1]=>4032
[7,5,2,1,8,6,4,3]=>[4,3,1]=>3360
[5,4,2,1,8,7,6,3]=>[6,2]=>3360
[7,3,2,1,8,6,5,4]=>[5,2,1]=>4032
[6,3,2,1,8,7,5,4]=>[6,2]=>3360
[9,7,5,3,1,10,8,6,4,2]=>[5,5]=>72576
[8,7,5,3,1,10,9,6,4,2]=>[10]=>362880
[9,6,5,3,1,10,8,7,4,2]=>[5,3,2]=>120960
[8,6,5,3,1,10,9,7,4,2]=>[7,3]=>172800
[7,6,5,3,1,10,9,8,4,2]=>[6,3,1]=>201600
[9,7,4,3,1,10,8,6,5,2]=>[5,3,2]=>120960
[8,7,4,3,1,10,9,6,5,2]=>[8,2]=>226800
[9,6,4,3,1,10,8,7,5,2]=>[3,3,2,2]=>25200
[8,6,4,3,1,10,9,7,5,2]=>[5,3,2]=>120960
[7,6,4,3,1,10,9,8,5,2]=>[4,3,2,1]=>151200
[9,5,4,3,1,10,8,7,6,2]=>[6,2,2]=>75600
[8,5,4,3,1,10,9,7,6,2]=>[8,2]=>226800
[7,5,4,3,1,10,9,8,6,2]=>[7,2,1]=>259200
[6,5,4,3,1,10,9,8,7,2]=>[5,2,2,1]=>90720
[9,7,5,2,1,10,8,6,4,3]=>[10]=>362880
[8,7,5,2,1,10,9,6,4,3]=>[6,4]=>151200
[9,6,5,2,1,10,8,7,4,3]=>[8,2]=>226800
[8,6,5,2,1,10,9,7,4,3]=>[10]=>362880
[7,6,5,2,1,10,9,8,4,3]=>[9,1]=>403200
[9,7,4,2,1,10,8,6,5,3]=>[7,3]=>172800
[8,7,4,2,1,10,9,6,5,3]=>[10]=>362880
[9,6,4,2,1,10,8,7,5,3]=>[5,3,2]=>120960
[8,6,4,2,1,10,9,7,5,3]=>[5,5]=>72576
[7,6,4,2,1,10,9,8,5,3]=>[5,4,1]=>181440
[9,5,4,2,1,10,8,7,6,3]=>[8,2]=>226800
[8,5,4,2,1,10,9,7,6,3]=>[10]=>362880
[7,5,4,2,1,10,9,8,6,3]=>[9,1]=>403200
[6,5,4,2,1,10,9,8,7,3]=>[7,2,1]=>259200
[9,7,3,2,1,10,8,6,5,4]=>[6,3,1]=>201600
[8,7,3,2,1,10,9,6,5,4]=>[9,1]=>403200
[9,6,3,2,1,10,8,7,5,4]=>[4,3,2,1]=>151200
[8,6,3,2,1,10,9,7,5,4]=>[5,4,1]=>181440
[7,6,3,2,1,10,9,8,5,4]=>[4,4,1,1]=>56700
[9,5,3,2,1,10,8,7,6,4]=>[7,2,1]=>259200
[8,5,3,2,1,10,9,7,6,4]=>[9,1]=>403200
[7,5,3,2,1,10,9,8,6,4]=>[8,1,1]=>226800
[6,5,3,2,1,10,9,8,7,4]=>[6,2,1,1]=>151200
[9,4,3,2,1,10,8,7,6,5]=>[5,2,2,1]=>90720
[8,4,3,2,1,10,9,7,6,5]=>[7,2,1]=>259200
[7,4,3,2,1,10,9,8,6,5]=>[6,2,1,1]=>151200
[6,4,3,2,1,10,9,8,7,5]=>[4,2,2,1,1]=>56700
[11,9,7,5,3,1,12,10,8,6,4,2]=>[12]=>39916800
[10,9,7,5,3,1,12,11,8,6,4,2]=>[9,3]=>17740800
[11,8,7,5,3,1,12,10,9,6,4,2]=>[11,1]=>43545600
[11,9,6,5,3,1,12,10,8,7,4,2]=>[6,6]=>6652800
[10,9,6,5,3,1,12,11,8,7,4,2]=>[12]=>39916800
[10,8,6,5,3,1,12,11,9,7,4,2]=>[11,1]=>43545600
[9,8,6,5,3,1,12,11,10,7,4,2]=>[12]=>39916800
[9,7,6,5,3,1,12,11,10,8,4,2]=>[9,3]=>17740800
[11,9,7,4,3,1,12,10,8,6,5,2]=>[11,1]=>43545600
[11,8,7,4,3,1,12,10,9,6,5,2]=>[10,1,1]=>23950080
[9,8,7,4,3,1,12,11,10,6,5,2]=>[7,4,1]=>17107200
[10,9,6,4,3,1,12,11,8,7,5,2]=>[11,1]=>43545600
[10,8,6,4,3,1,12,11,9,7,5,2]=>[10,1,1]=>23950080
[9,8,6,4,3,1,12,11,10,7,5,2]=>[11,1]=>43545600
[11,7,6,4,3,1,12,10,9,8,5,2]=>[5,3,2,1,1]=>7983360
[11,8,5,4,3,1,12,10,9,7,6,2]=>[5,3,2,1,1]=>7983360
[11,7,5,4,3,1,12,10,9,8,6,2]=>[3,3,2,2,1,1]=>1663200
[10,7,5,4,3,1,12,11,9,8,6,2]=>[5,3,2,1,1]=>7983360
[8,7,5,4,3,1,12,11,10,9,6,2]=>[4,3,2,2,1]=>4989600
[7,6,5,4,3,1,12,11,10,9,8,2]=>[5,2,2,2,1]=>1995840
[11,9,7,5,2,1,12,10,8,6,4,3]=>[9,3]=>17740800
[10,8,7,5,2,1,12,11,9,6,4,3]=>[5,3,3,1]=>5322240
[9,8,7,5,2,1,12,11,10,6,4,3]=>[5,4,3]=>7983360
[11,9,6,5,2,1,12,10,8,7,4,3]=>[12]=>39916800
[10,9,6,5,2,1,12,11,8,7,4,3]=>[6,6]=>6652800
[11,8,6,5,2,1,12,10,9,7,4,3]=>[11,1]=>43545600
[9,8,6,5,2,1,12,11,10,7,4,3]=>[7,5]=>13685760
[10,7,6,5,2,1,12,11,9,8,4,3]=>[11,1]=>43545600
[9,7,6,5,2,1,12,11,10,8,4,3]=>[12]=>39916800
[10,9,7,4,2,1,12,11,8,6,5,3]=>[5,3,3,1]=>5322240
[10,8,7,4,2,1,12,11,9,6,5,3]=>[4,3,3,1,1]=>3326400
[9,8,7,4,2,1,12,11,10,6,5,3]=>[4,4,3,1]=>4989600
[11,9,6,4,2,1,12,10,8,7,5,3]=>[11,1]=>43545600
[11,8,6,4,2,1,12,10,9,7,5,3]=>[10,1,1]=>23950080
[9,8,6,4,2,1,12,11,10,7,5,3]=>[7,4,1]=>17107200
[10,7,6,4,2,1,12,11,9,8,5,3]=>[10,1,1]=>23950080
[9,7,6,4,2,1,12,11,10,8,5,3]=>[11,1]=>43545600
[10,9,5,4,2,1,12,11,8,7,6,3]=>[11,1]=>43545600
[10,8,5,4,2,1,12,11,9,7,6,3]=>[10,1,1]=>23950080
[9,8,5,4,2,1,12,11,10,7,6,3]=>[11,1]=>43545600
[11,7,5,4,2,1,12,10,9,8,6,3]=>[5,3,2,1,1]=>7983360
[8,7,5,4,2,1,12,11,10,9,6,3]=>[5,4,2,1]=>11975040
[10,6,5,4,2,1,12,11,9,8,7,3]=>[10,1,1]=>23950080
[9,6,5,4,2,1,12,11,10,8,7,3]=>[11,1]=>43545600
[10,9,7,3,2,1,12,11,8,6,5,4]=>[5,4,3]=>7983360
[11,8,7,3,2,1,12,10,9,6,5,4]=>[7,4,1]=>17107200
[10,8,7,3,2,1,12,11,9,6,5,4]=>[4,4,3,1]=>4989600
[9,8,7,3,2,1,12,11,10,6,5,4]=>[4,4,4]=>1247400
[11,9,6,3,2,1,12,10,8,7,5,4]=>[12]=>39916800
[10,9,6,3,2,1,12,11,8,7,5,4]=>[7,5]=>13685760
[11,8,6,3,2,1,12,10,9,7,5,4]=>[11,1]=>43545600
[10,8,6,3,2,1,12,11,9,7,5,4]=>[7,4,1]=>17107200
[10,7,6,3,2,1,12,11,9,8,5,4]=>[11,1]=>43545600
[9,7,6,3,2,1,12,11,10,8,5,4]=>[12]=>39916800
[11,9,5,3,2,1,12,10,8,7,6,4]=>[9,3]=>17740800
[10,9,5,3,2,1,12,11,8,7,6,4]=>[12]=>39916800
[10,8,5,3,2,1,12,11,9,7,6,4]=>[11,1]=>43545600
[9,8,5,3,2,1,12,11,10,7,6,4]=>[12]=>39916800
[9,7,5,3,2,1,12,11,10,8,6,4]=>[6,6]=>6652800
[8,7,5,3,2,1,12,11,10,9,6,4]=>[6,4,2]=>9979200
[10,6,5,3,2,1,12,11,9,8,7,4]=>[11,1]=>43545600
[9,6,5,3,2,1,12,11,10,8,7,4]=>[12]=>39916800
[11,7,4,3,2,1,12,10,9,8,6,5]=>[4,3,2,2,1]=>4989600
[10,7,4,3,2,1,12,11,9,8,6,5]=>[5,4,2,1]=>11975040
[9,7,4,3,2,1,12,11,10,8,6,5]=>[6,4,2]=>9979200
[8,7,4,3,2,1,12,11,10,9,6,5]=>[4,4,2,2]=>1871100
[11,5,4,3,2,1,12,10,9,8,7,6]=>[5,2,2,2,1]=>1995840
[6,1,4,2,3,5,8,7]=>[6,2]=>3360
[8,6,1,4,2,3,5,7]=>[7,1]=>5760
[6,8,1,4,2,3,5,7]=>[4,3,1]=>3360
[8,1,4,2,3,6,5,7]=>[7,1]=>5760
[4,1,8,2,3,6,5,7]=>[4,3,1]=>3360
[8,2,3,6,1,4,5,7]=>[4,2,1,1]=>2520
[6,2,3,8,1,4,5,7]=>[6,1,1]=>3360
[4,6,2,3,8,1,5,7]=>[5,3]=>2688
[4,8,2,3,6,1,5,7]=>[8]=>5040
[8,2,3,6,4,1,5,7]=>[6,1,1]=>3360
[8,4,3,6,2,1,5,7]=>[7,1]=>5760
[6,2,3,8,4,1,5,7]=>[4,2,1,1]=>2520
[8,4,2,3,6,1,5,7]=>[5,3]=>2688
[6,4,2,3,8,1,5,7]=>[3,3,2]=>1120
[2,6,4,3,8,1,5,7]=>[3,3,2]=>1120
[2,8,4,3,6,1,5,7]=>[6,2]=>3360
[2,6,3,8,4,1,5,7]=>[4,3,1]=>3360
[6,3,8,4,2,1,5,7]=>[5,2,1]=>4032
[2,6,3,8,1,4,5,7]=>[7,1]=>5760
[2,8,3,6,1,4,5,7]=>[5,2,1]=>4032
[8,3,6,4,2,1,5,7]=>[7,1]=>5760
[2,8,3,6,4,1,5,7]=>[7,1]=>5760
[8,3,6,2,4,1,5,7]=>[8]=>5040
[8,3,6,2,1,4,5,7]=>[4,4]=>1260
[6,2,1,3,8,4,5,7]=>[4,3,1]=>3360
[8,2,1,3,6,4,5,7]=>[7,1]=>5760
[6,3,8,2,4,1,5,7]=>[6,2]=>3360
[6,2,4,3,8,1,5,7]=>[3,2,2,1]=>1680
[3,6,4,7,8,5,1,2]=>[4,4]=>1260
[6,4,8,5,3,7,1,2]=>[5,3]=>2688
[1,6,5,2,4,8,7,3]=>[6,1,1]=>3360
[7,8,1,4,2,5,6,3]=>[7,1]=>5760
[4,8,5,3,1,6,2,7]=>[4,3,1]=>3360
[6,1,8,7,4,2,3,5]=>[5,3]=>2688
[1,3,6,8,7,5,2,4]=>[5,2,1]=>4032
[1,8,2,5,4,7,6,3]=>[3,2,2,1]=>1680
[7,1,2,4,5,8,6,3]=>[6,1,1]=>3360
[1,2,7,3,5,8,6,4]=>[5,1,1,1]=>1344
[1,6,3,7,8,5,2,4]=>[6,1,1]=>3360
[4,6,2,3,7,8,1,5]=>[8]=>5040
[4,6,3,7,1,2,8,5]=>[5,2,1]=>4032
[7,3,2,4,5,1,8,6]=>[4,2,1,1]=>2520
[7,8,4,2,6,3,1,5]=>[6,2]=>3360
[4,2,6,3,8,7,1,5]=>[5,2,1]=>4032
[5,8,2,7,4,3,1,6]=>[4,4]=>1260
[6,4,3,5,2,8,1,7]=>[4,3,1]=>3360
[6,1,7,2,8,3,9,4,10,5]=>[10]=>362880
[6,1,7,8,9,10,2,3,4,5]=>[10]=>362880
[7,1,8,2,9,3,10,4,11,5,12,6]=>[12]=>39916800
[3,8,1,7,5,6,4,2]=>[2,2,2,1,1]=>420
[8,2,5,7,3,6,4,1]=>[2,2,2,1,1]=>420
[1,8,6,7,5,3,4,2]=>[2,2,2,1,1]=>420
[8,2,6,7,5,3,4,1]=>[2,2,2,1,1]=>420
[1,5,8,7,2,6,4,3]=>[2,2,2,1,1]=>420
[5,4,8,6,2,3,7,1]=>[7,1]=>5760
[2,7,6,1,3,5,4,8]=>[4,3,1]=>3360
[6,4,1,8,2,5,7,3]=>[7,1]=>5760
[2,8,6,1,3,5,4,7]=>[5,3]=>2688
[4,1,3,6,5,8,7,2]=>[5,1,1,1]=>1344
[2,1,6,3,5,8,7,4]=>[4,2,1,1]=>2520
[2,4,1,3,8,5,7,6]=>[4,3,1]=>3360
[2,4,1,3,5,8,7,6]=>[4,2,1,1]=>2520
[6,1,4,3,5,8,7,2]=>[4,2,1,1]=>2520
[6,2,1,8,3,5,7,4]=>[4,2,1,1]=>2520
[6,1,4,3,8,5,7,2]=>[5,2,1]=>4032
[1,6,4,3,8,5,7,2]=>[4,2,1,1]=>2520
[8,1,4,3,6,5,7,2]=>[3,2,2,1]=>1680
[8,2,1,3,6,5,7,4]=>[4,2,1,1]=>2520
[8,2,1,4,3,5,7,6]=>[5,1,1,1]=>1344
[6,2,1,4,3,5,7,8]=>[4,1,1,1,1]=>420
[8,2,6,1,3,5,7,4]=>[3,3,1,1]=>1120
[8,1,4,6,3,5,7,2]=>[4,3,1]=>3360
[1,8,4,6,3,5,7,2]=>[4,2,1,1]=>2520
[1,6,4,8,3,5,7,2]=>[6,1,1]=>3360
[6,4,8,1,3,5,7,2]=>[7,1]=>5760
[6,2,8,1,3,5,7,4]=>[6,1,1]=>3360
[2,1,6,8,3,5,7,4]=>[3,2,2,1]=>1680
[4,1,3,8,6,5,7,2]=>[4,2,1,1]=>2520
[2,1,8,3,6,5,7,4]=>[3,2,2,1]=>1680
[2,8,1,6,3,5,7,4]=>[7,1]=>5760
[2,8,4,1,3,5,7,6]=>[7,1]=>5760
[6,8,1,4,3,5,7,2]=>[4,2,1,1]=>2520
[6,1,8,4,3,5,7,2]=>[6,1,1]=>3360
[1,8,6,4,3,5,7,2]=>[3,2,1,1,1]=>1120
[8,6,1,4,3,5,7,2]=>[6,1,1]=>3360
[8,6,4,1,3,5,7,2]=>[7,1]=>5760
[8,4,2,1,3,5,7,6]=>[7,1]=>5760
[7,8,6,5,2,1,4,3]=>[8]=>5040
[5,7,4,1,8,6,3,2]=>[7,1]=>5760
[5,6,4,2,8,3,7,1]=>[4,3,1]=>3360
[5,6,4,2,7,3,1,8]=>[4,3,1]=>3360
[5,7,1,4,6,3,2,8]=>[4,2,1,1]=>2520
[5,8,1,4,6,3,7,2]=>[4,2,1,1]=>2520
[3,6,7,4,5,8,2,1]=>[6,1,1]=>3360
[3,5,7,4,6,8,2,1]=>[7,1]=>5760
[6,8,4,1,7,2,5,3]=>[6,2]=>3360
[5,4,6,1,7,8,3,2]=>[8]=>5040
[5,6,4,1,8,7,3,2]=>[8]=>5040
[3,5,8,4,6,7,2,1]=>[4,3,1]=>3360
[3,6,8,4,5,7,2,1]=>[3,3,1,1]=>1120
[3,7,8,4,5,6,2,1]=>[3,2,1,1,1]=>1120
[6,8,1,4,5,3,7,2]=>[3,2,1,1,1]=>1120
[6,7,1,4,5,3,2,8]=>[3,2,1,1,1]=>1120
[3,7,1,5,4,6,2,8]=>[2,2,2,1,1]=>420
[3,8,1,5,4,6,7,2]=>[2,2,2,1,1]=>420
[3,7,1,5,4,6,8,2]=>[3,2,2,1]=>1680
[6,7,1,4,5,3,8,2]=>[3,3,1,1]=>1120
[5,7,1,4,6,3,8,2]=>[4,3,1]=>3360
[5,6,4,2,7,3,8,1]=>[4,4]=>1260
[5,4,7,2,8,3,1,6]=>[6,2]=>3360
[5,4,7,2,8,3,6,1]=>[3,3,2]=>1120
[5,6,4,2,8,3,1,7]=>[4,4]=>1260
[5,8,1,4,6,3,2,7]=>[4,3,1]=>3360
[3,8,1,5,4,6,2,7]=>[3,2,2,1]=>1680
[3,6,1,5,4,2,7,8]=>[2,2,2,1,1]=>420
[3,6,1,5,4,8,2,7]=>[4,2,2]=>1260
[6,8,3,1,4,2,5,7]=>[7,1]=>5760
[7,3,8,1,4,2,5,6]=>[4,4]=>1260
[6,7,3,1,4,2,8,5]=>[7,1]=>5760
[3,6,1,5,4,7,8,2]=>[4,2,2]=>1260
[3,4,1,2,7,6,5,8]=>[2,2,2,1,1]=>420
[3,4,1,2,6,8,7,5]=>[3,2,2,1]=>1680
[6,8,3,1,4,7,2,5]=>[7,1]=>5760
[6,4,7,2,8,5,1,3]=>[6,2]=>3360
[5,8,1,4,7,3,2,6]=>[7,1]=>5760
[7,8,1,4,5,3,2,6]=>[6,1,1]=>3360
[3,8,1,5,4,7,2,6]=>[4,2,2]=>1260
[3,6,1,5,4,8,7,2]=>[3,2,2,1]=>1680
[3,6,1,5,4,7,2,8]=>[3,2,2,1]=>1680
[6,7,3,1,4,2,5,8]=>[6,1,1]=>3360
[6,8,3,1,4,2,7,5]=>[6,1,1]=>3360
[7,8,3,1,4,6,2,5]=>[6,1,1]=>3360
[7,8,4,2,6,5,1,3]=>[4,2,2]=>1260
[6,5,8,7,3,4,2,1]=>[8]=>5040
[7,8,3,1,4,6,5,2]=>[4,2,1,1]=>2520
[6,7,3,1,4,5,2,8]=>[4,2,1,1]=>2520
[3,7,1,5,4,2,6,8]=>[3,2,2,1]=>1680
[3,8,1,5,4,2,7,6]=>[3,2,2,1]=>1680
[5,8,1,4,7,3,6,2]=>[5,2,1]=>4032
[6,8,4,2,7,5,3,1]=>[8]=>5040
[6,4,7,2,8,5,3,1]=>[4,2,2]=>1260
[6,3,7,1,4,8,5,2]=>[8]=>5040
[6,8,3,1,4,7,5,2]=>[5,2,1]=>4032
[3,7,1,5,4,8,6,2]=>[4,2,2]=>1260
[3,4,1,2,8,5,7,6]=>[3,2,2,1]=>1680
[3,4,1,2,5,8,7,6]=>[2,2,2,1,1]=>420
[3,7,1,5,4,2,8,6]=>[4,2,2]=>1260
[6,7,3,1,4,5,8,2]=>[4,3,1]=>3360
[7,3,8,1,4,5,2,6]=>[8]=>5040
[7,3,8,1,4,5,6,2]=>[5,3]=>2688
[6,8,3,1,4,5,2,7]=>[4,3,1]=>3360
[3,8,1,5,4,2,6,7]=>[4,2,2]=>1260
[9,8,7,6,5,4,2,1,3]=>[6,2,1]=>30240
[9,8,7,6,4,3,2,1,5]=>[9]=>40320
[9,8,6,5,4,3,2,1,7]=>[5,2,2]=>9072
[9,7,6,5,4,3,2,1,8]=>[3,2,2,2]=>2520
[10,9,8,7,6,5,4,2,1,3]=>[6,2,2]=>75600
[9,8,7,6,5,2,4,1,3]=>[8,1]=>45360
[10,9,8,7,6,4,3,2,1,5]=>[10]=>362880
[8,7,3,6,5,2,1,4]=>[6,1,1]=>3360
[10,9,8,6,5,4,3,2,1,7]=>[7,2,1]=>259200
[6,5,8,4,3,2,1,7]=>[7,1]=>5760
[8,4,7,6,3,2,1,5]=>[5,3]=>2688
[5,8,7,4,3,2,1,6]=>[4,3,1]=>3360
[10,8,7,6,5,4,3,2,1,9]=>[3,2,2,2,1]=>25200
[5,8,6,2,3,4,7,1]=>[7,1]=>5760
[4,5,2,7,3,1,8,6]=>[5,3]=>2688
[4,8,2,6,3,5,7,1]=>[7,1]=>5760
[4,1,7,2,5,8,6,3]=>[4,3,1]=>3360
[7,8,2,1,5,6,4,3]=>[3,3,1,1]=>1120
[1,6,2,5,8,4,3,7]=>[7,1]=>5760
[7,3,1,6,8,5,2,4]=>[4,4]=>1260
[5,2,7,1,8,6,3,4]=>[4,2,1,1]=>2520
[6,5,2,8,1,7,3,4]=>[6,2]=>3360
[8,5,4,3,7,2,6,1]=>[4,2,2]=>1260
[8,3,7,4,2,6,5,1]=>[4,2,1,1]=>2520
[5,4,2,8,3,1,7,6]=>[7,1]=>5760
[8,4,7,6,2,5,3,1]=>[4,2,2]=>1260
[4,8,7,6,1,5,3,2]=>[4,2,2]=>1260
[7,4,8,6,2,1,5,3]=>[6,2]=>3360
[7,3,8,5,2,1,6,4]=>[5,3]=>2688
[7,3,8,4,2,1,6,5]=>[4,3,1]=>3360
[7,5,4,3,8,2,1,6]=>[4,2,2]=>1260
[3,7,8,4,1,2,6,5]=>[4,3,1]=>3360
[4,7,8,6,1,2,5,3]=>[6,2]=>3360
[8,7,4,6,3,5,2,1]=>[4,2,2]=>1260
[5,7,8,6,1,2,4,3]=>[4,2,2]=>1260
[6,4,7,8,3,1,2,5]=>[6,2]=>3360
[7,3,4,8,2,1,5,6]=>[8]=>5040
[7,6,4,8,3,2,1,5]=>[4,2,2]=>1260
[7,5,8,6,2,1,4,3]=>[4,2,2]=>1260
[6,5,8,7,3,1,4,2]=>[4,2,2]=>1260
[2,3,8,4,1,6,7,5]=>[5,1,1,1]=>1344
[6,4,8,7,3,1,5,2]=>[6,2]=>3360
[8,6,4,7,3,2,5,1]=>[4,2,2]=>1260
[8,3,4,7,2,5,6,1]=>[6,2]=>3360
[3,4,8,7,1,5,6,2]=>[8]=>5040
[8,3,5,7,2,4,6,1]=>[3,3,2]=>1120
[8,4,6,7,2,3,5,1]=>[4,2,2]=>1260
[4,6,8,7,1,3,5,2]=>[4,4]=>1260
[2,6,8,5,1,3,7,4]=>[7,1]=>5760
[2,5,8,3,1,4,7,6]=>[4,3,1]=>3360
[5,6,8,7,1,3,4,2]=>[4,2,2]=>1260
[7,4,6,8,2,1,3,5]=>[4,4]=>1260
[2,3,5,4,1,8,6,7]=>[4,3,1]=>3360
[2,3,6,4,8,1,5,7]=>[4,3,1]=>3360
[1,8,4,6,3,5,2,7]=>[4,3,1]=>3360
[5,4,8,6,2,1,3,7]=>[5,3]=>2688
[2,3,6,8,1,5,4,7]=>[5,3]=>2688
[2,5,6,1,4,7,8,3]=>[4,4]=>1260
[2,5,6,1,4,7,3,8]=>[4,3,1]=>3360
[7,3,5,1,6,8,4,2]=>[5,3]=>2688
[2,7,6,1,8,5,4,3]=>[4,4]=>1260
[2,7,6,8,1,4,5,3]=>[4,4]=>1260
[1,8,7,6,3,2,5,4]=>[4,3,1]=>3360
[1,8,7,6,3,2,4,5]=>[7,1]=>5760
[5,7,8,6,2,3,4,1]=>[8]=>5040
[2,7,6,1,8,5,3,4]=>[8]=>5040
[6,3,5,1,7,2,4,8]=>[7,1]=>5760
[2,3,4,7,6,1,5,8]=>[7,1]=>5760
[7,3,5,8,4,1,2,6]=>[8]=>5040
[1,8,4,5,2,7,3,6]=>[7,1]=>5760
[1,8,4,5,2,7,6,3]=>[5,2,1]=>4032
[7,3,5,8,4,1,6,2]=>[5,3]=>2688
[2,7,6,4,8,5,1,3]=>[4,3,1]=>3360
[7,3,5,4,6,8,1,2]=>[5,2,1]=>4032
[6,3,5,4,7,1,8,2]=>[5,2,1]=>4032
[6,3,5,4,7,1,2,8]=>[4,2,1,1]=>2520
[3,4,1,5,6,8,7,2]=>[5,2,1]=>4032
[3,7,1,6,8,5,2,4]=>[4,2,2]=>1260
[2,3,1,8,6,4,7,5]=>[4,3,1]=>3360
[1,8,4,3,6,2,5,7]=>[5,2,1]=>4032
[2,3,1,8,6,4,5,7]=>[5,3]=>2688
[3,7,1,6,8,5,4,2]=>[6,2]=>3360
[6,3,5,4,7,2,1,8]=>[6,1,1]=>3360
[7,3,5,4,6,8,2,1]=>[7,1]=>5760
[2,7,6,4,8,5,3,1]=>[7,1]=>5760
[1,8,4,5,2,6,3,7]=>[6,1,1]=>3360
[6,4,8,5,3,1,2,7]=>[6,2]=>3360
[7,3,5,8,4,6,2,1]=>[7,1]=>5760
[2,3,4,6,5,8,1,7]=>[7,1]=>5760
[2,3,4,7,5,1,8,6]=>[7,1]=>5760
[2,3,4,7,5,1,6,8]=>[6,1,1]=>3360
[2,3,4,7,1,6,5,8]=>[6,1,1]=>3360
[2,3,4,7,1,6,8,5]=>[7,1]=>5760
[2,3,4,6,1,8,7,5]=>[7,1]=>5760
[6,3,5,8,4,2,7,1]=>[7,1]=>5760
[7,4,8,5,3,2,1,6]=>[6,2]=>3360
[1,8,4,5,2,3,6,7]=>[7,1]=>5760
[7,4,8,5,3,2,6,1]=>[8]=>5040
[6,3,5,8,4,2,1,7]=>[8]=>5040
[5,2,4,6,8,3,7,1]=>[3,3,1,1]=>1120
[1,5,7,4,6,3,2,8]=>[5,1,1,1]=>1344
[5,2,8,4,6,3,7,1]=>[5,1,1,1]=>1344
[3,8,5,4,6,7,2,1]=>[7,1]=>5760
[6,8,3,4,5,7,2,1]=>[5,1,1,1]=>1344
[2,5,7,4,6,3,8,1]=>[7,1]=>5760
[5,4,1,7,8,3,2,6]=>[5,3]=>2688
[5,4,2,7,8,3,6,1]=>[5,3]=>2688
[5,1,4,6,8,3,2,7]=>[5,3]=>2688
[5,1,8,4,6,3,2,7]=>[7,1]=>5760
[8,1,6,4,5,3,2,7]=>[4,2,1,1]=>2520
[8,1,3,5,4,6,2,7]=>[4,2,1,1]=>2520
[8,1,6,2,4,3,5,7]=>[6,2]=>3360
[8,7,1,2,4,3,5,6]=>[4,4]=>1260
[1,7,6,2,4,3,5,8]=>[4,2,1,1]=>2520
[8,7,3,2,4,6,5,1]=>[4,2,1,1]=>2520
[8,2,6,3,4,5,7,1]=>[4,2,1,1]=>2520
[1,7,6,3,4,5,2,8]=>[4,2,1,1]=>2520
[1,7,2,5,4,3,6,8]=>[4,2,1,1]=>2520
[8,7,2,4,5,3,6,1]=>[4,2,1,1]=>2520
[5,8,2,4,7,3,6,1]=>[7,1]=>5760
[6,8,3,2,4,7,5,1]=>[7,1]=>5760
[8,7,1,3,4,5,2,6]=>[6,2]=>3360
[8,1,6,3,4,5,2,7]=>[4,4]=>1260
[8,1,2,5,4,3,6,7]=>[6,2]=>3360
[3,4,8,7,5,2,6,1]=>[4,3,1]=>3360
[3,2,8,6,1,5,4,7]=>[7,1]=>5760
[8,6,1,2,4,3,5,7]=>[8]=>5040
[8,7,3,6,4,2,5,1]=>[5,2,1]=>4032
[3,8,7,2,5,4,6,1]=>[7,1]=>5760
[8,7,2,4,5,6,3,1]=>[3,2,1,1,1]=>1120
[5,3,6,2,4,8,7,1]=>[7,1]=>5760
[3,5,2,8,6,1,4,7]=>[5,3]=>2688
[3,7,2,5,1,4,8,6]=>[8]=>5040
[5,1,8,6,2,3,4,7]=>[5,3]=>2688
[2,5,4,1,8,6,3,7]=>[7,1]=>5760
[3,7,6,1,8,2,5,4]=>[8]=>5040
[7,6,3,1,8,2,4,5]=>[3,2,2,1]=>1680
[8,2,3,6,1,4,7,5]=>[3,2,1,1,1]=>1120
[1,8,2,6,3,4,7,5]=>[4,2,1,1]=>2520
[8,1,3,6,4,7,2,5]=>[7,1]=>5760
[7,1,3,6,4,8,2,5]=>[4,3,1]=>3360
[8,2,1,3,5,7,4,6]=>[6,1,1]=>3360
[8,2,6,3,1,4,7,5]=>[3,3,1,1]=>1120
[7,5,4,1,3,8,2,6]=>[6,2]=>3360
[2,7,5,8,3,4,1,6]=>[3,3,2]=>1120
[7,3,8,5,4,1,2,6]=>[6,2]=>3360
[7,2,3,6,1,4,8,5]=>[4,2,1,1]=>2520
[1,3,7,2,5,8,4,6]=>[4,2,1,1]=>2520
[1,7,2,3,5,8,4,6]=>[4,2,1,1]=>2520
[7,4,8,1,3,6,2,5]=>[4,3,1]=>3360
[8,1,2,3,5,7,4,6]=>[7,1]=>5760
[7,1,2,3,5,8,4,6]=>[5,2,1]=>4032
[8,6,1,4,7,3,2,5]=>[7,1]=>5760
[2,6,3,7,1,4,8,5]=>[7,1]=>5760
[2,6,3,8,1,4,7,5]=>[6,1,1]=>3360
[7,5,4,8,1,3,2,6]=>[4,4]=>1260
[8,5,4,7,1,3,2,6]=>[8]=>5040
[2,3,1,8,5,4,6,7]=>[4,3,1]=>3360
[8,6,5,1,3,4,2,7]=>[6,2]=>3360
[8,5,1,7,6,3,4,2]=>[6,2]=>3360
[3,4,7,6,1,8,5,2]=>[4,4]=>1260
[3,5,2,6,7,1,8,4]=>[8]=>5040
[3,2,8,4,7,5,1,6]=>[6,1,1]=>3360
[8,4,7,5,1,3,2,6]=>[8]=>5040
[3,8,1,6,5,2,7,4]=>[4,2,1,1]=>2520
[6,1,2,8,3,4,7,5]=>[7,1]=>5760
[6,8,3,1,7,2,4,5]=>[7,1]=>5760
[3,7,2,5,6,1,8,4]=>[8]=>5040
[6,8,4,2,5,1,7,3]=>[4,2,1,1]=>2520
[2,7,5,3,8,4,1,6]=>[5,3]=>2688
[8,3,1,4,7,2,6,5]=>[7,1]=>5760
[8,3,2,1,5,7,4,6]=>[5,2,1]=>4032
[2,8,3,6,4,7,1,5]=>[7,1]=>5760
[7,3,6,4,8,1,2,5]=>[5,2,1]=>4032
[8,3,6,4,7,1,2,5]=>[7,1]=>5760
[1,2,8,3,5,7,4,6]=>[5,1,1,1]=>1344
[1,8,3,2,5,7,4,6]=>[5,1,1,1]=>1344
[6,5,1,7,4,2,8,3]=>[8]=>5040
[7,3,6,4,8,2,1,5]=>[3,2,2,1]=>1680
[4,6,1,7,3,5,2,8]=>[7,1]=>5760
[5,6,1,7,3,4,2,8]=>[4,3,1]=>3360
[6,1,7,3,4,2,8,5]=>[5,3]=>2688
[7,3,8,1,6,5,2,4]=>[6,2]=>3360
[8,3,7,1,6,5,2,4]=>[3,3,2]=>1120
[5,1,7,4,2,8,6,3]=>[4,3,1]=>3360
[2,8,1,7,6,5,3,4]=>[6,2]=>3360
[4,2,8,6,5,1,7,3]=>[3,2,1,1,1]=>1120
[6,4,2,8,5,1,7,3]=>[4,2,1,1]=>2520
[8,6,4,7,1,5,2,3]=>[8]=>5040
[7,6,4,8,1,5,2,3]=>[5,3]=>2688
[5,1,6,4,2,3,8,7]=>[3,2,2,1]=>1680
[4,2,3,8,7,5,1,6]=>[6,1,1]=>3360
[3,8,7,1,6,5,2,4]=>[6,2]=>3360
[2,4,3,8,1,6,7,5]=>[5,1,1,1]=>1344
[2,4,3,7,1,6,8,5]=>[6,1,1]=>3360
[4,2,3,7,8,5,1,6]=>[3,3,1,1]=>1120
[5,1,6,4,2,3,7,8]=>[3,2,1,1,1]=>1120
[6,4,7,8,1,5,2,3]=>[5,3]=>2688
[8,7,4,6,1,5,2,3]=>[6,2]=>3360
[6,5,7,8,1,4,2,3]=>[8]=>5040
[4,7,8,6,1,5,2,3]=>[4,2,2]=>1260
[3,2,4,7,8,1,5,6]=>[7,1]=>5760
[3,2,4,8,7,1,5,6]=>[5,2,1]=>4032
[4,8,7,6,1,5,2,3]=>[4,4]=>1260
[5,8,7,6,1,4,2,3]=>[4,2,2]=>1260
[8,6,5,7,1,4,2,3]=>[4,4]=>1260
[5,1,6,7,4,2,3,8]=>[7,1]=>5760
[6,7,4,8,1,5,2,3]=>[3,3,2]=>1120
[8,4,7,6,1,5,2,3]=>[8]=>5040
[8,3,2,4,7,1,5,6]=>[3,2,2,1]=>1680
[7,3,2,4,8,1,5,6]=>[5,2,1]=>4032
[2,5,3,7,1,6,4,8]=>[3,2,1,1,1]=>1120
[8,4,6,7,1,5,2,3]=>[5,3]=>2688
[7,4,6,8,1,5,2,3]=>[8]=>5040
[5,1,6,8,4,2,3,7]=>[8]=>5040
[4,2,3,7,5,1,6,8]=>[4,1,1,1,1]=>420
[3,7,5,8,1,6,2,4]=>[3,2,2,1]=>1680
[2,4,3,7,1,6,5,8]=>[5,1,1,1]=>1344
[2,4,7,1,5,8,6,3]=>[4,3,1]=>3360
[3,2,4,7,6,1,5,8]=>[6,1,1]=>3360
[4,7,6,8,1,5,2,3]=>[6,2]=>3360
[8,5,6,7,1,4,2,3]=>[8]=>5040
[8,6,7,5,1,4,2,3]=>[8]=>5040
[7,6,8,5,1,4,2,3]=>[6,2]=>3360
[6,8,7,5,1,4,2,3]=>[4,4]=>1260
[5,6,8,7,1,4,2,3]=>[4,2,2]=>1260
[4,6,8,7,1,5,2,3]=>[6,2]=>3360
[2,4,6,7,1,5,8,3]=>[8]=>5040
[3,2,4,6,1,5,7,8]=>[5,1,1,1]=>1344
[6,7,8,5,1,4,2,3]=>[4,2,2]=>1260
[7,8,6,5,1,4,2,3]=>[8]=>5040
[3,1,7,5,4,2,8,6]=>[6,2]=>3360
[4,1,8,5,2,3,6,7]=>[4,4]=>1260
[8,2,7,1,5,3,4,6]=>[6,1,1]=>3360
[6,3,7,1,5,4,2,8]=>[3,3,1,1]=>1120
[7,1,5,3,8,4,2,6]=>[5,3]=>2688
[4,5,1,3,6,8,2,7]=>[5,3]=>2688
[6,8,3,1,5,4,2,7]=>[3,3,1,1]=>1120
[3,6,2,1,5,8,4,7]=>[7,1]=>5760
[8,6,2,1,5,3,4,7]=>[4,3,1]=>3360
[4,8,2,1,7,5,3,6]=>[6,2]=>3360
[7,1,6,2,8,3,4,5]=>[4,2,2]=>1260
[4,7,1,2,6,3,8,5]=>[8]=>5040
[2,7,8,1,5,3,4,6]=>[4,3,1]=>3360
[4,7,2,1,8,5,3,6]=>[3,3,2]=>1120
[8,7,2,1,4,5,3,6]=>[5,3]=>2688
[8,7,5,6,1,4,3,2]=>[6,2]=>3360
[5,7,8,6,1,4,3,2]=>[4,2,2]=>1260
[3,7,1,4,5,6,8,2]=>[3,2,1,1,1]=>1120
[3,5,1,4,7,6,8,2]=>[4,2,1,1]=>2520
[5,6,8,7,1,4,3,2]=>[6,2]=>3360
[6,8,5,7,1,4,3,2]=>[6,2]=>3360
[8,6,5,7,1,4,3,2]=>[8]=>5040
[8,5,7,6,1,4,3,2]=>[4,2,2]=>1260
[6,5,7,8,1,4,3,2]=>[6,2]=>3360
[7,2,3,1,5,6,4,8]=>[3,1,1,1,1,1]=>112
[8,3,1,4,5,6,7,2]=>[4,1,1,1,1]=>420
[8,3,1,5,4,6,7,2]=>[4,2,1,1]=>2520
[6,2,8,1,4,5,3,7]=>[4,3,1]=>3360
[4,2,1,5,6,3,8,7]=>[5,2,1]=>4032
[8,5,6,7,1,4,3,2]=>[4,4]=>1260
[7,6,8,5,1,4,3,2]=>[8]=>5040
[6,8,7,5,1,4,3,2]=>[4,2,2]=>1260
[2,7,6,1,4,5,3,8]=>[7,1]=>5760
[5,7,6,8,1,4,3,2]=>[6,2]=>3360
[7,8,6,5,1,4,3,2]=>[6,2]=>3360
[5,3,1,2,4,8,7,6]=>[5,2,1]=>4032
[5,3,7,2,1,4,6,8]=>[5,2,1]=>4032
[5,3,7,2,8,4,1,6]=>[8]=>5040
[3,7,4,5,8,2,1,6]=>[8]=>5040
[1,7,4,2,6,3,5,8]=>[6,1,1]=>3360
[5,7,4,8,6,3,1,2]=>[8]=>5040
[1,4,8,3,6,7,5,2]=>[4,3,1]=>3360
[3,8,4,2,6,1,5,7]=>[8]=>5040
[1,8,2,5,6,7,4,3]=>[4,3,1]=>3360
[3,8,2,5,6,7,1,4]=>[8]=>5040
[7,8,4,3,6,2,1,5]=>[4,2,2]=>1260
[7,1,4,8,6,2,3,5]=>[8]=>5040
[7,5,4,1,6,2,3,8]=>[4,3,1]=>3360
[1,6,4,5,8,2,3,7]=>[5,2,1]=>4032
[7,3,6,1,8,2,4,5]=>[3,3,2]=>1120
[8,3,5,2,1,7,4,6]=>[8]=>5040
[8,4,2,5,6,7,1,3]=>[8]=>5040
[1,4,5,8,6,7,3,2]=>[4,3,1]=>3360
[4,3,5,8,1,7,2,6]=>[8]=>5040
[3,5,4,8,6,1,2,7]=>[8]=>5040
[3,4,8,5,6,7,1,2]=>[8]=>5040
[2,7,1,5,6,3,4,8]=>[7,1]=>5760
[2,7,1,4,3,6,5,8]=>[5,1,1,1]=>1344
[4,3,7,2,5,6,8,1]=>[6,1,1]=>3360
[2,6,3,1,4,5,8,7]=>[5,2,1]=>4032
[3,7,1,4,2,6,8,5]=>[4,2,1,1]=>2520
[3,7,1,5,6,2,8,4]=>[6,2]=>3360
[4,7,1,5,6,8,2,3]=>[6,2]=>3360
[8,5,2,6,7,3,1,4]=>[8]=>5040
[8,4,2,6,3,7,1,5]=>[8]=>5040
[8,4,2,3,5,7,1,6]=>[4,3,1]=>3360
[4,7,3,2,5,6,1,8]=>[4,1,1,1,1]=>420
[5,3,4,6,2,8,1,7]=>[8]=>5040
[5,3,7,4,2,8,1,6]=>[5,2,1]=>4032
[6,4,7,2,3,8,1,5]=>[6,2]=>3360
[6,5,7,2,8,3,1,4]=>[4,4]=>1260
[5,3,7,2,4,8,6,1]=>[8]=>5040
[2,6,5,1,8,3,4,7]=>[8]=>5040
[8,7,6,1,4,5,2,3]=>[6,2]=>3360
[8,7,6,1,3,2,5,4]=>[5,3]=>2688
[8,7,2,4,3,1,6,5]=>[7,1]=>5760
[8,7,4,5,1,6,2,3]=>[5,2,1]=>4032
[8,5,6,4,1,7,2,3]=>[7,1]=>5760
[8,5,6,3,1,2,7,4]=>[7,1]=>5760
[8,4,6,2,3,1,7,5]=>[5,2,1]=>4032
[8,3,5,4,2,1,7,6]=>[3,3,1,1]=>1120
[5,7,3,4,2,1,8,6]=>[6,1,1]=>3360
[6,7,4,2,3,1,8,5]=>[6,2]=>3360
[6,7,5,3,1,2,8,4]=>[8]=>5040
[6,7,5,4,1,8,2,3]=>[5,2,1]=>4032
[10,3,1,2,4,5,6,7,8,9]=>[10]=>362880
[5,10,1,2,3,4,6,7,8,9]=>[7,3]=>172800
[10,7,1,2,3,4,5,6,8,9]=>[10]=>362880
[8,10,1,2,3,4,5,6,7,9]=>[10]=>362880
[2,11,1,3,4,5,6,7,8,9,10]=>[11]=>3628800
[2,3,10,1,4,5,6,7,8,9]=>[10]=>362880
[4,3,1,10,2,5,6,7,8,9]=>[10]=>362880
[8,9,1,2,3,4,5,6,10,7]=>[10]=>362880
[11,9,1,2,3,4,5,6,7,8,10]=>[11]=>3628800
[7,3,5,4,1,8,6,2]=>[7,1]=>5760
[2,6,5,7,3,1,8,4]=>[3,3,2]=>1120
[6,3,2,4,7,5,1,8]=>[4,2,1,1]=>2520
[4,2,1,6,3,7,5,8]=>[6,1,1]=>3360
[4,2,1,6,3,7,8,5]=>[7,1]=>5760
[4,2,1,3,7,8,6,5]=>[4,3,1]=>3360
[4,2,1,8,3,5,6,7]=>[7,1]=>5760
[4,2,1,6,3,8,7,5]=>[6,1,1]=>3360
[3,6,7,5,2,4,8,1]=>[4,4]=>1260
[3,6,7,5,2,4,1,8]=>[4,3,1]=>3360
[3,7,6,8,4,2,5,1]=>[8]=>5040
[5,8,1,7,4,2,6,3]=>[8]=>5040
[3,7,8,6,2,4,5,1]=>[3,3,2]=>1120
[4,2,1,3,5,8,6,7]=>[3,3,1,1]=>1120
[4,8,1,7,3,6,5,2]=>[5,2,1]=>4032
[4,2,1,8,3,7,6,5]=>[5,2,1]=>4032
[2,6,1,5,4,7,8,3]=>[6,2]=>3360
[3,5,6,1,4,8,7,2]=>[7,1]=>5760
[2,7,5,1,8,3,4,6]=>[4,4]=>1260
[4,7,5,2,1,3,6,8]=>[7,1]=>5760
[3,5,6,2,4,1,7,8]=>[3,3,1,1]=>1120
[2,5,6,1,4,8,3,7]=>[4,4]=>1260
[7,1,6,8,4,5,3,2]=>[8]=>5040
[5,7,8,1,4,6,3,2]=>[4,3,1]=>3360
[6,1,8,4,7,5,3,2]=>[7,1]=>5760
[4,5,8,6,1,7,3,2]=>[8]=>5040
[4,8,5,1,6,7,3,2]=>[4,2,2]=>1260
[8,1,4,5,6,7,3,2]=>[5,3]=>2688
[5,6,7,1,4,2,3,8]=>[3,2,2,1]=>1680
[8,4,2,6,1,5,7,3]=>[7,1]=>5760
[4,8,5,2,1,6,7,3]=>[6,1,1]=>3360
[1,8,4,6,2,5,3,7]=>[7,1]=>5760
[8,2,4,3,6,7,1,5]=>[5,2,1]=>4032
[3,2,8,5,7,1,6,4]=>[7,1]=>5760
[2,8,7,1,4,6,5,3]=>[7,1]=>5760
[8,2,7,1,5,4,6,3]=>[6,1,1]=>3360
[7,2,5,3,6,8,1,4]=>[5,2,1]=>4032
[7,3,1,5,6,2,4,8]=>[7,1]=>5760
[2,7,3,6,5,8,1,4]=>[3,3,1,1]=>1120
[8,7,2,4,1,6,5,3]=>[6,1,1]=>3360
[1,2,7,3,6,4,5,8]=>[5,1,1,1]=>1344
[1,6,2,8,4,3,7,5]=>[3,3,1,1]=>1120
[8,1,4,7,3,2,5,6]=>[4,4]=>1260
[7,1,4,2,3,5,6,8]=>[7,1]=>5760
[1,2,3,4,8,5,7,6]=>[3,1,1,1,1,1]=>112
[2,4,7,5,6,8,3,1]=>[6,2]=>3360
[2,4,8,7,5,6,3,1]=>[6,1,1]=>3360
[2,5,3,8,4,7,6,1]=>[5,2,1]=>4032
[3,1,8,5,2,7,6,4]=>[6,2]=>3360
[2,8,6,3,4,5,7,1]=>[4,3,1]=>3360
[2,5,7,3,4,8,6,1]=>[8]=>5040
[8,3,7,6,1,4,5,2]=>[6,2]=>3360
[3,1,7,8,2,5,6,4]=>[6,2]=>3360
[7,3,8,5,1,6,4,2]=>[4,3,1]=>3360
[7,5,1,2,3,4,8,6]=>[8]=>5040
[4,8,1,5,2,7,3,6]=>[8]=>5040
[4,1,2,5,3,8,7,6]=>[5,2,1]=>4032
[6,4,8,1,2,5,3,7]=>[5,3]=>2688
[5,4,1,6,8,2,7,3]=>[4,3,1]=>3360
[5,4,7,1,2,8,6,3]=>[4,4]=>1260
[6,7,4,1,2,8,3,5]=>[8]=>5040
[6,5,1,2,3,7,8,4]=>[8]=>5040
[6,5,1,2,3,4,8,7]=>[6,2]=>3360
[6,7,4,1,2,5,3,8]=>[7,1]=>5760
[1,4,6,3,7,2,5,8]=>[4,2,1,1]=>2520
[8,6,2,5,3,1,7,4]=>[7,1]=>5760
[8,2,3,4,5,1,7,6]=>[3,1,1,1,1,1]=>112
[1,8,3,4,2,7,5,6]=>[5,1,1,1]=>1344
[7,8,2,4,3,1,6,5]=>[4,3,1]=>3360
[6,1,3,5,7,2,4,8]=>[3,3,1,1]=>1120
[7,1,8,2,5,6,3,4]=>[6,1,1]=>3360
[6,1,5,8,2,7,3,4]=>[6,2]=>3360
[4,5,2,8,1,6,7,3]=>[6,1,1]=>3360
[6,2,5,8,1,4,7,3]=>[6,1,1]=>3360
[1,3,8,2,5,7,4,6]=>[6,1,1]=>3360
[6,2,3,1,5,4,7,8]=>[3,1,1,1,1,1]=>112
[8,2,3,1,4,5,7,6]=>[5,1,1,1]=>1344
[8,5,1,3,2,4,7,6]=>[5,2,1]=>4032
[7,5,1,3,2,6,4,8]=>[4,2,1,1]=>2520
[3,6,4,1,5,2,7,8]=>[3,2,1,1,1]=>1120
[4,5,7,1,2,6,3,8]=>[2,2,2,1,1]=>420
[6,7,1,4,2,5,3,8]=>[6,1,1]=>3360
[2,7,1,3,5,6,4,8]=>[5,1,1,1]=>1344
[8,6,1,2,4,3,7,5]=>[7,1]=>5760
[7,8,1,2,5,3,6,4]=>[4,3,1]=>3360
[1,2,6,7,5,3,8,4]=>[3,2,1,1,1]=>1120
[1,7,5,3,2,8,4,6]=>[5,2,1]=>4032
[1,6,7,5,3,8,4,2]=>[4,3,1]=>3360
[1,6,5,7,2,3,8,4]=>[4,3,1]=>3360
[1,3,8,2,6,5,7,4]=>[4,2,1,1]=>2520
[1,2,5,7,6,3,4,8]=>[3,2,1,1,1]=>1120
[1,3,4,8,2,5,7,6]=>[6,1,1]=>3360
[1,5,7,6,2,3,4,8]=>[4,2,1,1]=>2520
[1,5,3,8,2,6,4,7]=>[3,2,1,1,1]=>1120
[1,4,8,3,2,5,7,6]=>[6,1,1]=>3360
[1,4,8,3,5,7,6,2]=>[4,2,1,1]=>2520
[1,2,4,8,3,5,7,6]=>[5,1,1,1]=>1344
[1,3,8,4,2,6,7,5]=>[4,1,1,1,1]=>420
[1,4,8,2,3,5,7,6]=>[4,2,1,1]=>2520
[6,5,7,3,8,2,4,1]=>[5,3]=>2688
[4,2,6,7,5,8,3,1]=>[6,1,1]=>3360
[6,7,5,2,1,8,4,3]=>[5,3]=>2688
[3,4,8,7,5,2,1,6]=>[7,1]=>5760
[1,7,5,2,8,4,6,3]=>[4,3,1]=>3360
[5,6,8,3,1,7,2,4]=>[3,3,2]=>1120
[6,1,4,8,3,2,7,5]=>[4,3,1]=>3360
[3,4,7,1,8,6,2,5]=>[5,2,1]=>4032
[3,4,6,8,2,1,5,7]=>[5,3]=>2688
[3,8,2,5,6,1,4,7]=>[8]=>5040
[3,5,2,8,6,4,1,7]=>[8]=>5040
[4,2,5,7,3,8,6,1]=>[5,2,1]=>4032
[7,4,2,5,3,8,1,6]=>[4,2,2]=>1260
[3,1,2,8,5,6,4,7]=>[3,3,1,1]=>1120
[5,2,1,6,8,3,4,7]=>[7,1]=>5760
[5,2,6,8,4,1,3,7]=>[7,1]=>5760
[1,5,6,8,3,4,2,7]=>[7,1]=>5760
[4,5,8,1,6,3,2,7]=>[6,2]=>3360
[4,5,1,6,8,3,2,7]=>[4,4]=>1260
[4,5,7,3,8,2,6,1]=>[8]=>5040
[6,4,3,7,8,2,5,1]=>[7,1]=>5760
[6,4,3,1,7,8,2,5]=>[7,1]=>5760
[4,5,3,1,7,8,2,6]=>[3,2,2,1]=>1680
[7,1,3,5,4,8,2,6]=>[3,2,2,1]=>1680
[7,5,2,8,1,4,3,6]=>[5,3]=>2688
[5,7,3,8,4,6,1,2]=>[6,1,1]=>3360
[1,4,5,7,3,8,6,2]=>[5,2,1]=>4032
[4,6,3,7,8,5,2,1]=>[7,1]=>5760
[5,3,6,7,8,4,2,1]=>[5,3]=>2688
[1,5,3,6,7,8,4,2]=>[6,1,1]=>3360
[4,6,1,7,3,8,5,2]=>[5,3]=>2688
[6,3,7,1,8,4,5,2]=>[5,3]=>2688
[6,7,2,4,8,1,5,3]=>[5,2,1]=>4032
[2,6,1,4,7,3,8,5]=>[4,3,1]=>3360
[3,2,5,6,7,8,1,4]=>[4,3,1]=>3360
[5,2,3,6,7,8,4,1]=>[6,1,1]=>3360
[6,7,1,3,2,8,4,5]=>[8]=>5040
[6,2,7,1,3,4,8,5]=>[4,3,1]=>3360
[5,2,1,7,3,8,4,6]=>[3,2,2,1]=>1680
[6,4,2,7,1,8,3,5]=>[4,4]=>1260
[4,2,6,3,7,8,1,5]=>[7,1]=>5760
[4,2,6,3,7,8,5,1]=>[5,2,1]=>4032
[6,7,3,8,2,4,5,1]=>[4,3,1]=>3360
[3,6,2,7,4,1,8,5]=>[4,4]=>1260
[6,7,3,2,1,4,8,5]=>[7,1]=>5760
[7,1,8,3,4,2,5,6]=>[8]=>5040
[7,2,4,1,8,3,5,6]=>[7,1]=>5760
[7,2,4,8,6,1,3,5]=>[7,1]=>5760
[7,3,4,8,6,2,1,5]=>[6,2]=>3360
[3,5,7,2,1,8,6,4]=>[8]=>5040
[6,7,8,3,2,5,1,4]=>[5,3]=>2688
[6,3,7,8,2,5,4,1]=>[8]=>5040
[2,6,7,4,8,5,3,1]=>[5,2,1]=>4032
[6,2,4,7,1,8,5,3]=>[7,1]=>5760
[4,6,2,7,1,8,5,3]=>[4,4]=>1260
[1,7,4,8,5,2,6,3]=>[3,3,1,1]=>1120
[1,3,7,8,5,2,6,4]=>[4,2,1,1]=>2520
[2,5,7,8,1,6,3,4]=>[3,2,2,1]=>1680
[6,3,7,1,8,2,5,4]=>[8]=>5040
[1,6,4,7,8,2,5,3]=>[5,2,1]=>4032
[2,5,6,1,7,8,4,3]=>[5,3]=>2688
[5,6,1,2,7,8,4,3]=>[8]=>5040
[6,7,2,1,8,5,3,4]=>[5,3]=>2688
[6,7,2,8,5,4,1,3]=>[7,1]=>5760
[1,6,7,4,8,5,3,2]=>[4,2,1,1]=>2520
[1,8,2,4,6,3,5,7]=>[6,1,1]=>3360
[1,5,7,4,3,6,2,8]=>[4,1,1,1,1]=>420
[1,8,4,5,3,6,2,7]=>[3,3,1,1]=>1120
[1,8,5,3,4,7,2,6]=>[4,3,1]=>3360
[1,8,2,4,6,3,7,5]=>[5,1,1,1]=>1344
[1,8,2,5,4,6,7,3]=>[3,2,1,1,1]=>1120
[3,6,2,7,1,4,5,8]=>[7,1]=>5760
[4,6,5,3,7,1,8,2]=>[8]=>5040
[4,2,3,8,6,7,1,5]=>[6,1,1]=>3360
[5,2,4,8,1,3,7,6]=>[4,2,1,1]=>2520
[6,2,5,4,8,3,7,1]=>[5,1,1,1]=>1344
[6,4,3,5,8,2,7,1]=>[6,1,1]=>3360
[5,2,3,4,8,1,6,7]=>[5,1,1,1]=>1344
[3,5,2,4,7,1,6,8]=>[6,1,1]=>3360
[5,3,4,8,1,6,2,7]=>[5,2,1]=>4032
[4,5,3,7,1,6,2,8]=>[5,1,1,1]=>1344
[7,6,3,8,5,1,2,4]=>[4,2,1,1]=>2520
[4,2,6,7,3,8,1,5]=>[4,3,1]=>3360
[1,5,7,4,2,8,6,3]=>[4,2,1,1]=>2520
[1,3,7,2,8,6,4,5]=>[4,2,1,1]=>2520
[1,4,3,7,8,6,2,5]=>[3,2,1,1,1]=>1120
[1,5,3,6,8,2,7,4]=>[5,1,1,1]=>1344
[4,2,3,5,6,8,1,7]=>[6,1,1]=>3360
[4,2,6,7,3,8,5,1]=>[7,1]=>5760
[3,2,5,6,8,1,7,4]=>[6,1,1]=>3360
[6,4,5,2,3,8,7,1]=>[3,2,2,1]=>1680
[6,4,2,5,3,8,7,1]=>[4,3,1]=>3360
[8,6,2,7,4,5,3,1]=>[6,2]=>3360
[6,4,2,5,8,7,3,1]=>[8]=>5040
[4,6,2,5,3,8,7,1]=>[7,1]=>5760
[4,6,5,2,3,8,7,1]=>[5,2,1]=>4032
[6,8,2,7,4,5,3,1]=>[8]=>5040
[6,8,7,2,4,5,3,1]=>[6,2]=>3360
[2,6,4,5,8,7,3,1]=>[8]=>5040
[2,6,4,8,7,5,3,1]=>[8]=>5040
[8,2,4,6,7,5,3,1]=>[5,2,1]=>4032
[4,2,6,8,7,5,3,1]=>[4,3,1]=>3360
[4,2,6,5,8,7,3,1]=>[4,3,1]=>3360
[4,2,3,6,8,7,5,1]=>[6,1,1]=>3360
[6,4,8,7,2,5,3,1]=>[8]=>5040
[6,4,8,7,5,2,3,1]=>[7,1]=>5760
[4,6,5,8,7,2,3,1]=>[3,3,2]=>1120
[4,6,8,2,7,5,3,1]=>[8]=>5040
[4,6,5,8,2,7,3,1]=>[5,3]=>2688
[2,1,8,6,4,7,5,3]=>[4,2,2]=>1260
[6,8,7,4,2,5,3,1]=>[5,2,1]=>4032
[9,8,7,3,6,2,5,1,4]=>[9]=>40320
[9,8,7,6,3,5,1,2,4]=>[7,2]=>25920
[9,4,8,3,7,2,6,1,5]=>[9]=>40320
[9,8,4,7,3,6,1,2,5]=>[6,2,1]=>30240
[9,8,7,2,4,6,1,3,5]=>[8,1]=>45360
[9,8,7,4,6,1,2,3,5]=>[4,4,1]=>11340
[5,9,4,8,3,7,1,2,6]=>[9]=>40320
[9,5,8,2,4,7,1,3,6]=>[4,3,2]=>15120
[9,5,8,4,7,1,2,3,6]=>[3,3,2,1]=>10080
[9,8,3,5,7,1,2,4,6]=>[5,3,1]=>24192
[9,8,5,7,1,2,3,4,6]=>[9]=>40320
[6,9,3,5,8,1,2,4,7]=>[3,3,2,1]=>10080
[6,9,5,8,1,2,3,4,7]=>[7,2]=>25920
[9,2,4,6,8,1,3,5,7]=>[6,2,1]=>30240
[9,4,6,8,1,2,3,5,7]=>[9]=>40320
[9,6,8,1,2,3,4,5,7]=>[5,4]=>18144
[3,5,7,9,1,2,4,6,8]=>[9]=>40320
[5,7,9,1,2,3,4,6,8]=>[5,4]=>18144
[7,9,1,2,3,4,5,6,8]=>[5,4]=>18144
[10,9,8,7,6,5,2,4,1,3]=>[8,2]=>226800
[10,9,8,7,3,6,2,5,1,4]=>[6,3,1]=>201600
[10,9,8,7,6,3,5,1,2,4]=>[8,2]=>226800
[10,9,4,8,3,7,2,6,1,5]=>[10]=>362880
[10,9,8,4,7,3,6,1,2,5]=>[7,2,1]=>259200
[10,9,8,7,2,4,6,1,3,5]=>[7,3]=>172800
[10,9,8,7,4,6,1,2,3,5]=>[5,4,1]=>181440
[10,5,9,4,8,3,7,1,2,6]=>[8,1,1]=>226800
[10,9,5,8,2,4,7,1,3,6]=>[5,4,1]=>181440
[10,9,5,8,4,7,1,2,3,6]=>[6,4]=>151200
[10,9,8,3,5,7,1,2,4,6]=>[5,4,1]=>181440
[10,9,8,5,7,1,2,3,4,6]=>[5,3,2]=>120960
[6,10,5,9,2,4,8,1,3,7]=>[10]=>362880
[6,10,5,9,4,8,1,2,3,7]=>[6,4]=>151200
[10,3,6,9,2,5,8,1,4,7]=>[4,4,2]=>56700
[10,6,9,3,5,8,1,2,4,7]=>[3,3,3,1]=>22400
[10,6,9,5,8,1,2,3,4,7]=>[5,5]=>72576
[10,9,2,4,6,8,1,3,5,7]=>[6,3,1]=>201600
[10,9,4,6,8,1,2,3,5,7]=>[10]=>362880
[10,9,6,8,1,2,3,4,5,7]=>[8,2]=>226800
[4,7,10,3,6,9,1,2,5,8]=>[7,3]=>172800
[7,10,2,4,6,9,1,3,5,8]=>[4,3,2,1]=>151200
[7,10,4,6,9,1,2,3,5,8]=>[8,2]=>226800
[7,10,6,9,1,2,3,4,5,8]=>[10]=>362880
[10,3,5,7,9,1,2,4,6,8]=>[10]=>362880
[10,5,7,9,1,2,3,4,6,8]=>[8,2]=>226800
[10,7,9,1,2,3,4,5,6,8]=>[7,3]=>172800
[4,6,8,10,1,2,3,5,7,9]=>[8,2]=>226800
[6,8,10,1,2,3,4,5,7,9]=>[7,3]=>172800
[4,2,5,6,3,8,1,7]=>[5,2,1]=>4032
[6,2,5,7,4,8,3,1]=>[4,3,1]=>3360
[8,5,2,1,4,7,6,3]=>[6,2]=>3360
[6,7,3,2,5,8,4,1]=>[3,3,1,1]=>1120
[3,2,6,4,8,1,5,7]=>[3,3,1,1]=>1120
[2,3,6,4,7,8,5,1]=>[5,2,1]=>4032
[7,5,1,8,3,4,6,2]=>[8]=>5040
[5,7,8,2,6,3,4,1]=>[5,3]=>2688
[7,1,6,3,5,8,4,2]=>[7,1]=>5760
[6,3,1,7,8,4,5,2]=>[8]=>5040
[5,3,6,7,4,1,8,2]=>[8]=>5040
[7,3,1,2,5,8,6,4]=>[7,1]=>5760
[1,6,3,5,2,4,8,7]=>[4,2,1,1]=>2520
[3,4,8,2,7,5,1,6]=>[6,2]=>3360
[6,3,2,8,5,7,4,1]=>[5,2,1]=>4032
[3,8,4,7,2,5,6,1]=>[8]=>5040
[2,4,8,1,5,3,7,6]=>[3,3,1,1]=>1120
[3,4,8,1,6,2,7,5]=>[7,1]=>5760
[1,8,4,6,7,3,5,2]=>[3,2,2,1]=>1680
[8,1,6,3,4,5,7,2]=>[4,3,1]=>3360
[7,6,5,4,1,2,8,3]=>[5,2,1]=>4032
[5,7,6,8,3,4,2,1]=>[6,2]=>3360
[2,8,1,6,5,7,4,3]=>[4,3,1]=>3360
[4,6,8,2,5,3,7,1]=>[6,1,1]=>3360
[5,2,3,7,6,1,8,4]=>[3,3,1,1]=>1120
[8,1,2,4,6,7,3,5]=>[7,1]=>5760
[5,2,3,7,4,8,6,1]=>[6,1,1]=>3360
[5,2,6,8,4,3,1,7]=>[5,2,1]=>4032
[7,8,1,5,4,3,6,2]=>[4,2,2]=>1260
[7,2,4,8,5,3,6,1]=>[6,1,1]=>3360
[3,7,5,1,8,4,6,2]=>[8]=>5040
[2,7,8,5,4,6,1,3]=>[3,2,2,1]=>1680
[5,7,4,3,8,6,2,1]=>[3,2,2,1]=>1680
[4,8,1,6,3,5,2,7]=>[5,3]=>2688
[8,3,1,7,4,2,5,6]=>[5,3]=>2688
[3,1,8,2,4,5,7,6]=>[7,1]=>5760
[8,1,3,7,6,2,4,5]=>[5,2,1]=>4032
[2,3,6,8,7,1,4,5]=>[4,4]=>1260
[4,3,2,8,5,7,1,6]=>[5,2,1]=>4032
[3,6,4,2,8,5,7,1]=>[7,1]=>5760
[4,7,3,2,5,1,8,6]=>[6,1,1]=>3360
[3,2,4,7,5,8,6,1]=>[6,1,1]=>3360
[4,2,3,8,6,5,1,7]=>[4,2,1,1]=>2520
[2,4,3,5,1,8,6,7]=>[4,3,1]=>3360
[3,2,8,1,4,6,5,7]=>[6,1,1]=>3360
[4,7,8,3,1,2,6,5]=>[5,3]=>2688
[4,7,8,2,1,3,6,5]=>[8]=>5040
[4,1,6,8,2,3,7,5]=>[5,2,1]=>4032
[4,5,1,2,8,3,7,6]=>[7,1]=>5760
[4,6,2,8,1,3,7,5]=>[4,3,1]=>3360
[3,6,2,8,4,7,1,5]=>[5,3]=>2688
[3,2,6,8,4,7,1,5]=>[4,3,1]=>3360
[4,2,6,8,3,1,7,5]=>[6,1,1]=>3360
[4,2,5,1,8,3,7,6]=>[4,2,1,1]=>2520
[4,1,2,5,8,3,7,6]=>[7,1]=>5760
[5,2,4,1,3,8,7,6]=>[4,2,1,1]=>2520
[4,2,5,3,8,1,7,6]=>[6,1,1]=>3360
[3,2,5,4,8,7,1,6]=>[6,1,1]=>3360
[5,1,4,2,3,8,7,6]=>[5,2,1]=>4032
[5,4,1,3,2,8,7,6]=>[5,2,1]=>4032
[5,4,3,1,2,8,7,6]=>[4,2,1,1]=>2520
[3,5,1,4,8,7,2,6]=>[5,2,1]=>4032
[3,4,5,1,8,7,2,6]=>[8]=>5040
[4,3,6,8,2,1,7,5]=>[7,1]=>5760
[2,4,6,8,3,7,5,1]=>[4,4]=>1260
[3,4,5,2,8,7,1,6]=>[6,2]=>3360
[5,3,2,1,4,8,7,6]=>[3,2,2,1]=>1680
[4,3,2,5,8,1,7,6]=>[5,2,1]=>4032
[5,1,2,3,4,8,7,6]=>[5,2,1]=>4032
[8,6,2,5,4,1,3,7]=>[6,2]=>3360
[6,5,7,4,2,8,3,1]=>[3,2,2,1]=>1680
[6,7,5,3,8,2,4,1]=>[8]=>5040
[8,2,1,6,3,4,5,7]=>[5,2,1]=>4032
[8,3,5,6,2,4,1,7]=>[3,3,2]=>1120
[8,6,2,1,3,5,4,7]=>[4,4]=>1260
[8,1,2,3,4,6,5,7]=>[7,1]=>5760
[6,2,3,7,8,4,5,1]=>[6,1,1]=>3360
[7,5,8,2,6,3,4,1]=>[8]=>5040
[7,3,1,6,5,8,4,2]=>[7,1]=>5760
[1,5,6,7,3,4,8,2]=>[7,1]=>5760
[6,7,8,2,1,4,5,3]=>[6,2]=>3360
[8,4,7,6,2,1,3,5]=>[6,2]=>3360
[5,3,8,4,7,2,6,1]=>[7,1]=>5760
[8,1,3,7,6,4,2,5]=>[7,1]=>5760
[5,3,1,7,8,6,2,4]=>[7,1]=>5760
[3,5,8,2,7,1,6,4]=>[8]=>5040
[6,2,8,5,3,1,7,4]=>[4,2,1,1]=>2520
[8,2,6,4,7,1,3,5]=>[6,1,1]=>3360
[3,4,2,8,5,1,7,6]=>[6,1,1]=>3360
[3,8,6,5,2,1,7,4]=>[4,3,1]=>3360
[8,3,7,4,2,5,6,1]=>[5,2,1]=>4032
[4,8,5,7,2,1,3,6]=>[8]=>5040
[3,4,1,8,2,6,7,5]=>[4,2,1,1]=>2520
[8,4,6,3,7,1,5,2]=>[6,2]=>3360
[6,8,3,4,1,5,7,2]=>[3,2,1,1,1]=>1120
[5,1,7,6,2,8,4,3]=>[5,3]=>2688
[6,8,2,5,7,4,1,3]=>[5,3]=>2688
[2,8,5,6,7,1,3,4]=>[5,3]=>2688
[2,5,7,6,3,1,8,4]=>[8]=>5040
[4,2,8,3,1,5,6,7]=>[7,1]=>5760
[2,5,7,3,8,4,6,1]=>[4,4]=>1260
[4,2,7,1,8,5,3,6]=>[3,2,2,1]=>1680
[4,2,1,8,7,5,6,3]=>[4,3,1]=>3360
[8,3,6,7,1,5,4,2]=>[6,2]=>3360
[1,3,7,5,8,6,4,2]=>[6,1,1]=>3360
[5,7,8,4,3,1,6,2]=>[7,1]=>5760
[2,7,4,5,8,3,6,1]=>[8]=>5040
[3,5,7,1,4,8,6,2]=>[8]=>5040
[7,2,8,5,1,4,6,3]=>[5,2,1]=>4032
[1,6,5,3,8,4,2,7]=>[7,1]=>5760
[5,7,4,8,3,6,2,1]=>[5,2,1]=>4032
[4,8,6,1,3,5,2,7]=>[3,3,2]=>1120
[1,8,3,2,4,7,5,6]=>[6,1,1]=>3360
[8,4,3,2,5,7,1,6]=>[4,2,1,1]=>2520
[3,6,4,8,2,5,7,1]=>[4,3,1]=>3360
[4,3,7,2,5,8,1,6]=>[5,2,1]=>4032
[3,2,4,7,8,5,6,1]=>[7,1]=>5760
[2,6,4,3,8,5,1,7]=>[6,2]=>3360
[3,8,2,1,6,4,5,7]=>[8]=>5040
[8,2,1,3,4,5,7,6]=>[6,1,1]=>3360
[4,6,8,3,2,1,5,7]=>[8]=>5040
[3,2,6,8,5,4,1,7]=>[6,1,1]=>3360
[7,3,8,2,5,4,1,6]=>[5,2,1]=>4032
[4,2,5,3,8,7,6,1]=>[5,2,1]=>4032
[4,8,2,6,5,3,1,7]=>[7,1]=>5760
[2,6,8,5,4,1,3,7]=>[3,3,2]=>1120
[3,1,8,6,5,4,2,7]=>[5,2,1]=>4032
[5,4,8,7,3,2,6,1]=>[4,4]=>1260
[6,4,8,3,7,2,5,1]=>[6,2]=>3360
[4,7,3,6,2,1,8,5]=>[4,3,1]=>3360
[5,4,3,7,1,8,2,6]=>[3,2,2,1]=>1680
[7,3,8,5,1,4,2,6]=>[8]=>5040
[5,4,8,7,6,2,1,3]=>[6,2]=>3360
[3,8,1,5,7,4,6,2]=>[4,2,2]=>1260
[4,8,5,7,3,1,6,2]=>[4,2,2]=>1260
[1,5,4,8,3,7,6,2]=>[5,2,1]=>4032
[4,8,3,6,7,1,5,2]=>[3,2,2,1]=>1680
[4,7,8,3,1,6,5,2]=>[7,1]=>5760
[8,7,5,3,6,4,2,1]=>[4,2,2]=>1260
[4,6,1,3,8,7,5,2]=>[5,3]=>2688
[6,8,2,1,7,4,5,3]=>[3,3,2]=>1120
[3,7,1,6,4,2,8,5]=>[6,2]=>3360
[3,1,2,7,5,6,8,4]=>[3,3,1,1]=>1120
[3,6,1,2,7,5,8,4]=>[6,2]=>3360
[3,7,6,2,5,8,1,4]=>[7,1]=>5760
[3,6,2,5,8,7,4,1]=>[8]=>5040
[8,5,2,3,6,7,4,1]=>[6,2]=>3360
[4,7,2,6,3,8,1,5]=>[8]=>5040
[6,3,2,4,8,7,5,1]=>[5,2,1]=>4032
[3,7,2,4,6,1,8,5]=>[7,1]=>5760
[5,3,7,2,8,1,4,6]=>[4,4]=>1260
[6,3,2,8,7,5,1,4]=>[4,2,2]=>1260
[7,3,8,2,6,5,1,4]=>[4,2,2]=>1260
[6,4,8,7,2,5,1,3]=>[6,2]=>3360
[2,5,4,8,1,7,6,3]=>[3,3,2]=>1120
[5,2,8,1,7,6,3,4]=>[6,1,1]=>3360
[6,2,1,3,8,7,5,4]=>[7,1]=>5760
[3,6,1,8,7,5,2,4]=>[4,2,2]=>1260
[5,6,1,2,8,7,4,3]=>[4,4]=>1260
[7,5,2,8,1,6,4,3]=>[7,1]=>5760
[2,7,6,8,1,5,4,3]=>[8]=>5040
[7,8,5,1,6,2,4,3]=>[5,3]=>2688
[7,4,8,6,1,2,5,3]=>[3,3,2]=>1120
[7,2,1,8,3,6,5,4]=>[4,2,1,1]=>2520
[5,8,7,1,6,4,3,2]=>[4,2,2]=>1260
[7,6,5,4,3,2,9,8,1]=>[3,2,2,1,1]=>7560
[11,9,8,7,6,5,4,3,2,1,10]=>[3,2,2,2,2]=>34650
[10,7,6,5,4,3,2,1,9,8]=>[3,2,2,2,1]=>25200
[9,6,5,4,3,2,8,1,7]=>[4,2,2,1]=>11340
[9,7,5,4,3,2,1,8,6]=>[5,2,1,1]=>18144
[8,5,4,3,7,2,1,6]=>[6,2]=>3360
[6,5,4,8,3,2,7,1]=>[7,1]=>5760
[7,6,5,4,3,9,2,8,1]=>[5,2,1,1]=>18144
[7,6,4,3,2,8,5,1]=>[6,2]=>3360
[8,6,5,4,3,2,9,7,1]=>[4,2,2,1]=>11340
[8,7,6,5,4,3,2,10,9,1]=>[3,2,2,2,1]=>25200
[10,9,8,7,6,5,4,3,2,11,1]=>[3,2,2,2,2]=>34650
[7,3,1,4,8,2,5,6]=>[7,1]=>5760
[7,4,1,2,5,8,3,6]=>[3,2,2,1]=>1680
[6,7,4,2,5,1,3,8]=>[4,2,1,1]=>2520
[5,7,2,4,6,8,1,3]=>[7,1]=>5760
[4,7,5,1,6,2,8,3]=>[6,2]=>3360
[5,7,4,6,3,1,8,2]=>[5,3]=>2688
[7,5,1,4,3,2,8,6]=>[7,1]=>5760
[8,6,4,2,3,7,5,1]=>[6,2]=>3360
[6,4,7,1,3,8,5,2]=>[5,3]=>2688
[5,4,2,7,3,1,6,8]=>[7,1]=>5760
[4,5,1,2,7,6,8,3]=>[7,1]=>5760
[5,4,6,8,3,1,2,7]=>[4,4]=>1260
[6,4,8,1,3,7,2,5]=>[5,3]=>2688
[4,6,1,3,8,5,2,7]=>[5,3]=>2688
[1,3,8,4,5,7,2,6]=>[5,1,1,1]=>1344
[2,6,7,4,5,3,1,8]=>[5,1,1,1]=>1344
[2,6,8,4,3,5,1,7]=>[7,1]=>5760
[1,3,7,4,2,8,5,6]=>[4,2,1,1]=>2520
[4,6,1,3,7,2,5,8]=>[3,2,2,1]=>1680
[7,5,8,6,2,1,3,4]=>[6,2]=>3360
[2,8,1,3,6,5,4,7]=>[6,2]=>3360
[2,8,7,3,5,4,1,6]=>[7,1]=>5760
[3,4,2,6,8,7,1,5]=>[6,2]=>3360
[7,4,2,3,6,1,8,5]=>[5,3]=>2688
[8,4,2,3,6,5,7,1]=>[3,2,2,1]=>1680
[7,3,8,4,1,2,6,5]=>[7,1]=>5760
[6,8,3,2,7,1,5,4]=>[3,2,2,1]=>1680
[2,8,5,6,3,7,1,4]=>[6,2]=>3360
[7,4,2,5,8,1,6,3]=>[5,3]=>2688
[2,7,8,3,4,5,1,6]=>[5,3]=>2688
[3,7,1,2,4,6,5,8]=>[4,2,1,1]=>2520
[7,5,6,8,2,1,4,3]=>[6,2]=>3360
[3,1,6,5,2,7,4,8]=>[7,1]=>5760
[2,8,6,5,3,4,1,7]=>[4,4]=>1260
[1,7,2,3,5,6,8,4]=>[5,1,1,1]=>1344
[3,7,4,2,1,5,6,8]=>[7,1]=>5760
[3,4,6,2,8,5,7,1]=>[5,2,1]=>4032
[4,2,1,7,5,8,3,6]=>[4,2,1,1]=>2520
[4,7,2,6,5,1,3,8]=>[3,3,1,1]=>1120
[3,7,4,1,2,5,8,6]=>[5,3]=>2688
[4,7,1,6,5,2,8,3]=>[7,1]=>5760
[4,7,3,6,5,1,8,2]=>[3,3,1,1]=>1120
[4,3,7,1,6,8,5,2]=>[6,2]=>3360
[4,2,1,7,5,6,8,3]=>[5,1,1,1]=>1344
[3,2,4,8,6,7,1,5]=>[7,1]=>5760
[4,2,6,8,7,3,1,5]=>[5,2,1]=>4032
[3,4,6,1,8,5,2,7]=>[8]=>5040
[4,1,6,7,5,8,2,3]=>[4,3,1]=>3360
[4,3,6,7,5,1,2,8]=>[6,1,1]=>3360
[4,3,7,1,6,8,2,5]=>[3,3,2]=>1120
[4,3,7,5,6,8,2,1]=>[5,3]=>2688
[4,1,7,3,6,5,2,8]=>[5,2,1]=>4032
[2,8,7,4,5,3,1,6]=>[6,1,1]=>3360
[2,8,7,4,3,5,1,6]=>[7,1]=>5760
[3,8,1,4,2,6,5,7]=>[4,2,1,1]=>2520
[4,1,7,3,6,2,5,8]=>[7,1]=>5760
[5,8,7,6,1,2,4,3]=>[6,2]=>3360
[5,8,7,6,2,1,3,4]=>[6,2]=>3360
[4,1,7,2,6,8,5,3]=>[5,3]=>2688
[4,2,7,3,6,1,8,5]=>[7,1]=>5760
[4,2,7,3,6,5,8,1]=>[5,2,1]=>4032
[3,8,2,4,5,6,7,1]=>[4,1,1,1,1]=>420
[3,8,2,4,1,6,7,5]=>[5,1,1,1]=>1344
[3,8,5,6,2,4,1,7]=>[6,2]=>3360
[2,8,6,5,3,7,1,4]=>[8]=>5040
[3,8,6,5,1,4,7,2]=>[5,2,1]=>4032
[3,8,2,1,4,6,7,5]=>[6,1,1]=>3360
[3,8,2,5,4,6,7,1]=>[4,2,1,1]=>2520
[4,2,7,5,6,3,8,1]=>[7,1]=>5760
[4,2,7,5,6,1,8,3]=>[4,3,1]=>3360
[4,2,6,7,5,3,1,8]=>[3,2,1,1,1]=>1120
[3,2,6,1,4,5,8,7]=>[5,2,1]=>4032
[2,8,7,3,4,5,1,6]=>[8]=>5040
[3,8,1,2,4,6,5,7]=>[5,2,1]=>4032
[5,8,7,6,1,3,4,2]=>[4,2,2]=>1260
[5,8,7,6,2,3,4,1]=>[4,4]=>1260
[4,1,7,5,6,2,3,8]=>[5,2,1]=>4032
[3,8,1,5,2,6,4,7]=>[5,2,1]=>4032
[2,8,7,5,3,4,1,6]=>[8]=>5040
[2,8,7,5,4,3,1,6]=>[6,2]=>3360
[4,1,7,5,6,3,2,8]=>[7,1]=>5760
[5,8,7,6,1,3,2,4]=>[6,2]=>3360
[5,8,7,6,4,1,2,3]=>[4,4]=>1260
[5,4,2,3,7,6,8,1]=>[4,3,1]=>3360
[7,4,3,5,2,8,1,6]=>[3,2,2,1]=>1680
[8,4,3,7,5,1,6,2]=>[6,1,1]=>3360
[8,4,7,2,5,1,6,3]=>[5,2,1]=>4032
[7,4,6,2,3,5,8,1]=>[3,3,2]=>1120
[5,1,7,2,4,6,8,3]=>[4,3,1]=>3360
[4,5,7,1,2,6,8,3]=>[3,2,2,1]=>1680
[5,4,1,7,3,6,8,2]=>[4,3,1]=>3360
[3,6,4,7,5,2,8,1]=>[5,2,1]=>4032
[3,4,7,6,2,5,8,1]=>[4,4]=>1260
[4,7,5,6,1,3,8,2]=>[5,3]=>2688
[5,7,6,4,3,1,8,2]=>[4,3,1]=>3360
[5,7,6,3,1,4,8,2]=>[3,3,2]=>1120
[7,5,2,3,4,8,1,6]=>[4,2,2]=>1260
[8,7,5,3,4,1,6,2]=>[5,3]=>2688
[6,7,1,3,8,4,2,5]=>[4,2,2]=>1260
[7,6,1,3,4,8,5,2]=>[5,3]=>2688
[3,6,5,2,7,8,1,4]=>[4,4]=>1260
[3,2,8,6,7,1,4,5]=>[7,1]=>5760
[4,8,3,6,5,2,1,7]=>[6,1,1]=>3360
[1,8,6,5,4,2,3,7]=>[5,2,1]=>4032
[1,8,7,2,3,5,4,6]=>[7,1]=>5760
[1,8,7,2,5,3,4,6]=>[6,1,1]=>3360
[3,6,8,5,1,2,4,7]=>[6,2]=>3360
[3,7,5,1,8,2,6,4]=>[5,3]=>2688
[7,1,2,8,3,5,6,4]=>[6,2]=>3360
[6,1,7,8,2,5,3,4]=>[4,2,2]=>1260
[6,7,5,2,8,1,4,3]=>[3,3,2]=>1120
[7,1,4,5,8,6,2,3]=>[4,3,1]=>3360
[5,7,6,4,2,8,1,3]=>[4,3,1]=>3360
[7,5,6,1,2,8,4,3]=>[3,3,2]=>1120
[4,1,3,7,8,6,2,5]=>[4,2,1,1]=>2520
[5,1,4,3,6,8,7,2]=>[5,2,1]=>4032
[4,5,7,6,8,2,1,3]=>[8]=>5040
[5,7,6,8,4,2,1,3]=>[8]=>5040
[5,1,6,8,4,2,7,3]=>[7,1]=>5760
[7,4,8,2,3,6,5,1]=>[5,2,1]=>4032
[5,6,8,4,7,3,2,1]=>[7,1]=>5760
[6,4,7,8,5,2,1,3]=>[7,1]=>5760
[3,6,4,8,5,1,2,7]=>[7,1]=>5760
[3,7,4,8,1,2,5,6]=>[8]=>5040
[7,4,3,8,2,6,5,1]=>[6,1,1]=>3360
[7,6,8,3,2,5,4,1]=>[5,3]=>2688
[8,7,1,3,5,4,6,2]=>[7,1]=>5760
[7,1,8,3,4,2,6,5]=>[4,4]=>1260
[7,6,8,3,1,4,5,2]=>[5,3]=>2688
[3,1,4,8,2,5,7,6]=>[7,1]=>5760
[4,8,5,2,1,3,6,7]=>[8]=>5040
[5,8,2,6,3,1,4,7]=>[8]=>5040
[6,8,2,3,7,4,1,5]=>[8]=>5040
[7,8,2,3,4,6,5,1]=>[7,1]=>5760
[8,1,7,2,4,5,3,6]=>[6,2]=>3360
[8,1,3,6,2,5,4,7]=>[7,1]=>5760
[7,2,1,6,3,5,4,8]=>[6,1,1]=>3360
[2,7,1,6,3,5,4,8]=>[7,1]=>5760
[2,7,1,5,4,3,6,8]=>[5,2,1]=>4032
[7,2,1,5,4,3,6,8]=>[4,2,1,1]=>2520
[8,1,3,5,4,2,6,7]=>[5,2,1]=>4032
[8,1,5,3,4,2,6,7]=>[5,3]=>2688
[8,1,5,6,2,3,7,4]=>[7,1]=>5760
[8,1,4,5,3,2,6,7]=>[5,3]=>2688
[8,1,4,3,5,2,6,7]=>[5,2,1]=>4032
[7,2,1,4,5,3,6,8]=>[4,1,1,1,1]=>420
[2,7,1,4,5,3,6,8]=>[5,1,1,1]=>1344
[2,6,3,1,5,4,7,8]=>[4,1,1,1,1]=>420
[6,3,2,1,5,4,7,8]=>[3,2,1,1,1]=>1120
[7,3,1,4,5,2,6,8]=>[5,1,1,1]=>1344
[7,3,1,5,4,2,6,8]=>[5,2,1]=>4032
[7,3,1,6,2,5,4,8]=>[7,1]=>5760
[3,7,1,6,2,5,4,8]=>[5,2,1]=>4032
[3,7,1,4,5,2,6,8]=>[3,2,1,1,1]=>1120
[3,6,2,1,5,4,7,8]=>[5,1,1,1]=>1344
[2,3,6,1,5,4,7,8]=>[5,1,1,1]=>1344
[3,5,2,4,1,6,7,8]=>[4,1,1,1,1]=>420
[6,3,4,1,5,2,7,8]=>[5,1,1,1]=>1344
[6,2,4,1,5,3,7,8]=>[4,1,1,1,1]=>420
[2,6,4,1,5,3,7,8]=>[5,1,1,1]=>1344
[2,6,5,1,3,7,4,8]=>[5,2,1]=>4032
[6,2,5,1,3,7,4,8]=>[4,2,1,1]=>2520
[6,5,2,1,3,7,4,8]=>[4,3,1]=>3360
[7,6,1,2,4,5,3,8]=>[4,3,1]=>3360
[6,7,1,2,8,3,5,4]=>[5,3]=>2688
[6,7,1,2,5,4,3,8]=>[6,1,1]=>3360
[5,6,2,1,3,7,4,8]=>[7,1]=>5760
[5,2,6,1,3,7,4,8]=>[6,1,1]=>3360
[2,4,6,1,5,3,7,8]=>[3,2,1,1,1]=>1120
[4,7,1,3,5,2,6,8]=>[3,3,1,1]=>1120
[4,7,1,5,3,2,6,8]=>[4,3,1]=>3360
[5,7,1,4,2,6,3,8]=>[5,1,1,1]=>1344
[5,7,1,6,2,3,8,4]=>[8]=>5040
[5,6,3,1,2,7,4,8]=>[6,1,1]=>3360
[4,2,5,3,1,6,7,8]=>[4,1,1,1,1]=>420
[5,3,6,1,2,7,4,8]=>[7,1]=>5760
[3,4,6,1,5,2,7,8]=>[5,1,1,1]=>1344
[6,5,1,8,7,3,4,2]=>[5,3]=>2688
[8,2,7,5,4,1,3,6]=>[3,2,2,1]=>1680
[6,8,5,2,3,4,1,7]=>[6,2]=>3360
[8,5,6,2,7,1,4,3]=>[4,4]=>1260
[6,5,1,2,7,8,4,3]=>[4,4]=>1260
[4,7,6,1,5,3,8,2]=>[3,2,2,1]=>1680
[5,7,6,4,1,3,8,2]=>[3,2,2,1]=>1680
[7,6,2,4,5,3,8,1]=>[3,3,1,1]=>1120
[6,1,7,5,3,8,4,2]=>[4,4]=>1260
[8,6,7,5,3,1,4,2]=>[4,4]=>1260
[8,5,2,7,1,6,4,3]=>[5,2,1]=>4032
[7,6,1,5,3,8,4,2]=>[5,3]=>2688
[5,6,2,4,7,8,1,3]=>[4,3,1]=>3360
[3,4,6,1,7,8,5,2]=>[6,2]=>3360
[3,4,8,6,7,1,5,2]=>[6,2]=>3360
[4,8,5,6,7,2,3,1]=>[5,3]=>2688
[5,8,6,4,1,2,7,3]=>[4,2,1,1]=>2520
[5,8,6,1,7,2,4,3]=>[4,4]=>1260
[5,8,7,3,2,6,4,1]=>[4,3,1]=>3360
[5,8,1,7,2,6,4,3]=>[5,2,1]=>4032
[8,1,5,7,2,6,4,3]=>[5,2,1]=>4032
[8,1,7,2,5,6,3,4]=>[4,2,1,1]=>2520
[6,8,7,2,5,1,3,4]=>[3,2,2,1]=>1680
[5,8,7,2,1,6,3,4]=>[3,2,2,1]=>1680
[4,8,1,5,2,6,7,3]=>[6,1,1]=>3360
[3,7,8,5,1,6,2,4]=>[5,2,1]=>4032
[6,5,2,7,8,1,4,3]=>[4,2,2]=>1260
[7,1,2,8,5,6,3,4]=>[4,2,1,1]=>2520
[8,7,2,1,5,6,3,4]=>[3,3,1,1]=>1120
[8,6,7,1,5,2,3,4]=>[3,2,2,1]=>1680
[6,1,7,8,5,2,3,4]=>[3,2,2,1]=>1680
[7,5,6,2,1,8,4,3]=>[5,3]=>2688
[8,7,5,2,1,6,4,3]=>[4,3,1]=>3360
[7,1,3,5,8,6,2,4]=>[3,3,1,1]=>1120
[5,1,3,4,6,8,7,2]=>[5,1,1,1]=>1344
[4,5,3,6,8,2,7,1]=>[6,1,1]=>3360
[5,6,3,4,8,1,7,2]=>[5,1,1,1]=>1344
[4,6,7,8,5,1,3,2]=>[5,2,1]=>4032
[8,4,3,1,2,6,7,5]=>[5,1,1,1]=>1344
[8,5,1,6,3,4,7,2]=>[5,2,1]=>4032
[5,1,8,6,3,4,7,2]=>[5,2,1]=>4032
[4,6,8,1,5,3,7,2]=>[4,2,1,1]=>2520
[6,4,5,8,3,2,7,1]=>[5,2,1]=>4032
[3,6,4,8,7,1,5,2]=>[6,2]=>3360
[6,5,8,1,3,4,7,2]=>[4,3,1]=>3360
[5,6,8,3,1,2,7,4]=>[3,2,2,1]=>1680
[6,1,8,3,5,2,7,4]=>[3,3,1,1]=>1120
[7,6,8,3,5,2,1,4]=>[3,2,2,1]=>1680
[8,6,1,3,5,2,7,4]=>[4,2,1,1]=>2520
[8,7,1,3,5,6,2,4]=>[4,2,1,1]=>2520
[6,7,8,3,5,1,2,4]=>[3,2,2,1]=>1680
[3,4,8,1,2,6,7,5]=>[6,1,1]=>3360
[5,8,2,4,3,6,7,1]=>[5,1,1,1]=>1344
[5,8,2,3,1,6,7,4]=>[4,2,1,1]=>2520
[6,8,2,3,5,1,7,4]=>[4,2,1,1]=>2520
[7,8,2,3,5,6,1,4]=>[4,2,1,1]=>2520
[8,6,5,1,4,3,7,2]=>[7,1]=>5760
[2,6,5,4,1,3,8,7]=>[5,2,1]=>4032
[4,1,7,6,3,8,2,5]=>[8]=>5040
[4,8,2,5,7,6,3,1]=>[7,1]=>5760
[3,4,6,5,1,8,2,7]=>[8]=>5040
[2,6,5,3,4,1,8,7]=>[3,3,2]=>1120
[4,6,1,5,2,3,8,7]=>[6,2]=>3360
[6,2,3,5,1,4,8,7]=>[4,2,1,1]=>2520
[2,6,7,5,1,8,4,3]=>[8]=>5040
[8,6,1,2,5,3,4,7]=>[7,1]=>5760
[6,2,5,1,8,3,4,7]=>[7,1]=>5760
[7,6,5,2,8,3,4,1]=>[8]=>5040
[2,6,3,5,1,8,7,4]=>[6,1,1]=>3360
[2,4,7,6,5,8,1,3]=>[7,1]=>5760
[2,1,4,8,7,6,3,5]=>[5,2,1]=>4032
[7,4,6,8,5,3,2,1]=>[5,2,1]=>4032
[8,1,3,5,7,4,6,2]=>[4,3,1]=>3360
[3,2,8,7,5,1,6,4]=>[6,1,1]=>3360
[4,8,5,1,6,7,2,3]=>[6,2]=>3360
[3,8,5,1,6,7,2,4]=>[8]=>5040
[7,8,6,1,3,5,2,4]=>[5,3]=>2688
[5,6,7,2,8,1,3,4]=>[6,2]=>3360
[2,5,1,8,6,7,4,3]=>[8]=>5040
[3,5,1,8,6,7,4,2]=>[6,2]=>3360
[5,2,3,8,6,7,4,1]=>[6,1,1]=>3360
[8,3,5,4,6,7,1,2]=>[7,1]=>5760
[5,1,3,8,6,7,4,2]=>[7,1]=>5760
[3,2,5,8,6,7,4,1]=>[7,1]=>5760
[6,2,1,5,3,8,7,4]=>[6,1,1]=>3360
[5,6,3,2,8,1,4,7]=>[7,1]=>5760
[8,1,6,3,5,2,7,4]=>[6,1,1]=>3360
[8,7,6,2,5,3,1,4]=>[5,2,1]=>4032
[4,7,6,8,3,2,5,1]=>[5,3]=>2688
[2,7,5,8,1,3,4,6]=>[8]=>5040
[7,6,2,8,5,1,4,3]=>[7,1]=>5760
[8,1,3,7,5,2,6,4]=>[6,1,1]=>3360
[3,4,8,7,5,1,6,2]=>[7,1]=>5760
[6,3,8,1,4,2,5,7]=>[8]=>5040
[6,3,8,5,7,4,1,2]=>[5,3]=>2688
[7,4,6,8,5,1,3,2]=>[4,3,1]=>3360
[2,1,4,8,7,5,6,3]=>[3,3,2]=>1120
[7,1,5,8,2,6,4,3]=>[7,1]=>5760
[3,6,8,2,4,1,7,5]=>[7,1]=>5760
[4,5,8,2,6,7,3,1]=>[8]=>5040
[5,2,8,1,6,7,3,4]=>[7,1]=>5760
[2,5,8,4,6,7,3,1]=>[7,1]=>5760
[5,8,3,4,6,7,2,1]=>[6,1,1]=>3360
[8,4,3,2,6,7,1,5]=>[5,2,1]=>4032
[4,2,8,1,6,7,3,5]=>[5,2,1]=>4032
[2,4,8,1,6,7,3,5]=>[5,3]=>2688
[5,1,8,2,6,7,3,4]=>[8]=>5040
[3,4,8,7,2,1,5,6]=>[4,4]=>1260
[7,8,5,3,6,4,2,1]=>[4,4]=>1260
[2,8,5,7,4,1,3,6]=>[4,4]=>1260
[5,8,4,1,6,7,2,3]=>[8]=>5040
[3,8,1,4,6,7,2,5]=>[5,2,1]=>4032
[8,2,3,4,6,7,1,5]=>[5,1,1,1]=>1344
[6,2,7,3,8,4,1,5]=>[5,2,1]=>4032
[7,4,3,2,8,5,1,6]=>[3,2,2,1]=>1680
[5,3,2,8,4,6,1,7]=>[5,2,1]=>4032
[8,4,2,6,5,3,1,7]=>[4,3,1]=>3360
[7,4,2,5,3,1,6,8]=>[4,3,1]=>3360
[8,3,6,2,5,4,1,7]=>[4,3,1]=>3360
[5,4,8,3,2,6,1,7]=>[7,1]=>5760
[3,5,8,2,4,6,1,7]=>[4,3,1]=>3360
[6,4,7,8,2,3,1,5]=>[4,4]=>1260
[5,8,3,6,4,2,1,7]=>[7,1]=>5760
[4,8,6,2,5,3,1,7]=>[5,2,1]=>4032
[1,6,4,3,2,8,7,5]=>[4,2,1,1]=>2520
[1,5,3,2,8,4,7,6]=>[5,1,1,1]=>1344
[5,7,4,3,1,2,6,8]=>[3,2,2,1]=>1680
[2,8,7,3,5,1,4,6]=>[4,3,1]=>3360
[7,3,8,6,4,1,2,5]=>[8]=>5040
[6,1,2,7,3,8,5,4]=>[8]=>5040
[2,1,7,4,3,8,6,5]=>[5,2,1]=>4032
[6,1,4,3,8,2,7,5]=>[3,2,2,1]=>1680
[5,1,3,2,8,7,4,6]=>[7,1]=>5760
[1,8,4,2,7,6,5,3]=>[4,2,1,1]=>2520
[1,8,3,7,2,6,5,4]=>[5,1,1,1]=>1344
[5,1,4,8,3,7,2,6]=>[8]=>5040
[2,1,6,8,5,4,7,3]=>[4,2,1,1]=>2520
[6,1,5,7,8,2,4,3]=>[3,3,2]=>1120
[8,3,1,6,7,2,5,4]=>[6,2]=>3360
[7,4,8,6,1,3,2,5]=>[8]=>5040
[4,7,6,1,2,5,3,8]=>[5,2,1]=>4032
[3,7,6,1,5,2,4,8]=>[6,1,1]=>3360
[1,5,4,8,3,2,7,6]=>[6,1,1]=>3360
[7,3,6,1,2,5,4,8]=>[4,3,1]=>3360
[5,4,7,1,3,2,6,8]=>[7,1]=>5760
[5,7,4,8,2,1,3,6]=>[8]=>5040
[4,6,8,2,5,1,3,7]=>[4,3,1]=>3360
[7,4,6,2,1,5,3,8]=>[5,2,1]=>4032
[1,2,6,3,8,5,7,4]=>[5,1,1,1]=>1344
[1,5,2,6,8,4,7,3]=>[4,2,1,1]=>2520
[5,7,2,3,8,1,4,6]=>[4,4]=>1260
[6,4,7,5,8,1,2,3]=>[6,2]=>3360
[7,4,8,5,1,6,3,2]=>[7,1]=>5760
[5,8,3,6,1,7,4,2]=>[3,2,2,1]=>1680
[8,6,4,2,1,7,5,3]=>[8]=>5040
[7,4,2,1,5,8,6,3]=>[7,1]=>5760
[7,6,4,1,8,5,2,3]=>[8]=>5040
[1,6,4,8,7,5,3,2]=>[7,1]=>5760
[6,3,1,2,8,4,7,5]=>[5,2,1]=>4032
[7,5,1,3,2,8,6,4]=>[6,2]=>3360
[4,7,1,2,5,8,6,3]=>[7,1]=>5760
[6,8,4,1,2,7,5,3]=>[8]=>5040
[7,5,8,1,2,6,4,3]=>[3,2,2,1]=>1680
[7,4,8,1,6,3,5,2]=>[8]=>5040
[5,8,2,1,7,3,6,4]=>[8]=>5040
[3,6,1,8,2,4,7,5]=>[5,2,1]=>4032
[1,3,8,7,6,2,5,4]=>[7,1]=>5760
[5,4,1,8,7,3,2,6]=>[8]=>5040
[3,5,1,8,7,2,4,6]=>[6,2]=>3360
[4,6,1,8,3,7,2,5]=>[5,3]=>2688
[4,7,1,2,8,6,3,5]=>[5,2,1]=>4032
[5,8,4,1,7,6,2,3]=>[7,1]=>5760
[7,6,8,1,5,4,2,3]=>[5,2,1]=>4032
[8,6,1,7,5,4,3,2]=>[7,1]=>5760
[7,1,5,8,6,4,3,2]=>[8]=>5040
[5,1,8,7,3,6,4,2]=>[5,2,1]=>4032
[4,1,8,7,6,2,5,3]=>[6,2]=>3360
[3,1,8,7,6,5,2,4]=>[6,2]=>3360
[1,6,4,5,2,3,7,8]=>[5,1,1,1]=>1344
[1,7,4,5,2,3,6,8]=>[6,1,1]=>3360
[1,7,3,5,2,4,6,8]=>[5,1,1,1]=>1344
[1,6,3,5,2,4,7,8]=>[4,1,1,1,1]=>420
[1,6,3,4,2,5,7,8]=>[3,1,1,1,1,1]=>112
[1,7,3,4,2,5,6,8]=>[4,1,1,1,1]=>420
[1,8,6,7,3,4,2,5]=>[7,1]=>5760
[1,8,5,7,3,4,2,6]=>[5,2,1]=>4032
[1,7,3,4,2,6,5,8]=>[3,1,1,1,1,1]=>112
[1,5,2,8,4,7,3,6]=>[7,1]=>5760
[1,4,2,8,5,7,3,6]=>[6,1,1]=>3360
[1,7,3,5,2,6,4,8]=>[4,1,1,1,1]=>420
[1,8,4,7,3,5,2,6]=>[7,1]=>5760
[1,7,3,6,2,5,4,8]=>[5,1,1,1]=>1344
[1,7,3,6,2,4,5,8]=>[3,2,1,1,1]=>1120
[1,7,4,6,2,3,5,8]=>[3,3,1,1]=>1120
[1,8,5,6,2,3,4,7]=>[7,1]=>5760
[1,8,5,6,2,4,3,7]=>[5,2,1]=>4032
[1,3,2,8,5,6,4,7]=>[3,2,1,1,1]=>1120
[1,4,2,8,5,6,3,7]=>[5,1,1,1]=>1344
[1,5,2,8,4,6,3,7]=>[6,1,1]=>3360
[1,6,2,8,4,5,3,7]=>[7,1]=>5760
[9,1,2,3,5,4,6,7,8]=>[8,1]=>45360
[8,1,2,4,5,3,6,7]=>[6,1,1]=>3360
[2,3,4,6,5,7,8,9,1]=>[8,1]=>45360
[10,1,2,3,4,6,5,7,8,9]=>[9,1]=>403200
[9,1,2,3,5,6,4,7,8]=>[7,1,1]=>25920
[2,3,4,7,5,6,8,9,1]=>[7,1,1]=>25920
[2,3,4,6,7,5,8,9,1]=>[9]=>40320
[2,3,4,5,7,6,8,9,10,1]=>[9,1]=>403200
[9,10,5,6,7,8,3,4,1,2]=>[3,3,2,2]=>25200
[5,8,9,6,7,10,3,4,1,2]=>[5,5]=>72576
[9,10,7,8,3,4,5,6,1,2]=>[3,3,2,2]=>25200
[9,10,3,6,7,4,5,8,1,2]=>[2,2,2,2,1,1]=>4725
[3,8,9,6,7,4,5,10,1,2]=>[3,3,2,2]=>25200
[3,6,7,8,9,4,5,10,1,2]=>[5,5]=>72576
[9,10,3,4,5,6,7,8,1,2]=>[2,2,1,1,1,1,1,1]=>630
[3,8,9,4,5,6,7,10,1,2]=>[3,3,1,1,1,1]=>8400
[3,4,7,8,5,6,9,10,1,2]=>[4,4,1,1]=>56700
[7,8,9,10,5,6,1,2,3,4]=>[2,2,2,2,1,1]=>4725
[5,8,9,6,7,10,1,2,3,4]=>[3,3,2,2]=>25200
[9,10,7,8,1,4,5,2,3,6]=>[5,5]=>72576
[7,8,9,10,1,4,5,2,3,6]=>[3,3,2,2]=>25200
[9,10,1,6,7,4,5,2,3,8]=>[3,3,2,2]=>25200
[1,8,9,6,7,4,5,2,3,10]=>[2,2,2,2,1,1]=>4725
[1,6,7,8,9,4,5,2,3,10]=>[4,4,1,1]=>56700
[9,10,1,4,5,6,7,2,3,8]=>[3,3,1,1,1,1]=>8400
[1,8,9,4,5,6,7,2,3,10]=>[2,2,1,1,1,1,1,1]=>630
[1,4,7,8,5,6,9,2,3,10]=>[3,3,1,1,1,1]=>8400
[1,4,5,6,7,8,9,2,3,10]=>[4,4,1,1]=>56700
[9,10,1,6,7,2,3,4,5,8]=>[5,5]=>72576
[1,8,9,6,7,2,3,4,5,10]=>[4,4,1,1]=>56700
[1,6,7,8,9,2,3,4,5,10]=>[2,2,2,2,1,1]=>4725
[9,10,1,2,5,6,3,4,7,8]=>[4,4,1,1]=>56700
[1,8,9,2,5,6,3,4,7,10]=>[3,3,1,1,1,1]=>8400
[1,2,7,8,5,6,3,4,9,10]=>[2,2,1,1,1,1,1,1]=>630
[1,2,5,6,7,8,3,4,9,10]=>[3,3,1,1,1,1]=>8400
[1,8,9,2,3,4,5,6,7,10]=>[4,4,1,1]=>56700
[1,2,7,8,3,4,5,6,9,10]=>[3,3,1,1,1,1]=>8400
[1,2,3,6,7,4,5,8,9,10]=>[2,2,1,1,1,1,1,1]=>630
[9,10,11,12,7,8,5,6,3,4,1,2]=>[4,4,2,2]=>1871100
[11,12,7,8,9,10,5,6,3,4,1,2]=>[4,4,2,2]=>1871100
[7,10,11,8,9,12,5,6,3,4,1,2]=>[6,6]=>6652800
[7,8,9,10,11,12,5,6,3,4,1,2]=>[4,4,2,2]=>1871100
[11,12,5,8,9,6,7,10,3,4,1,2]=>[3,3,2,2,1,1]=>1663200
[5,8,9,10,11,6,7,12,3,4,1,2]=>[3,3,2,2,1,1]=>1663200
[11,12,5,6,7,8,9,10,3,4,1,2]=>[4,4,2,2]=>1871100
[5,10,11,6,7,8,9,12,3,4,1,2]=>[6,6]=>6652800
[5,6,9,10,7,8,11,12,3,4,1,2]=>[4,4,2,2]=>1871100
[5,6,7,8,9,10,11,12,3,4,1,2]=>[6,6]=>6652800
[11,12,9,10,7,8,3,4,5,6,1,2]=>[4,4,2,2]=>1871100
[9,10,11,12,7,8,3,4,5,6,1,2]=>[6,6]=>6652800
[11,12,7,8,9,10,3,4,5,6,1,2]=>[2,2,2,2,2,2]=>10395
[7,10,11,8,9,12,3,4,5,6,1,2]=>[4,4,2,2]=>1871100
[7,8,9,10,11,12,3,4,5,6,1,2]=>[6,6]=>6652800
[11,12,9,10,3,6,7,4,5,8,1,2]=>[3,3,2,2,1,1]=>1663200
[3,10,11,8,9,6,7,4,5,12,1,2]=>[3,3,2,2,1,1]=>1663200
[11,12,3,6,7,8,9,4,5,10,1,2]=>[3,3,2,2,1,1]=>1663200
[3,10,11,6,7,8,9,4,5,12,1,2]=>[3,3,3,3]=>246400
[3,6,9,10,7,8,11,4,5,12,1,2]=>[6,6]=>6652800
[3,6,7,8,9,10,11,4,5,12,1,2]=>[4,4,2,2]=>1871100
[11,12,9,10,3,4,5,6,7,8,1,2]=>[4,4,2,2]=>1871100
[9,10,11,12,3,4,5,6,7,8,1,2]=>[6,6]=>6652800
[11,12,3,8,9,4,5,6,7,10,1,2]=>[3,3,2,2,1,1]=>1663200
[3,10,11,8,9,4,5,6,7,12,1,2]=>[3,3,3,3]=>246400
[3,8,9,10,11,4,5,6,7,12,1,2]=>[6,6]=>6652800
[3,10,11,4,7,8,5,6,9,12,1,2]=>[3,3,2,2,1,1]=>1663200
[3,4,9,10,7,8,5,6,11,12,1,2]=>[4,4,2,2]=>1871100
[3,4,7,8,9,10,5,6,11,12,1,2]=>[6,6]=>6652800
[3,4,5,6,7,8,9,10,11,12,1,2]=>[6,6]=>6652800
[11,12,9,10,7,8,5,6,1,2,3,4]=>[4,4,2,2]=>1871100
[9,10,11,12,7,8,5,6,1,2,3,4]=>[2,2,2,2,2,2]=>10395
[11,12,7,8,9,10,5,6,1,2,3,4]=>[6,6]=>6652800
[7,10,11,8,9,12,5,6,1,2,3,4]=>[4,4,2,2]=>1871100
[7,8,9,10,11,12,5,6,1,2,3,4]=>[6,6]=>6652800
[5,10,11,8,9,6,7,12,1,2,3,4]=>[3,3,2,2,1,1]=>1663200
[11,12,5,6,7,8,9,10,1,2,3,4]=>[6,6]=>6652800
[5,10,11,6,7,8,9,12,1,2,3,4]=>[4,4,2,2]=>1871100
[5,6,9,10,7,8,11,12,1,2,3,4]=>[6,6]=>6652800
[5,6,7,8,9,10,11,12,1,2,3,4]=>[3,3,3,3]=>246400
[11,12,9,10,7,8,1,4,5,2,3,6]=>[6,6]=>6652800
[9,10,11,12,7,8,1,4,5,2,3,6]=>[4,4,2,2]=>1871100
[11,12,7,8,9,10,1,4,5,2,3,6]=>[4,4,2,2]=>1871100
[7,10,11,8,9,12,1,4,5,2,3,6]=>[2,2,2,2,2,2]=>10395
[7,8,9,10,11,12,1,4,5,2,3,6]=>[4,4,2,2]=>1871100
[9,10,11,12,1,6,7,4,5,2,3,8]=>[3,3,2,2,1,1]=>1663200
[11,12,1,8,9,6,7,4,5,2,3,10]=>[3,3,2,2,1,1]=>1663200
[11,12,1,6,7,8,9,4,5,2,3,10]=>[3,3,3,3]=>246400
[1,10,11,6,7,8,9,4,5,2,3,12]=>[3,3,2,2,1,1]=>1663200
[1,6,7,8,9,10,11,4,5,2,3,12]=>[3,3,2,2,1,1]=>1663200
[11,12,9,10,1,4,5,6,7,2,3,8]=>[6,6]=>6652800
[9,10,11,12,1,4,5,6,7,2,3,8]=>[4,4,2,2]=>1871100
[11,12,1,8,9,4,5,6,7,2,3,10]=>[3,3,3,3]=>246400
[1,10,11,8,9,4,5,6,7,2,3,12]=>[3,3,2,2,1,1]=>1663200
[11,12,1,4,7,8,5,6,9,2,3,10]=>[3,3,2,2,1,1]=>1663200
[1,4,9,10,7,8,5,6,11,2,3,12]=>[3,3,2,2,1,1]=>1663200
[11,12,9,10,7,8,1,2,3,4,5,6]=>[4,4,2,2]=>1871100
[9,10,11,12,7,8,1,2,3,4,5,6]=>[6,6]=>6652800
[11,12,7,8,9,10,1,2,3,4,5,6]=>[6,6]=>6652800
[7,10,11,8,9,12,1,2,3,4,5,6]=>[4,4,2,2]=>1871100
[11,12,9,10,1,6,7,2,3,4,5,8]=>[3,3,2,2,1,1]=>1663200
[11,12,1,6,7,8,9,2,3,4,5,10]=>[6,6]=>6652800
[1,6,9,10,7,8,11,2,3,4,5,12]=>[3,3,2,2,1,1]=>1663200
[11,12,9,10,1,2,5,6,3,4,7,8]=>[4,4,2,2]=>1871100
[9,10,11,12,1,2,5,6,3,4,7,8]=>[6,6]=>6652800
[11,12,1,8,9,2,5,6,3,4,7,10]=>[6,6]=>6652800
[1,8,9,10,11,2,5,6,3,4,7,12]=>[3,3,2,2,1,1]=>1663200
[11,12,1,2,7,8,5,6,3,4,9,10]=>[4,4,2,2]=>1871100
[1,10,11,2,7,8,5,6,3,4,9,12]=>[3,3,2,2,1,1]=>1663200
[11,12,9,10,1,2,3,4,5,6,7,8]=>[6,6]=>6652800
[9,10,11,12,1,2,3,4,5,6,7,8]=>[3,3,3,3]=>246400
[11,12,1,8,9,2,3,4,5,6,7,10]=>[4,4,2,2]=>1871100
[1,10,11,8,9,2,3,4,5,6,7,12]=>[3,3,2,2,1,1]=>1663200
[11,12,1,2,7,8,3,4,5,6,9,10]=>[6,6]=>6652800
[11,12,1,2,3,4,5,6,7,8,9,10]=>[6,6]=>6652800
[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[8,6,4,7,2,1,3,5]=>[5,3]=>2688
[1,6,4,7,2,8,3,5]=>[4,3,1]=>3360
[1,4,7,3,5,8,2,6]=>[4,2,1,1]=>2520
[8,4,6,2,3,5,1,7]=>[3,3,2]=>1120
[5,4,8,2,3,6,1,7]=>[5,2,1]=>4032
[7,4,8,5,2,3,1,6]=>[3,3,2]=>1120
[3,8,6,2,4,5,1,7]=>[8]=>5040
[4,8,6,2,3,5,1,7]=>[5,3]=>2688
[1,7,5,3,4,8,2,6]=>[3,2,2,1]=>1680
[1,7,6,4,8,2,3,5]=>[4,2,1,1]=>2520
[5,8,7,4,1,2,3,6]=>[3,2,2,1]=>1680
[6,8,5,3,4,1,2,7]=>[3,3,2]=>1120
[6,8,3,7,2,1,4,5]=>[3,2,2,1]=>1680
[8,5,1,6,3,7,2,4]=>[8]=>5040
[6,1,3,7,4,8,2,5]=>[7,1]=>5760
[4,1,7,3,5,8,2,6]=>[5,2,1]=>4032
[7,1,6,4,8,2,3,5]=>[5,2,1]=>4032
[1,8,5,7,2,3,4,6]=>[5,2,1]=>4032
[6,1,5,8,2,3,4,7]=>[5,3]=>2688
[5,1,7,3,8,2,4,6]=>[5,3]=>2688
[6,1,5,7,8,2,3,4]=>[5,3]=>2688
[7,4,8,6,1,2,3,5]=>[5,3]=>2688
[3,8,7,5,1,2,4,6]=>[5,3]=>2688
[3,7,6,1,2,4,5,8]=>[4,3,1]=>3360
[4,7,6,1,2,3,5,8]=>[3,2,2,1]=>1680
[1,6,5,8,2,3,4,7]=>[4,3,1]=>3360
[6,5,8,4,1,2,3,7]=>[4,3,1]=>3360
[8,5,7,4,1,2,3,6]=>[5,2,1]=>4032
[1,5,7,4,8,2,3,6]=>[4,2,1,1]=>2520
[7,6,4,8,2,1,3,5]=>[8]=>5040
[7,6,2,3,8,1,4,5]=>[6,2]=>3360
[7,4,8,5,1,6,2,3]=>[5,2,1]=>4032
[8,6,2,3,1,7,4,5]=>[5,3]=>2688
[8,6,4,1,2,7,3,5]=>[8]=>5040
[1,7,2,8,6,3,4,5]=>[7,1]=>5760
[7,6,1,3,8,2,4,5]=>[4,2,2]=>1260
[7,5,8,1,3,6,2,4]=>[7,1]=>5760
[5,4,1,8,2,3,6,7]=>[8]=>5040
[1,4,8,7,2,3,5,6]=>[4,3,1]=>3360
[1,5,8,7,2,3,4,6]=>[3,2,2,1]=>1680
[6,5,1,8,2,3,4,7]=>[3,3,2]=>1120
[5,7,1,3,8,2,4,6]=>[8]=>5040
[7,6,8,1,5,2,3,4]=>[5,2,1]=>4032
[7,1,5,8,6,2,3,4]=>[6,2]=>3360
[6,1,8,2,7,3,4,5]=>[8]=>5040
[4,1,8,7,2,3,5,6]=>[5,3]=>2688
[5,1,8,7,2,3,4,6]=>[3,3,2]=>1120
[1,8,7,6,4,5,3,2]=>[3,2,2,1]=>1680
[9,8,7,6,4,5,3,2,1,10]=>[3,2,2,2,1]=>25200
[1,8,7,3,6,5,4,2]=>[3,2,2,1]=>1680
[6,4,2,7,5,8,3,1]=>[4,3,1]=>3360
[2,4,1,7,5,8,3,6]=>[5,2,1]=>4032
[7,1,4,6,5,8,2,3]=>[4,3,1]=>3360
[7,1,4,6,3,8,2,5]=>[5,3]=>2688
[7,1,4,6,5,3,2,8]=>[3,3,1,1]=>1120
[6,4,2,7,5,3,8,1]=>[7,1]=>5760
[3,4,7,1,6,8,2,5]=>[5,3]=>2688
[3,4,1,7,8,6,2,5]=>[3,2,2,1]=>1680
[6,4,2,7,5,3,1,8]=>[6,1,1]=>3360
[4,8,3,2,5,6,1,7]=>[5,1,1,1]=>1344
[4,8,7,3,5,1,2,6]=>[7,1]=>5760
[3,4,7,2,6,5,8,1]=>[4,2,2]=>1260
[4,8,3,1,2,6,7,5]=>[3,2,1,1,1]=>1120
[5,4,7,3,6,2,8,1]=>[8]=>5040
[6,4,3,7,5,1,8,2]=>[4,2,1,1]=>2520
[3,8,7,4,1,5,2,6]=>[7,1]=>5760
[5,8,3,2,1,6,4,7]=>[4,2,1,1]=>2520
[5,4,7,3,6,2,1,8]=>[7,1]=>5760
[7,3,8,2,1,6,5,4]=>[4,3,1]=>3360
[7,4,3,8,5,2,1,6]=>[4,2,1,1]=>2520
[6,5,2,8,4,3,1,7]=>[8]=>5040
[4,3,2,8,6,5,1,7]=>[4,2,2]=>1260
[4,3,8,7,5,1,6,2]=>[4,3,1]=>3360
[3,2,5,8,6,1,4,7]=>[4,3,1]=>3360
[8,4,3,7,5,2,6,1]=>[4,2,1,1]=>2520
[4,3,7,8,5,1,2,6]=>[4,3,1]=>3360
[5,3,7,8,4,1,2,6]=>[5,3]=>2688
[6,2,5,8,3,1,4,7]=>[3,2,2,1]=>1680
[6,2,4,8,3,1,5,7]=>[5,2,1]=>4032
[5,2,3,8,4,1,6,7]=>[6,1,1]=>3360
[5,3,8,7,4,1,6,2]=>[5,3]=>2688
[5,3,2,8,6,4,1,7]=>[6,2]=>3360
[7,5,3,8,4,2,1,6]=>[5,2,1]=>4032
[8,7,5,3,6,2,4,1]=>[6,2]=>3360
[8,6,5,3,7,2,4,1]=>[4,2,2]=>1260
[7,5,4,3,8,2,6,1]=>[6,2]=>3360
[6,4,5,3,8,2,7,1]=>[7,1]=>5760
[7,4,6,3,8,2,5,1]=>[4,4]=>1260
[7,5,6,3,8,2,4,1]=>[8]=>5040
[8,5,6,3,7,2,4,1]=>[6,2]=>3360
[7,4,6,3,5,2,8,1]=>[4,3,1]=>3360
[8,4,6,3,5,2,7,1]=>[4,2,1,1]=>2520
[8,4,7,3,5,2,6,1]=>[5,2,1]=>4032
[8,5,7,3,4,2,6,1]=>[6,2]=>3360
[7,5,8,4,3,2,6,1]=>[7,1]=>5760
[6,5,8,4,3,2,7,1]=>[6,1,1]=>3360
[6,5,8,3,4,2,7,1]=>[7,1]=>5760
[7,5,8,3,4,2,6,1]=>[8]=>5040
[7,5,8,4,6,2,3,1]=>[4,3,1]=>3360
[7,4,8,3,6,2,5,1]=>[8]=>5040
[7,4,8,3,5,2,6,1]=>[7,1]=>5760
[6,4,8,3,5,2,7,1]=>[6,1,1]=>3360
[6,4,7,3,5,2,8,1]=>[7,1]=>5760
[5,4,8,3,7,2,6,1]=>[8]=>5040
[6,5,8,3,7,2,4,1]=>[8]=>5040
[6,5,8,4,7,2,3,1]=>[7,1]=>5760
[6,5,8,4,7,3,2,1]=>[4,3,1]=>3360
[6,4,7,3,8,2,5,1]=>[8]=>5040
[5,4,7,3,8,2,6,1]=>[5,3]=>2688
[5,4,6,3,8,2,7,1]=>[4,3,1]=>3360
[5,3,6,2,4,7,8,1]=>[8]=>5040
[4,2,1,5,8,6,3,7]=>[6,1,1]=>3360
[4,2,1,5,8,7,6,3]=>[5,2,1]=>4032
[4,3,1,7,5,8,6,2]=>[7,1]=>5760
[6,7,3,1,4,8,2,5]=>[5,2,1]=>4032
[3,2,1,8,5,4,6,7]=>[4,2,1,1]=>2520
[5,2,7,1,8,4,3,6]=>[5,2,1]=>4032
[4,2,1,6,8,7,5,3]=>[7,1]=>5760
[4,2,1,6,8,5,3,7]=>[7,1]=>5760
[5,2,6,1,8,7,4,3]=>[7,1]=>5760
[5,2,6,1,8,3,4,7]=>[5,2,1]=>4032
[4,2,1,6,8,3,7,5]=>[4,2,1,1]=>2520
[4,2,1,7,8,6,3,5]=>[4,2,1,1]=>2520
[3,2,1,8,6,4,7,5]=>[4,2,1,1]=>2520
[3,2,1,8,6,4,5,7]=>[5,2,1]=>4032
[3,2,1,8,4,6,5,7]=>[4,2,1,1]=>2520
[3,2,1,8,4,6,7,5]=>[3,2,1,1,1]=>1120
[3,2,1,8,4,7,6,5]=>[3,2,2,1]=>1680
[3,2,1,8,7,4,6,5]=>[5,2,1]=>4032
[5,2,7,1,8,3,4,6]=>[7,1]=>5760
[4,2,1,7,8,3,5,6]=>[7,1]=>5760
[3,2,1,8,4,5,7,6]=>[4,2,1,1]=>2520
[7,5,2,8,6,3,4,1]=>[4,4]=>1260
[7,4,8,6,2,5,3,1]=>[4,4]=>1260
[7,3,8,6,2,4,5,1]=>[6,2]=>3360
[7,3,8,5,2,4,6,1]=>[8]=>5040
[7,3,8,4,5,6,2,1]=>[5,1,1,1]=>1344
[6,3,8,2,4,5,1,7]=>[8]=>5040
[6,4,3,8,1,5,2,7]=>[4,3,1]=>3360
[6,3,7,8,2,4,1,5]=>[8]=>5040
[5,6,7,3,8,2,4,1]=>[3,3,2]=>1120
[5,3,8,2,4,6,7,1]=>[6,1,1]=>3360
[5,6,3,7,8,2,4,1]=>[3,2,2,1]=>1680
[6,3,7,2,5,8,4,1]=>[4,3,1]=>3360
[5,3,6,8,2,4,7,1]=>[7,1]=>5760
[5,3,6,7,8,2,4,1]=>[3,3,2]=>1120
[3,6,4,2,1,5,8,7]=>[6,2]=>3360
[3,5,8,6,4,2,1,7]=>[4,4]=>1260
[5,8,6,3,4,2,1,7]=>[8]=>5040
[5,6,3,4,2,1,8,7]=>[4,2,1,1]=>2520
[6,3,4,2,1,5,8,7]=>[3,3,2]=>1120
[5,6,4,2,1,3,8,7]=>[4,2,2]=>1260
[2,5,4,1,7,8,6,3]=>[8]=>5040
[2,7,8,5,4,1,6,3]=>[4,2,2]=>1260
[2,8,5,4,1,6,3,7]=>[6,1,1]=>3360
[2,6,3,8,5,4,1,7]=>[6,1,1]=>3360
[2,8,6,3,5,4,1,7]=>[4,3,1]=>3360
[5,8,6,4,2,1,3,7]=>[7,1]=>5760
[4,2,1,5,7,8,6,3]=>[7,1]=>5760
[2,7,8,6,3,5,4,1]=>[8]=>5040
[4,3,8,5,7,6,2,1]=>[7,1]=>5760
[7,6,2,1,8,4,3,5]=>[6,2]=>3360
[2,1,8,5,6,4,3,7]=>[3,3,2]=>1120
[4,2,1,8,5,6,3,7]=>[5,1,1,1]=>1344
[8,4,2,1,5,6,3,7]=>[6,1,1]=>3360
[2,5,6,3,8,4,1,7]=>[5,3]=>2688
[6,3,4,2,1,8,5,7]=>[5,3]=>2688
[3,7,8,5,6,4,2,1]=>[3,3,2]=>1120
[3,8,5,6,4,2,1,7]=>[8]=>5040
[3,6,4,2,1,8,5,7]=>[8]=>5040
[3,8,6,4,2,1,5,7]=>[4,3,1]=>3360
[3,7,8,6,4,2,1,5]=>[8]=>5040
[8,5,3,7,6,2,4,1]=>[3,2,2,1]=>1680
[7,6,2,4,1,8,5,3]=>[4,3,1]=>3360
[8,5,4,1,7,6,2,3]=>[4,3,1]=>3360
[7,6,2,3,8,5,4,1]=>[8]=>5040
[2,1,7,8,6,4,3,5]=>[4,2,2]=>1260
[2,1,6,4,3,7,8,5]=>[5,2,1]=>4032
[6,4,2,1,3,7,8,5]=>[8]=>5040
[6,3,7,8,4,2,1,5]=>[5,3]=>2688
[7,8,4,2,1,6,3,5]=>[7,1]=>5760
[5,7,6,2,3,8,4,1]=>[5,3]=>2688
[2,6,1,8,4,3,7,5]=>[4,3,1]=>3360
[2,6,1,7,5,8,4,3]=>[5,2,1]=>4032
[8,4,2,3,7,5,6,1]=>[3,3,2]=>1120
[8,5,7,6,2,1,4,3]=>[6,2]=>3360
[4,8,5,7,6,2,1,3]=>[5,3]=>2688
[4,7,6,2,1,3,8,5]=>[6,2]=>3360
[7,5,6,1,8,4,2,3]=>[8]=>5040
[2,7,5,8,4,3,6,1]=>[8]=>5040
[2,8,4,3,6,1,7,5]=>[5,2,1]=>4032
[6,4,7,8,3,2,1,5]=>[8]=>5040
[7,6,5,8,4,3,2,1,9]=>[8,1]=>45360
[7,6,5,4,9,3,2,1,8]=>[8,1]=>45360
[7,6,5,4,3,8,2,1,9]=>[5,2,1,1]=>18144
[7,6,5,4,3,2,8,1,9]=>[3,2,2,1,1]=>7560
[6,9,8,5,4,3,2,1,7]=>[4,3,2]=>15120
[8,7,9,6,5,4,3,2,1,10]=>[6,2,1,1]=>151200
[7,5,8,9,4,3,2,1,6]=>[9]=>40320
[8,7,6,9,5,4,3,2,1,10]=>[8,1,1]=>226800
[6,4,3,7,5,2,1,8]=>[5,1,1,1]=>1344
[7,6,4,8,9,3,2,1,5]=>[7,2]=>25920
[8,7,6,5,10,4,3,2,1,9]=>[10]=>362880
[6,5,3,2,8,4,1,7]=>[7,1]=>5760
[7,6,5,3,9,8,2,1,4]=>[5,4]=>18144
[8,7,6,5,4,9,3,2,1,10]=>[7,2,1]=>259200
[6,5,2,7,8,4,1,3]=>[4,4]=>1260
[7,6,5,4,2,8,9,1,3]=>[8,1]=>45360
[8,7,6,5,4,3,9,2,1,10]=>[5,2,2,1]=>90720
[7,6,5,4,3,1,8,9,2]=>[6,2,1]=>30240
[7,10,9,6,5,4,3,2,1,8]=>[4,3,2,1]=>151200
[6,5,8,7,4,3,2,1,9]=>[4,4,1]=>11340
[8,6,9,10,5,4,3,2,1,7]=>[9,1]=>403200
[7,5,4,8,6,3,2,1,9]=>[8,1]=>45360
[5,9,8,7,4,3,2,1,6]=>[9]=>40320
[8,7,5,9,10,4,3,2,1,6]=>[10]=>362880
[9,8,7,6,11,5,4,3,2,1,10]=>[11]=>3628800
[6,4,3,2,5,8,1,7]=>[4,2,1,1]=>2520
[7,6,4,3,9,5,2,1,8]=>[7,2]=>25920
[7,4,8,9,6,3,2,1,5]=>[9]=>40320
[8,7,6,4,10,9,3,2,1,5]=>[7,2,1]=>259200
[9,8,7,6,5,10,4,3,2,1,11]=>[9,1,1]=>2217600
[6,3,7,2,5,4,1,8]=>[6,1,1]=>3360
[7,6,5,3,2,8,4,1,9]=>[8,1]=>45360
[7,6,3,8,9,5,2,1,4]=>[8,1]=>45360
[8,7,6,5,3,9,10,2,1,4]=>[10]=>362880
[7,6,5,4,2,1,8,3,9]=>[7,1,1]=>25920
[6,3,2,7,5,4,1,8]=>[4,2,1,1]=>2520
[7,6,5,2,9,8,4,1,3]=>[6,3]=>20160
[8,7,6,5,4,2,9,10,1,3]=>[8,2]=>226800
[7,6,5,4,1,8,9,3,2]=>[8,1]=>45360
[8,7,6,5,4,3,1,10,9,2]=>[5,2,2,1]=>90720
[8,4,2,6,3,1,7,5]=>[7,1]=>5760
[1,5,3,7,4,2,8,6]=>[6,1,1]=>3360
[1,6,7,3,4,2,8,5]=>[5,2,1]=>4032
[8,6,5,2,3,1,7,4]=>[5,2,1]=>4032
[1,7,6,3,4,2,8,5]=>[7,1]=>5760
[1,8,6,3,2,5,7,4]=>[6,1,1]=>3360
[8,7,5,2,1,4,6,3]=>[4,4]=>1260
[7,8,5,2,1,4,6,3]=>[8]=>5040
[6,8,5,2,3,1,7,4]=>[3,2,2,1]=>1680
[5,8,6,2,3,1,7,4]=>[4,3,1]=>3360
[4,8,2,6,3,1,7,5]=>[4,3,1]=>3360
[3,2,8,6,4,1,7,5]=>[6,1,1]=>3360
[3,2,1,7,5,4,8,6]=>[4,2,1,1]=>2520
[4,1,3,7,5,2,8,6]=>[6,1,1]=>3360
[5,1,7,3,4,2,8,6]=>[8]=>5040
[7,1,6,3,2,5,8,4]=>[8]=>5040
[1,2,7,4,3,6,8,5]=>[4,1,1,1,1]=>420
[6,1,8,2,4,5,7,3]=>[5,2,1]=>4032
[5,1,8,3,2,6,7,4]=>[3,3,1,1]=>1120
[3,2,8,7,1,5,6,4]=>[7,1]=>5760
[4,8,2,7,1,5,6,3]=>[5,3]=>2688
[5,8,7,2,1,4,6,3]=>[6,2]=>3360
[6,8,7,1,3,4,5,2]=>[3,3,2]=>1120
[7,8,6,1,3,4,5,2]=>[6,2]=>3360
[1,7,8,2,4,5,6,3]=>[5,2,1]=>4032
[8,6,7,1,3,4,5,2]=>[5,3]=>2688
[7,6,8,1,3,4,5,2]=>[8]=>5040
[6,5,8,2,3,1,7,4]=>[5,2,1]=>4032
[1,6,8,3,2,5,7,4]=>[3,3,1,1]=>1120
[1,5,3,8,2,6,7,4]=>[2,2,1,1,1,1]=>210
[8,4,2,7,1,5,6,3]=>[8]=>5040
[7,4,2,8,1,5,6,3]=>[4,4]=>1260
[6,4,2,8,3,1,7,5]=>[5,2,1]=>4032
[5,4,2,3,8,1,7,6]=>[4,3,1]=>3360
[4,5,2,3,1,6,8,7]=>[5,2,1]=>4032
[7,4,2,1,3,6,8,5]=>[7,1]=>5760
[8,4,2,1,3,6,7,5]=>[6,1,1]=>3360
[1,5,3,2,4,7,8,6]=>[3,3,1,1]=>1120
[8,5,1,3,2,6,7,4]=>[4,2,1,1]=>2520
[5,6,1,3,4,2,8,7]=>[4,2,2]=>1260
[4,6,2,1,5,3,8,7]=>[3,2,2,1]=>1680
[4,7,2,1,3,6,8,5]=>[5,2,1]=>4032
[5,7,1,3,2,6,8,4]=>[7,1]=>5760
[6,7,1,2,4,5,8,3]=>[8]=>5040
[8,6,1,2,4,5,7,3]=>[4,3,1]=>3360
[1,8,2,3,5,6,7,4]=>[4,1,1,1,1]=>420
[8,7,1,2,4,5,6,3]=>[5,3]=>2688
[7,8,1,2,4,5,6,3]=>[8]=>5040
[5,8,1,3,2,6,7,4]=>[6,1,1]=>3360
[4,8,2,1,3,6,7,5]=>[4,2,1,1]=>2520
[4,1,3,2,5,7,8,6]=>[3,3,1,1]=>1120
[5,1,2,4,3,7,8,6]=>[4,3,1]=>3360
[5,4,8,1,2,3,7,6]=>[4,3,1]=>3360
[1,4,7,6,3,2,5,8]=>[3,3,1,1]=>1120
[4,3,8,2,7,1,6,5]=>[8]=>5040
[4,3,2,8,1,7,6,5]=>[4,2,2]=>1260
[4,1,8,7,3,2,5,6]=>[8]=>5040
[4,7,8,1,2,5,3,6]=>[6,2]=>3360
[2,3,6,7,4,1,8,5]=>[4,4]=>1260
[3,1,7,8,4,2,5,6]=>[8]=>5040
[3,7,2,4,8,6,1,5]=>[4,2,1,1]=>2520
[1,3,6,4,7,2,5,8]=>[3,2,1,1,1]=>1120
[4,7,1,5,8,2,3,6]=>[8]=>5040
[2,6,7,3,8,4,1,5]=>[6,2]=>3360
[8,7,5,2,6,3,4,1]=>[3,3,2]=>1120
[8,6,5,2,7,3,4,1]=>[6,2]=>3360
[7,4,8,5,6,3,2,1]=>[8]=>5040
[3,4,6,7,8,5,1,2]=>[8]=>5040
[6,3,8,5,4,7,1,2]=>[3,3,2]=>1120
[1,2,6,4,8,5,7,3]=>[4,1,1,1,1]=>420
[7,8,3,1,4,2,5,6]=>[4,3,1]=>3360
[5,1,6,3,8,7,2,4]=>[8]=>5040
[6,1,8,7,4,3,2,5]=>[8]=>5040
[1,2,7,5,8,3,6,4]=>[3,3,1,1]=>1120
[4,1,6,3,7,8,2,5]=>[8]=>5040
[3,1,6,4,8,2,7,5]=>[4,2,1,1]=>2520
[7,8,4,1,6,3,2,5]=>[8]=>5040
[4,1,6,3,8,7,2,5]=>[6,2]=>3360
[5,4,6,1,3,8,2,7]=>[8]=>5040
[1,3,5,7,4,6,8,2]=>[6,1,1]=>3360
[1,3,5,4,7,2,6,8]=>[5,1,1,1]=>1344
[1,3,5,7,4,8,2,6]=>[5,2,1]=>4032
[1,3,5,7,4,8,6,2]=>[7,1]=>5760
[1,3,5,7,8,4,2,6]=>[7,1]=>5760
[1,6,3,2,7,4,8,5]=>[3,3,1,1]=>1120
[3,5,1,6,2,8,7,4]=>[3,2,2,1]=>1680
[1,3,7,2,5,4,8,6]=>[6,1,1]=>3360
[1,3,7,5,2,4,8,6]=>[7,1]=>5760
[2,5,7,4,3,8,1,6]=>[5,2,1]=>4032
[3,2,6,7,8,1,5,4]=>[4,3,1]=>3360
[3,5,2,7,8,4,1,6]=>[8]=>5040
[1,5,7,4,8,3,2,6]=>[6,1,1]=>3360
[3,5,2,6,8,4,7,1]=>[5,2,1]=>4032
[2,5,7,4,3,8,6,1]=>[7,1]=>5760
[4,6,3,7,2,8,5,1]=>[7,1]=>5760
[1,4,7,3,8,6,2,5]=>[4,2,1,1]=>2520
[5,3,7,8,2,4,1,6]=>[5,3]=>2688
[2,4,7,8,3,1,5,6]=>[5,3]=>2688
[6,3,1,5,8,2,4,7]=>[4,4]=>1260
[3,2,4,8,1,5,6,7]=>[7,1]=>5760
[3,2,4,6,8,1,5,7]=>[4,3,1]=>3360
[7,2,4,8,3,1,5,6]=>[7,1]=>5760
[5,3,8,7,2,4,1,6]=>[8]=>5040
[2,4,8,7,3,1,5,6]=>[8]=>5040
[8,7,4,6,2,3,1,5]=>[5,3]=>2688
[5,6,8,7,2,3,1,4]=>[8]=>5040
[5,7,6,8,2,3,1,4]=>[4,2,2]=>1260
[4,7,6,8,2,3,1,5]=>[6,2]=>3360
[8,6,4,7,2,3,1,5]=>[8]=>5040
[2,3,7,8,4,1,6,5]=>[5,3]=>2688
[3,7,4,8,2,5,1,6]=>[8]=>5040
[2,3,7,4,1,6,8,5]=>[6,1,1]=>3360
[6,3,1,7,4,2,8,5]=>[4,4]=>1260
[7,5,8,6,2,3,1,4]=>[4,2,2]=>1260
[7,1,6,4,2,3,8,5]=>[5,2,1]=>4032
[3,1,7,6,4,2,8,5]=>[8]=>5040
[6,8,7,5,2,3,1,4]=>[4,4]=>1260
[4,6,3,1,5,8,7,2]=>[3,2,1,1,1]=>1120
[4,1,6,5,3,8,7,2]=>[7,1]=>5760
[2,6,5,1,8,7,3,4]=>[8]=>5040
[2,6,5,8,1,7,3,4]=>[6,2]=>3360
[2,6,5,8,1,3,7,4]=>[5,2,1]=>4032
[2,6,5,8,3,1,7,4]=>[3,2,2,1]=>1680
[6,4,3,8,7,1,5,2]=>[3,2,2,1]=>1680
[6,4,8,3,7,1,5,2]=>[4,2,2]=>1260
[4,1,6,8,5,7,3,2]=>[4,3,1]=>3360
[2,6,8,5,3,1,7,4]=>[4,3,1]=>3360
[2,6,8,5,1,7,3,4]=>[8]=>5040
[4,6,8,3,5,1,7,2]=>[6,1,1]=>3360
[4,6,8,3,1,5,7,2]=>[7,1]=>5760
[4,6,3,8,1,5,7,2]=>[6,1,1]=>3360
[4,3,6,1,8,5,7,2]=>[5,2,1]=>4032
[4,1,3,6,8,7,5,2]=>[7,1]=>5760
[4,3,6,1,8,7,5,2]=>[6,2]=>3360
[4,6,8,1,3,7,5,2]=>[6,2]=>3360
[6,2,8,5,7,1,3,4]=>[5,2,1]=>4032
[2,4,8,7,1,5,3,6]=>[8]=>5040
[6,4,1,8,7,5,3,2]=>[5,3]=>2688
[6,1,4,8,7,5,3,2]=>[8]=>5040
[2,3,4,5,6,8,9,7,1]=>[9]=>40320
[2,3,4,5,7,8,9,6,1]=>[7,2]=>25920
[2,4,5,6,7,8,9,3,1]=>[9]=>40320
[2,3,7,1,4,8,6,5]=>[8]=>5040
[2,6,1,3,7,8,5,4]=>[6,2]=>3360
[2,3,4,5,6,7,10,1,8,9]=>[10]=>362880
[3,4,5,6,7,8,9,10,11,2,1]=>[6,5]=>1330560
[1,5,3,2,6,4,7,8]=>[4,1,1,1,1]=>420
[1,5,3,2,6,7,4,8]=>[5,1,1,1]=>1344
[1,7,3,2,8,5,4,6]=>[3,3,1,1]=>1120
[1,3,2,7,5,4,8,6]=>[4,2,1,1]=>2520
[6,5,2,4,3,7,1,8]=>[3,3,1,1]=>1120
[6,4,2,5,3,7,1,8]=>[4,3,1]=>3360
[5,4,7,6,2,3,1,8]=>[7,1]=>5760
[3,6,4,8,2,1,5,7]=>[8]=>5040
[1,6,2,8,5,3,4,7]=>[3,3,1,1]=>1120
[4,6,2,3,7,5,1,8]=>[7,1]=>5760
[4,7,2,3,6,5,1,8]=>[5,2,1]=>4032
[4,7,2,3,5,6,1,8]=>[5,1,1,1]=>1344
[5,3,2,7,4,6,1,8]=>[4,2,1,1]=>2520
[5,3,2,6,4,7,1,8]=>[5,2,1]=>4032
[4,6,2,3,5,7,1,8]=>[6,1,1]=>3360
[3,5,2,1,6,8,4,7]=>[8]=>5040
[1,5,2,6,8,4,3,7]=>[5,2,1]=>4032
[1,5,7,2,8,4,3,6]=>[5,2,1]=>4032
[3,5,2,1,8,6,4,7]=>[7,1]=>5760
[3,6,8,4,2,1,5,7]=>[7,1]=>5760
[4,3,2,6,1,8,5,7]=>[6,2]=>3360
[1,5,8,2,7,4,3,6]=>[7,1]=>5760
[1,7,2,3,4,8,6,5]=>[7,1]=>5760
[6,8,2,3,4,1,7,5]=>[5,2,1]=>4032
[4,1,8,2,3,5,7,6]=>[4,3,1]=>3360
[2,3,1,8,4,5,7,6]=>[4,3,1]=>3360
[7,3,2,1,4,5,8,6]=>[6,2]=>3360
[7,8,1,4,3,5,2,6]=>[7,1]=>5760
[7,1,2,3,4,6,8,5]=>[7,1]=>5760
[6,1,2,3,4,8,7,5]=>[7,1]=>5760
[1,8,2,3,4,7,6,5]=>[5,2,1]=>4032
[8,1,2,3,4,6,7,5]=>[6,1,1]=>3360
[2,8,1,3,5,4,7,6]=>[6,1,1]=>3360
[8,7,1,4,3,5,2,6]=>[5,2,1]=>4032
[8,3,2,1,4,5,7,6]=>[5,2,1]=>4032
[3,8,2,1,5,6,4,7]=>[6,1,1]=>3360
[3,8,2,1,6,5,4,7]=>[6,2]=>3360
[1,7,8,3,5,4,2,6]=>[4,2,1,1]=>2520
[7,4,1,8,3,5,2,6]=>[8]=>5040
[8,4,1,7,3,5,2,6]=>[5,3]=>2688
[3,8,4,6,2,1,5,7]=>[4,4]=>1260
[8,4,2,5,3,1,6,7]=>[4,4]=>1260
[8,5,2,4,3,1,6,7]=>[4,3,1]=>3360
[8,3,2,5,4,1,6,7]=>[4,2,2]=>1260
[4,3,2,5,1,8,6,7]=>[3,3,2]=>1120
[3,5,2,4,1,8,6,7]=>[4,3,1]=>3360
[2,4,7,8,1,5,3,6]=>[6,2]=>3360
[1,8,7,3,5,4,2,6]=>[6,1,1]=>3360
[5,1,8,2,7,4,3,6]=>[8]=>5040
[5,1,7,2,8,4,3,6]=>[6,2]=>3360
[6,1,2,8,5,3,4,7]=>[4,3,1]=>3360
[6,3,2,1,8,4,5,7]=>[3,3,2]=>1120
[7,3,2,8,4,5,1,6]=>[4,2,2]=>1260
[2,7,8,4,3,5,1,6]=>[4,3,1]=>3360
[7,1,8,3,5,4,2,6]=>[4,3,1]=>3360
[7,8,2,3,4,6,1,5]=>[5,2,1]=>4032
[6,7,1,3,4,8,2,5]=>[6,2]=>3360
[6,8,1,3,4,7,2,5]=>[8]=>5040
[1,7,2,3,4,6,8,5]=>[6,1,1]=>3360
[1,6,2,3,4,8,7,5]=>[6,1,1]=>3360
[7,6,2,3,4,1,8,5]=>[8]=>5040
[8,6,2,3,4,1,7,5]=>[7,1]=>5760
[8,1,7,3,5,4,2,6]=>[7,1]=>5760
[8,3,2,7,4,5,1,6]=>[6,2]=>3360
[6,7,2,3,4,1,8,5]=>[6,2]=>3360
[7,6,2,3,4,8,1,5]=>[6,2]=>3360
[8,6,2,3,4,7,1,5]=>[8]=>5040
[6,3,4,8,7,5,1,2]=>[4,4]=>1260
[4,8,7,3,5,6,1,2]=>[4,2,1,1]=>2520
[5,8,4,2,1,6,7,3]=>[4,2,1,1]=>2520
[7,8,4,1,2,6,5,3]=>[7,1]=>5760
[4,8,1,5,2,7,6,3]=>[6,2]=>3360
[3,8,7,6,2,4,1,5]=>[3,3,2]=>1120
[2,8,7,6,4,1,3,5]=>[6,2]=>3360
[2,8,7,6,3,1,4,5]=>[8]=>5040
[1,8,7,6,2,4,3,5]=>[3,2,2,1]=>1680
[1,8,7,6,3,4,2,5]=>[5,2,1]=>4032
[2,1,7,3,6,5,8,4]=>[4,2,2]=>1260
[3,1,7,2,6,5,8,4]=>[6,2]=>3360
[6,1,2,8,5,7,3,4]=>[5,2,1]=>4032
[6,2,1,8,5,7,3,4]=>[4,2,1,1]=>2520
[6,1,3,8,5,2,7,4]=>[3,2,1,1,1]=>1120
[2,3,7,1,6,8,5,4]=>[8]=>5040
[3,2,6,7,5,8,1,4]=>[6,1,1]=>3360
[3,8,7,6,2,1,5,4]=>[8]=>5040
[4,8,7,6,2,1,3,5]=>[3,3,2]=>1120
[4,8,7,6,1,3,2,5]=>[8]=>5040
[5,1,4,6,8,2,3,7]=>[8]=>5040
[1,7,6,3,5,4,8,2]=>[3,3,1,1]=>1120
[4,3,7,2,6,5,1,8]=>[5,2,1]=>4032
[3,4,6,1,5,7,2,8]=>[6,1,1]=>3360
[1,6,8,5,7,3,4,2]=>[4,3,1]=>3360
[2,4,1,5,8,6,3,7]=>[7,1]=>5760
[4,6,1,2,5,8,3,7]=>[7,1]=>5760
[5,6,7,2,1,4,8,3]=>[3,3,2]=>1120
[7,8,6,5,1,2,4,3]=>[4,4]=>1260
[1,3,6,5,7,8,2,4]=>[7,1]=>5760
[7,4,8,5,3,1,6,2]=>[5,3]=>2688
[6,8,5,2,4,1,7,3]=>[5,2,1]=>4032
[2,3,1,6,8,5,7,4]=>[4,3,1]=>3360
[7,3,2,5,1,4,8,6]=>[6,2]=>3360
[7,1,4,2,3,6,8,5]=>[7,1]=>5760
[1,5,8,3,4,6,7,2]=>[5,1,1,1]=>1344
[8,3,1,2,4,7,6,5]=>[6,2]=>3360
[2,3,8,1,6,5,4,7]=>[6,2]=>3360
[8,1,4,7,2,5,3,6]=>[5,3]=>2688
[3,5,2,4,1,7,8,6]=>[4,3,1]=>3360
[3,4,7,8,6,2,1,5]=>[5,3]=>2688
[3,4,8,6,2,7,1,5]=>[8]=>5040
[5,8,2,1,6,7,3,4]=>[8]=>5040
[5,7,2,8,6,4,3,1]=>[5,3]=>2688
[6,1,2,7,5,3,8,4]=>[4,3,1]=>3360
[7,3,2,8,6,4,1,5]=>[4,2,2]=>1260
[2,7,8,4,6,3,1,5]=>[4,3,1]=>3360
[1,4,5,7,2,6,8,3]=>[6,1,1]=>3360
[7,3,5,2,6,1,8,4]=>[8]=>5040
[8,5,2,3,6,1,7,4]=>[7,1]=>5760
[8,1,6,3,5,7,2,4]=>[7,1]=>5760
[2,8,6,4,3,7,1,5]=>[7,1]=>5760
[8,3,2,6,4,7,1,5]=>[6,2]=>3360
[2,3,8,7,6,5,1,4]=>[6,2]=>3360
[1,5,8,7,3,2,6,4]=>[7,1]=>5760
[4,5,8,7,3,2,1,6]=>[5,3]=>2688
[2,6,8,1,7,5,4,3]=>[6,2]=>3360
[2,5,8,3,7,6,1,4]=>[4,3,1]=>3360
[3,2,8,4,7,6,1,5]=>[5,1,1,1]=>1344
[1,5,8,4,2,7,6,3]=>[2,2,2,1,1]=>420
[1,5,8,2,3,7,6,4]=>[5,2,1]=>4032
[2,1,8,4,3,7,6,5]=>[3,2,2,1]=>1680
[5,6,8,4,1,2,7,3]=>[2,2,2,1,1]=>420
[7,1,2,8,6,5,4,3]=>[6,2]=>3360
[7,1,4,8,6,2,5,3]=>[5,3]=>2688
[7,3,1,8,6,2,5,4]=>[6,2]=>3360
[3,2,4,8,7,6,1,5]=>[6,1,1]=>3360
[3,1,4,8,7,2,6,5]=>[8]=>5040
[1,6,4,8,2,7,5,3]=>[4,3,1]=>3360
[2,4,5,8,3,7,1,6]=>[6,2]=>3360
[7,6,1,4,8,2,5,3]=>[5,2,1]=>4032
[7,6,3,4,8,2,1,5]=>[2,2,2,1,1]=>420
[7,2,1,3,8,6,5,4]=>[6,1,1]=>3360
[7,2,3,4,8,6,1,5]=>[2,2,1,1,1,1]=>210
[1,6,3,4,8,2,7,5]=>[2,2,1,1,1,1]=>210
[7,6,2,4,3,8,1,5]=>[5,2,1]=>4032
[7,1,5,2,3,8,6,4]=>[6,2]=>3360
[2,6,5,4,3,8,1,7]=>[5,2,1]=>4032
[7,1,5,4,3,2,8,6]=>[5,2,1]=>4032
[3,4,2,6,7,8,1,5]=>[8]=>5040
[3,1,4,2,6,8,7,5]=>[4,3,1]=>3360
[8,3,4,2,6,1,7,5]=>[4,3,1]=>3360
[2,6,7,3,5,4,1,8]=>[6,1,1]=>3360
[2,7,8,3,5,4,1,6]=>[4,3,1]=>3360
[2,6,8,3,5,4,1,7]=>[7,1]=>5760
[4,7,1,2,8,5,3,6]=>[5,3]=>2688
[4,8,1,2,7,5,3,6]=>[8]=>5040
[2,1,6,3,7,5,4,8]=>[5,2,1]=>4032
[2,7,1,3,6,8,4,5]=>[5,3]=>2688
[6,7,3,2,8,1,4,5]=>[3,2,2,1]=>1680
[7,3,4,2,6,1,8,5]=>[5,3]=>2688
[7,4,1,2,8,5,3,6]=>[3,3,2]=>1120
[8,7,4,2,1,5,3,6]=>[4,4]=>1260
[7,4,1,2,6,5,3,8]=>[3,2,2,1]=>1680
[7,4,3,1,5,6,8,2]=>[5,1,1,1]=>1344
[6,7,4,1,5,8,3,2]=>[7,1]=>5760
[4,7,5,1,6,8,3,2]=>[6,2]=>3360
[4,5,3,1,7,6,8,2]=>[4,2,1,1]=>2520
[4,6,1,2,7,5,3,8]=>[7,1]=>5760
[2,7,1,3,6,5,4,8]=>[5,2,1]=>4032
[4,1,8,2,6,5,3,7]=>[3,3,2]=>1120
[4,6,1,2,8,5,3,7]=>[8]=>5040
[8,4,3,1,5,6,7,2]=>[4,1,1,1,1]=>420
[4,5,3,1,8,6,7,2]=>[3,2,1,1,1]=>1120
[4,8,5,6,3,1,7,2]=>[3,2,2,1]=>1680
[5,1,3,4,8,6,7,2]=>[4,1,1,1,1]=>420
[5,4,3,8,1,6,7,2]=>[3,2,1,1,1]=>1120
[8,5,3,4,1,6,7,2]=>[4,1,1,1,1]=>420
[6,4,8,2,1,5,3,7]=>[3,3,2]=>1120
[6,7,3,2,5,1,4,8]=>[3,2,1,1,1]=>1120
[6,8,3,2,5,1,4,7]=>[4,2,1,1]=>2520
[5,7,1,4,6,8,3,2]=>[7,1]=>5760
[5,1,3,4,7,6,8,2]=>[5,1,1,1]=>1344
[6,1,4,2,7,5,3,8]=>[7,1]=>5760
[5,4,3,7,1,6,8,2]=>[4,2,1,1]=>2520
[6,7,5,4,1,8,3,2]=>[7,1]=>5760
[7,6,4,2,1,5,3,8]=>[7,1]=>5760
[8,2,7,6,5,4,1,3]=>[4,2,1,1]=>2520
[7,2,8,6,5,4,3,1]=>[4,2,1,1]=>2520
[8,1,9,7,6,5,4,3,2]=>[5,2,2]=>9072
[2,10,9,8,7,6,5,4,1,3]=>[5,2,2,1]=>90720
[3,2,8,7,6,5,1,4]=>[5,2,1]=>4032
[4,8,7,6,5,3,1,2]=>[5,2,1]=>4032
[7,8,6,1,5,4,3,2]=>[5,2,1]=>4032
[8,9,1,7,6,5,4,3,2]=>[3,2,2,2]=>2520
[7,3,8,6,5,4,2,1]=>[5,2,1]=>4032
[9,1,10,8,7,6,5,4,3,2]=>[5,2,2,1]=>90720
[4,8,5,7,6,3,2,1]=>[5,3]=>2688
[8,5,6,1,3,2,4,7]=>[4,4]=>1260
[8,6,1,5,3,2,4,7]=>[6,2]=>3360
[7,8,1,5,3,2,4,6]=>[5,3]=>2688
[8,1,7,5,3,2,4,6]=>[4,4]=>1260
[8,6,1,4,5,2,3,7]=>[4,2,1,1]=>2520
[8,6,3,1,5,2,4,7]=>[4,2,1,1]=>2520
[8,4,6,1,5,2,3,7]=>[7,1]=>5760
[8,6,2,1,5,4,3,7]=>[7,1]=>5760
[8,5,2,6,1,4,3,7]=>[6,2]=>3360
[8,5,2,1,7,4,3,6]=>[4,4]=>1260
[7,8,2,1,5,4,3,6]=>[7,1]=>5760
[7,8,3,1,5,2,4,6]=>[3,3,1,1]=>1120
[8,2,7,5,1,3,4,6]=>[7,1]=>5760
[8,4,1,7,5,2,3,6]=>[7,1]=>5760
[8,2,7,1,5,4,3,6]=>[4,2,1,1]=>2520
[8,2,6,1,7,4,3,5]=>[7,1]=>5760
[8,1,7,4,3,2,6,5]=>[7,1]=>5760
[8,1,5,7,3,2,6,4]=>[6,2]=>3360
[5,7,8,1,3,2,6,4]=>[5,3]=>2688
[8,2,6,1,5,7,3,4]=>[3,3,1,1]=>1120
[5,8,1,6,7,2,3,4]=>[4,4]=>1260
[5,7,6,1,8,2,3,4]=>[4,4]=>1260
[6,7,2,5,1,8,3,4]=>[5,3]=>2688
[7,5,1,6,8,2,3,4]=>[5,3]=>2688
[6,5,7,1,8,2,3,4]=>[6,2]=>3360
[6,7,3,8,1,2,4,5]=>[7,1]=>5760
[7,5,4,1,8,2,3,6]=>[4,4]=>1260
[7,6,1,4,8,2,3,5]=>[3,2,2,1]=>1680
[8,1,6,4,7,2,3,5]=>[7,1]=>5760
[7,5,8,1,3,2,4,6]=>[5,3]=>2688
[7,8,4,1,3,2,5,6]=>[5,3]=>2688
[8,3,7,4,1,2,5,6]=>[7,1]=>5760
[8,5,1,7,3,2,4,6]=>[6,2]=>3360
[6,8,1,7,3,2,4,5]=>[6,2]=>3360
[7,1,8,4,3,6,2,5]=>[3,3,1,1]=>1120
[7,3,1,8,6,4,2,5]=>[4,4]=>1260
[8,3,1,7,4,6,2,5]=>[7,1]=>5760
[8,4,5,1,7,2,3,6]=>[5,3]=>2688
[5,6,8,1,7,2,3,4]=>[6,2]=>3360
[6,5,8,1,2,7,3,4]=>[6,2]=>3360
[7,3,1,8,5,6,2,4]=>[4,2,1,1]=>2520
[6,2,7,8,3,1,5,4]=>[3,2,2,1]=>1680
[5,8,1,7,3,2,6,4]=>[5,3]=>2688
[8,4,1,7,3,2,6,5]=>[4,4]=>1260
[8,3,4,7,1,2,6,5]=>[5,3]=>2688
[8,2,7,4,1,3,6,5]=>[3,3,1,1]=>1120
[7,4,8,2,1,3,6,5]=>[6,2]=>3360
[7,4,3,8,1,2,6,5]=>[7,1]=>5760
[8,2,3,6,7,1,5,4]=>[4,2,1,1]=>2520
[7,8,5,2,3,6,4,1]=>[5,2,1]=>4032
[6,8,5,2,3,4,7,1]=>[5,2,1]=>4032
[3,5,2,6,8,1,4,7]=>[8]=>5040
[3,5,2,4,6,8,1,7]=>[7,1]=>5760
[2,4,5,7,3,6,8,1]=>[5,2,1]=>4032
[2,4,5,3,6,8,1,7]=>[8]=>5040
[5,2,4,6,8,1,3,7]=>[7,1]=>5760
[5,1,3,4,6,8,2,7]=>[6,1,1]=>3360
[4,3,5,2,6,8,1,7]=>[8]=>5040
[4,3,5,7,2,8,1,6]=>[3,3,2]=>1120
[4,3,5,7,2,6,8,1]=>[4,3,1]=>3360
[4,6,3,7,2,5,8,1]=>[4,3,1]=>3360
[4,6,3,1,7,8,2,5]=>[5,2,1]=>4032
[4,3,5,1,7,8,2,6]=>[4,2,2]=>1260
[5,7,1,3,4,8,2,6]=>[4,2,2]=>1260
[5,7,1,3,4,6,8,2]=>[4,3,1]=>3360
[4,5,7,1,3,6,8,2]=>[5,2,1]=>4032
[4,3,6,7,1,5,8,2]=>[8]=>5040
[4,6,3,5,1,7,8,2]=>[4,3,1]=>3360
[4,6,3,5,7,2,8,1]=>[5,2,1]=>4032
[3,5,6,4,1,7,8,2]=>[7,1]=>5760
[3,1,5,6,7,4,8,2]=>[6,2]=>3360
[5,1,6,7,3,4,8,2]=>[8]=>5040
[6,4,7,1,3,5,8,2]=>[8]=>5040
[1,6,7,3,4,5,8,2]=>[7,1]=>5760
[2,6,7,4,5,8,1,3]=>[6,1,1]=>3360
[2,6,7,4,8,1,3,5]=>[3,2,2,1]=>1680
[5,3,6,1,2,7,8,4]=>[8]=>5040
[3,5,2,6,1,7,8,4]=>[4,4]=>1260
[3,5,2,6,7,4,8,1]=>[6,2]=>3360
[5,2,3,6,7,4,8,1]=>[4,2,1,1]=>2520
[5,2,3,6,1,7,8,4]=>[4,2,1,1]=>2520
[5,2,6,1,3,7,8,4]=>[7,1]=>5760
[4,2,6,7,3,5,8,1]=>[4,3,1]=>3360
[6,3,7,2,4,5,8,1]=>[8]=>5040
[3,5,7,2,8,1,4,6]=>[8]=>5040
[3,7,2,4,8,1,5,6]=>[7,1]=>5760
[7,2,4,6,8,1,3,5]=>[5,2,1]=>4032
[7,1,3,4,6,8,2,5]=>[3,3,1,1]=>1120
[3,7,2,4,6,8,1,5]=>[4,3,1]=>3360
[3,5,7,2,6,8,1,4]=>[5,3]=>2688
[6,3,7,2,5,8,1,4]=>[7,1]=>5760
[6,3,5,7,2,8,1,4]=>[5,3]=>2688
[6,3,5,7,2,4,8,1]=>[5,3]=>2688
[6,2,4,5,7,3,8,1]=>[7,1]=>5760
[6,2,4,5,1,7,8,3]=>[7,1]=>5760
[4,7,1,2,5,6,8,3]=>[6,1,1]=>3360
[2,6,7,5,8,1,3,4]=>[3,3,2]=>1120
[4,6,7,1,2,5,8,3]=>[3,3,2]=>1120
[5,6,2,4,7,3,8,1]=>[4,3,1]=>3360
[5,4,2,6,7,3,8,1]=>[4,4]=>1260
[5,4,2,6,1,7,8,3]=>[6,2]=>3360
[1,5,4,6,2,7,8,3]=>[5,2,1]=>4032
[5,6,4,1,2,7,8,3]=>[8]=>5040
[6,4,5,1,2,7,8,3]=>[8]=>5040
[6,3,5,1,7,8,2,4]=>[4,4]=>1260
[6,5,7,2,8,1,3,4]=>[4,2,2]=>1260
[6,5,7,1,3,4,8,2]=>[5,3]=>2688
[5,6,4,7,1,3,8,2]=>[6,2]=>3360
[5,4,6,3,1,7,8,2]=>[6,2]=>3360
[7,5,3,2,4,8,1,6]=>[3,2,2,1]=>1680
[8,4,5,2,6,1,3,7]=>[6,2]=>3360
[8,5,4,2,1,6,3,7]=>[7,1]=>5760
[8,5,3,4,1,6,2,7]=>[5,1,1,1]=>1344
[8,4,5,3,1,6,2,7]=>[7,1]=>5760
[7,5,4,2,1,8,3,6]=>[6,2]=>3360
[7,5,4,2,1,6,8,3]=>[7,1]=>5760
[7,4,5,3,1,6,8,2]=>[7,1]=>5760
[7,4,3,5,6,1,8,2]=>[7,1]=>5760
[5,6,3,7,4,1,8,2]=>[7,1]=>5760
[5,6,7,3,1,4,8,2]=>[6,2]=>3360
[6,7,3,4,1,5,8,2]=>[3,3,1,1]=>1120
[6,7,4,2,1,5,8,3]=>[5,3]=>2688
[5,6,7,3,1,8,2,4]=>[6,2]=>3360
[5,6,3,7,8,1,2,4]=>[7,1]=>5760
[5,6,3,7,2,4,8,1]=>[7,1]=>5760
[5,6,7,2,3,8,1,4]=>[4,4]=>1260
[7,4,5,2,8,1,3,6]=>[6,2]=>3360
[6,7,3,2,4,8,1,5]=>[7,1]=>5760
[7,6,4,2,1,3,8,5]=>[4,4]=>1260
[7,6,3,4,1,2,8,5]=>[4,2,1,1]=>2520
[7,6,3,2,4,1,8,5]=>[7,1]=>5760
[6,7,3,2,5,1,8,4]=>[4,2,1,1]=>2520
[6,5,3,2,7,8,1,4]=>[7,1]=>5760
[6,5,3,2,7,4,8,1]=>[7,1]=>5760
[6,4,5,2,7,3,8,1]=>[6,2]=>3360
[6,4,5,2,7,8,1,3]=>[6,2]=>3360
[7,4,5,2,6,1,8,3]=>[6,2]=>3360
[7,4,5,6,1,2,8,3]=>[5,3]=>2688
[7,5,6,2,1,3,8,4]=>[6,2]=>3360
[6,7,3,5,1,2,8,4]=>[7,1]=>5760
[5,6,7,4,1,2,8,3]=>[3,2,2,1]=>1680
[5,6,7,2,4,1,8,3]=>[5,3]=>2688
[5,6,4,2,7,8,1,3]=>[5,3]=>2688
[6,5,7,2,1,8,3,4]=>[6,2]=>3360
[6,5,7,2,1,4,8,3]=>[5,3]=>2688
[5,4,6,7,3,1,8,2]=>[4,4]=>1260
[3,7,8,5,6,1,4,2]=>[8]=>5040
[1,7,8,5,6,3,4,2]=>[7,1]=>5760
[1,7,5,8,6,3,4,2]=>[4,3,1]=>3360
[3,7,5,8,6,1,4,2]=>[4,4]=>1260
[5,7,3,8,6,4,1,2]=>[7,1]=>5760
[1,5,7,8,6,3,4,2]=>[7,1]=>5760
[1,5,7,8,3,6,4,2]=>[6,1,1]=>3360
[5,3,7,8,1,6,4,2]=>[5,2,1]=>4032
[7,8,1,5,6,3,4,2]=>[6,2]=>3360
[7,1,8,5,6,3,4,2]=>[8]=>5040
[7,1,5,8,6,3,4,2]=>[5,3]=>2688
[5,1,7,8,3,6,4,2]=>[7,1]=>5760
[3,1,7,8,5,6,4,2]=>[6,1,1]=>3360
[1,3,7,8,5,6,4,2]=>[5,1,1,1]=>1344
[3,1,7,5,8,6,4,2]=>[7,1]=>5760
[5,1,7,3,8,6,4,2]=>[4,3,1]=>3360
[7,1,5,3,8,6,4,2]=>[7,1]=>5760
[7,1,5,8,3,6,4,2]=>[5,2,1]=>4032
[7,3,5,8,1,6,4,2]=>[7,1]=>5760
[5,3,7,1,8,6,4,2]=>[7,1]=>5760
[3,5,7,1,8,6,4,2]=>[4,3,1]=>3360
[1,7,5,3,8,6,4,2]=>[6,1,1]=>3360
[5,7,3,1,8,6,4,2]=>[6,1,1]=>3360
[5,7,3,8,6,1,4,2]=>[4,3,1]=>3360
[3,7,5,8,1,6,4,2]=>[4,3,1]=>3360
[1,7,5,8,3,6,4,2]=>[4,2,1,1]=>2520
[1,7,8,5,3,6,4,2]=>[6,1,1]=>3360
[5,7,8,6,3,1,4,2]=>[8]=>5040
[7,5,8,6,1,3,4,2]=>[8]=>5040
[5,7,8,1,6,3,4,2]=>[8]=>5040
[3,7,8,1,5,6,4,2]=>[6,1,1]=>3360
[1,7,8,3,5,6,4,2]=>[5,1,1,1]=>1344
[1,7,3,8,5,6,4,2]=>[4,1,1,1,1]=>420
[3,7,1,8,5,6,4,2]=>[4,2,1,1]=>2520
[5,7,1,8,3,6,4,2]=>[4,3,1]=>3360
[5,7,1,8,6,3,4,2]=>[4,4]=>1260
[7,5,1,8,6,3,4,2]=>[8]=>5040
[7,5,8,1,6,3,4,2]=>[5,3]=>2688
[7,8,5,1,6,3,4,2]=>[3,3,2]=>1120
[7,5,8,1,3,6,4,2]=>[4,3,1]=>3360
[7,5,1,8,3,6,4,2]=>[7,1]=>5760
[7,5,1,3,8,6,4,2]=>[4,3,1]=>3360
[5,7,1,3,8,6,4,2]=>[7,1]=>5760
[3,7,1,5,8,6,4,2]=>[5,2,1]=>4032
[1,7,3,5,8,6,4,2]=>[5,1,1,1]=>1344
[1,5,3,7,8,6,4,2]=>[3,2,1,1,1]=>1120
[3,5,1,7,8,6,4,2]=>[3,2,2,1]=>1680
[5,3,1,7,8,6,4,2]=>[5,2,1]=>4032
[7,3,1,5,8,6,4,2]=>[7,1]=>5760
[7,3,1,8,5,6,4,2]=>[6,1,1]=>3360
[7,8,3,1,5,6,4,2]=>[3,2,1,1,1]=>1120
[7,1,8,3,5,6,4,2]=>[6,1,1]=>3360
[7,1,3,8,5,6,4,2]=>[5,1,1,1]=>1344
[7,1,3,5,8,6,4,2]=>[6,1,1]=>3360
[3,1,5,7,8,6,4,2]=>[5,2,1]=>4032
[5,7,3,4,8,1,6,2]=>[6,1,1]=>3360
[5,7,3,4,1,8,6,2]=>[4,2,1,1]=>2520
[5,7,3,1,4,6,2,8]=>[3,2,1,1,1]=>1120
[5,7,3,1,4,8,6,2]=>[4,3,1]=>3360
[5,3,7,4,1,2,6,8]=>[4,2,1,1]=>2520
[5,3,7,1,4,2,6,8]=>[4,3,1]=>3360
[5,3,7,1,4,2,8,6]=>[5,3]=>2688
[3,7,5,1,2,8,6,4]=>[8]=>5040
[7,8,3,5,1,2,6,4]=>[7,1]=>5760
[7,3,5,8,1,2,6,4]=>[6,2]=>3360
[3,7,5,1,2,6,8,4]=>[7,1]=>5760
[6,1,4,3,5,2,8,7]=>[3,2,2,1]=>1680
[2,5,7,3,8,4,1,6]=>[8]=>5040
[5,4,7,8,6,1,3,2]=>[3,3,2]=>1120
[7,5,6,2,8,3,1,4]=>[4,2,2]=>1260
[4,7,2,5,8,3,1,6]=>[8]=>5040
[6,2,4,5,1,3,8,7]=>[5,2,1]=>4032
[5,1,4,6,3,2,8,7]=>[6,2]=>3360
[3,5,6,2,4,1,8,7]=>[3,3,2]=>1120
[3,8,6,7,5,4,1,2]=>[5,2,1]=>4032
[6,2,7,8,3,4,1,5]=>[7,1]=>5760
[2,5,3,4,8,1,7,6]=>[5,1,1,1]=>1344
[8,7,1,2,5,3,4,6]=>[4,3,1]=>3360
[5,1,8,2,3,4,7,6]=>[7,1]=>5760
[5,4,7,6,2,8,1,3]=>[8]=>5040
[3,7,8,1,5,4,6,2]=>[7,1]=>5760
[7,1,3,4,6,8,5,2]=>[6,1,1]=>3360
[8,3,6,5,7,1,4,2]=>[5,3]=>2688
[5,8,7,1,4,6,2,3]=>[4,3,1]=>3360
[4,7,6,1,8,3,5,2]=>[4,2,2]=>1260
[4,7,2,6,3,8,5,1]=>[4,4]=>1260
[2,1,8,4,6,7,3,5]=>[5,2,1]=>4032
[4,7,8,6,3,1,2,5]=>[3,3,2]=>1120
[3,8,1,5,6,7,2,4]=>[6,2]=>3360
[6,7,2,4,8,5,3,1]=>[4,3,1]=>3360
[2,8,3,6,7,5,1,4]=>[7,1]=>5760
[8,2,1,7,6,3,5,4]=>[7,1]=>5760
[3,2,4,5,8,1,7,6]=>[6,1,1]=>3360
[7,4,6,3,2,1,8,5]=>[8]=>5040
[4,7,3,2,1,8,6,5]=>[7,1]=>5760
[6,4,7,5,2,3,8,1]=>[5,3]=>2688
[6,4,8,1,7,3,2,5]=>[8]=>5040
[4,8,7,2,3,1,5,6]=>[5,3]=>2688
[4,2,3,1,8,7,5,6]=>[4,2,1,1]=>2520
[7,6,8,1,3,5,2,4]=>[8]=>5040
[6,7,5,2,3,1,8,4]=>[4,2,2]=>1260
[4,7,2,6,5,1,8,3]=>[4,3,1]=>3360
[6,4,2,1,8,5,7,3]=>[7,1]=>5760
[7,2,1,5,6,8,4,3]=>[7,1]=>5760
[8,7,2,6,4,1,5,3]=>[8]=>5040
[6,7,8,2,5,3,1,4]=>[7,1]=>5760
[2,1,7,3,6,8,5,4]=>[6,2]=>3360
[2,1,5,7,8,4,6,3]=>[3,3,2]=>1120
[2,5,7,8,3,6,1,4]=>[5,2,1]=>4032
[6,4,1,5,7,2,8,3]=>[8]=>5040
[7,4,8,1,2,5,6,3]=>[6,2]=>3360
[4,2,7,8,6,3,5,1]=>[4,3,1]=>3360
[6,1,7,4,3,2,8,5]=>[4,3,1]=>3360
[6,8,3,4,2,1,7,5]=>[3,2,1,1,1]=>1120
[4,2,6,1,5,7,8,3]=>[4,2,1,1]=>2520
[2,4,6,7,3,5,8,1]=>[5,3]=>2688
[6,5,8,3,7,4,1,2]=>[8]=>5040
[7,1,4,8,3,5,6,2]=>[8]=>5040
[6,8,7,5,3,4,1,2]=>[6,2]=>3360
[4,8,6,3,1,5,7,2]=>[5,2,1]=>4032
[3,4,8,2,5,7,6,1]=>[3,2,2,1]=>1680
[2,5,7,4,8,6,1,3]=>[6,1,1]=>3360
[2,6,3,7,5,1,8,4]=>[3,3,1,1]=>1120
[2,6,4,8,7,5,1,3]=>[5,3]=>2688
[6,3,7,2,8,5,1,4]=>[8]=>5040
[3,6,2,5,8,7,1,4]=>[5,3]=>2688
[7,2,4,8,6,5,1,3]=>[3,2,2,1]=>1680
[6,2,4,8,7,5,1,3]=>[4,3,1]=>3360
[2,4,5,8,7,6,1,3]=>[7,1]=>5760
[4,2,7,3,8,1,6,5]=>[5,2,1]=>4032
[6,1,3,8,7,2,5,4]=>[3,2,2,1]=>1680
[3,1,5,6,2,8,7,4]=>[4,3,1]=>3360
[1,2,4,6,3,8,7,5]=>[5,1,1,1]=>1344
[4,1,5,2,8,7,6,3]=>[3,3,2]=>1120
[4,1,5,3,2,8,7,6]=>[5,2,1]=>4032
[7,2,3,5,1,8,6,4]=>[6,1,1]=>3360
[3,4,5,1,8,7,6,2]=>[6,2]=>3360
[1,6,4,2,8,7,5,3]=>[7,1]=>5760
[7,4,2,5,1,8,6,3]=>[8]=>5040
[4,6,2,7,5,1,8,3]=>[7,1]=>5760
[1,5,3,6,2,8,7,4]=>[3,2,1,1,1]=>1120
[1,5,8,3,2,7,6,4]=>[3,2,2,1]=>1680
[4,5,8,2,1,7,6,3]=>[4,2,2]=>1260
[3,6,2,5,1,4,8,7]=>[6,2]=>3360
[2,4,8,7,1,3,6,5]=>[8]=>5040
[1,3,8,2,4,7,6,5]=>[5,2,1]=>4032
[3,5,2,1,7,4,8,6]=>[8]=>5040
[7,5,1,2,8,6,4,3]=>[7,1]=>5760
[1,5,2,3,8,7,6,4]=>[5,2,1]=>4032
[6,4,1,2,8,7,5,3]=>[6,2]=>3360
[5,2,8,1,3,7,6,4]=>[5,2,1]=>4032
[4,7,5,6,8,3,1,2]=>[8]=>5040
[8,6,4,7,5,3,1,2]=>[7,1]=>5760
[7,5,2,6,4,1,3,8]=>[7,1]=>5760
[1,6,3,7,5,8,4,2]=>[3,2,1,1,1]=>1120
[1,3,7,4,5,8,6,2]=>[5,1,1,1]=>1344
[7,2,6,3,4,1,5,8]=>[6,1,1]=>3360
[8,3,7,4,6,5,1,2]=>[5,2,1]=>4032
[6,8,4,7,5,3,1,2]=>[5,2,1]=>4032
[4,8,7,5,6,3,1,2]=>[6,2]=>3360
[3,8,7,6,4,5,1,2]=>[3,3,2]=>1120
[1,6,5,2,8,3,7,4]=>[6,1,1]=>3360
[8,6,5,2,1,4,3,7]=>[5,3]=>2688
[2,7,6,3,1,4,5,8]=>[4,3,1]=>3360
[6,8,5,3,2,1,4,7]=>[6,2]=>3360
[2,7,6,4,5,1,3,8]=>[5,1,1,1]=>1344
[5,7,2,6,4,1,3,8]=>[4,3,1]=>3360
[6,1,3,7,5,8,4,2]=>[4,2,1,1]=>2520
[4,1,7,3,6,8,5,2]=>[8]=>5040
[8,1,6,4,3,7,5,2]=>[4,3,1]=>3360
[2,1,7,4,8,6,3,5]=>[2,2,2,1,1]=>420
[1,8,6,3,7,5,4,2]=>[5,2,1]=>4032
[1,8,2,7,3,6,5,4]=>[6,1,1]=>3360
[2,1,3,8,4,7,5,6]=>[5,2,1]=>4032
[8,1,2,7,4,3,6,5]=>[8]=>5040
[5,3,1,6,8,4,7,2]=>[5,2,1]=>4032
[6,2,8,7,1,4,3,5]=>[7,1]=>5760
[8,7,2,1,5,4,3,6]=>[4,3,1]=>3360
[8,2,3,1,4,6,5,7]=>[5,1,1,1]=>1344
[2,4,8,3,1,5,6,7]=>[8]=>5040
[3,4,2,7,1,5,6,8]=>[7,1]=>5760
[4,7,3,8,2,1,5,6]=>[4,3,1]=>3360
[5,2,7,3,1,4,6,8]=>[4,2,1,1]=>2520
[8,3,7,2,1,5,4,6]=>[4,4]=>1260
[1,3,7,2,8,4,6,5]=>[5,2,1]=>4032
[1,4,2,5,8,6,7,3]=>[5,1,1,1]=>1344
[6,5,3,8,2,1,4,7]=>[3,2,2,1]=>1680
[2,6,4,5,7,1,3,8]=>[4,3,1]=>3360
[5,4,6,2,7,1,3,8]=>[5,2,1]=>4032
[7,6,3,1,8,4,5,2]=>[7,1]=>5760
[7,6,2,1,8,5,3,4]=>[8]=>5040
[1,7,5,8,6,4,3,2]=>[7,1]=>5760
[6,5,1,2,8,3,7,4]=>[4,3,1]=>3360
[8,6,1,4,3,7,5,2]=>[7,1]=>5760
[6,8,4,1,3,7,5,2]=>[6,2]=>3360
[6,5,7,1,3,8,4,2]=>[8]=>5040
[5,8,3,1,7,4,6,2]=>[5,2,1]=>4032
[8,3,1,7,5,4,6,2]=>[4,3,1]=>3360
[1,3,8,7,4,6,5,2]=>[3,3,1,1]=>1120
[1,2,8,7,6,3,5,4]=>[6,1,1]=>3360
[8,2,1,7,6,4,3,5]=>[7,1]=>5760
[2,3,1,8,7,4,5,6]=>[3,3,2]=>1120
[2,4,1,8,5,7,3,6]=>[7,1]=>5760
[5,8,2,1,7,6,3,4]=>[7,1]=>5760
[6,2,7,1,8,5,3,4]=>[5,2,1]=>4032
[8,7,1,6,5,4,3,2]=>[5,2,1]=>4032
[7,1,8,3,6,5,4,2]=>[6,2]=>3360
[4,1,8,7,5,6,3,2]=>[6,1,1]=>3360
[8,1,2,3,4,5,9,6,7]=>[7,2]=>25920
[8,1,2,3,4,9,5,6,7]=>[9]=>40320
[8,1,2,9,3,4,5,6,7]=>[9]=>40320
[8,1,9,2,3,4,5,6,7]=>[5,4]=>18144
[9,1,2,3,4,5,6,10,7,8]=>[8,2]=>226800
[4,1,2,3,8,9,5,6,7]=>[5,4]=>18144
[2,1,8,9,3,4,5,6,7]=>[7,2]=>25920
[3,5,8,7,2,6,4,1]=>[3,2,2,1]=>1680
[5,8,2,7,1,6,4,3]=>[3,2,2,1]=>1680
[2,1,6,4,5,8,3,7]=>[4,2,1,1]=>2520
[4,6,3,7,5,2,8,1]=>[4,2,1,1]=>2520
[3,5,7,8,2,6,1,4]=>[3,2,2,1]=>1680
[8,2,3,4,6,1,5,7]=>[5,1,1,1]=>1344
[7,2,3,4,6,8,5,1]=>[5,1,1,1]=>1344
[4,8,3,7,5,1,6,2]=>[4,2,1,1]=>2520
[5,2,3,4,8,7,1,6]=>[5,1,1,1]=>1344
[5,2,3,4,6,8,1,7]=>[5,1,1,1]=>1344
[4,2,8,5,7,6,1,3]=>[4,2,1,1]=>2520
[3,7,6,4,5,1,8,2]=>[3,3,1,1]=>1120
[8,7,3,6,5,1,2,4]=>[4,2,1,1]=>2520
[4,2,7,5,8,6,3,1]=>[4,2,1,1]=>2520
[5,8,1,7,3,6,4,2]=>[3,2,2,1]=>1680
[5,2,7,8,4,6,3,1]=>[4,2,1,1]=>2520
[5,2,8,3,7,6,1,4]=>[3,3,1,1]=>1120
[8,2,7,3,1,6,4,5]=>[3,3,1,1]=>1120
[6,2,3,4,8,5,1,7]=>[5,1,1,1]=>1344
[6,2,3,4,1,8,5,7]=>[5,1,1,1]=>1344
[7,2,3,4,1,8,6,5]=>[5,1,1,1]=>1344
[7,2,3,4,1,5,8,6]=>[5,1,1,1]=>1344
[1,2,3,4,8,7,5,6]=>[4,1,1,1,1]=>420
[1,2,8,5,3,4,6,7]=>[6,1,1]=>3360
[1,8,4,2,3,5,6,7]=>[7,1]=>5760
[8,6,7,4,1,5,3,2]=>[5,2,1]=>4032
[7,1,8,4,6,5,2,3]=>[3,2,2,1]=>1680
[8,7,1,5,4,6,2,3]=>[3,2,2,1]=>1680
[8,5,7,1,4,6,3,2]=>[5,2,1]=>4032
[6,4,8,5,1,7,3,2]=>[8]=>5040
[8,7,5,1,4,6,2,3]=>[5,2,1]=>4032
[8,7,2,5,1,4,6,3]=>[8]=>5040
[1,6,4,8,5,2,7,3]=>[3,2,1,1,1]=>1120
[8,7,1,4,2,5,6,3]=>[4,3,1]=>3360
[3,8,7,1,2,5,6,4]=>[8]=>5040
[2,3,8,5,7,1,6,4]=>[8]=>5040
[3,5,8,7,1,6,2,4]=>[7,1]=>5760
[2,3,8,6,7,5,1,4]=>[8]=>5040
[4,1,8,6,2,7,5,3]=>[6,2]=>3360
[5,7,1,8,2,6,3,4]=>[5,2,1]=>4032
[2,8,7,1,5,6,3,4]=>[4,2,1,1]=>2520
[1,3,8,5,7,2,6,4]=>[7,1]=>5760
[1,8,3,7,2,5,6,4]=>[6,1,1]=>3360
[2,8,7,1,3,5,6,4]=>[4,4]=>1260
[7,1,8,2,3,5,6,4]=>[8]=>5040
[8,6,3,7,4,1,5,2]=>[4,3,1]=>3360
[4,2,8,6,7,5,1,3]=>[5,2,1]=>4032
[8,4,2,7,5,6,1,3]=>[6,1,1]=>3360
[4,8,3,6,1,7,5,2]=>[5,2,1]=>4032
[8,3,4,7,5,1,6,2]=>[7,1]=>5760
[8,3,7,4,5,1,6,2]=>[6,1,1]=>3360
[8,7,4,2,5,6,1,3]=>[6,1,1]=>3360
[8,7,5,1,6,2,3,4]=>[5,3]=>2688
[8,7,2,4,1,5,6,3]=>[7,1]=>5760
[4,8,6,1,7,2,5,3]=>[4,2,2]=>1260
[4,7,1,8,2,6,5,3]=>[4,3,1]=>3360
[4,2,8,6,7,1,5,3]=>[3,2,2,1]=>1680
[8,7,4,1,2,5,6,3]=>[4,4]=>1260
[8,2,7,1,6,3,4,5]=>[7,1]=>5760
[8,2,7,1,3,6,4,5]=>[6,1,1]=>3360
[2,8,3,6,7,1,5,4]=>[5,2,1]=>4032
[8,7,2,1,3,5,6,4]=>[5,3]=>2688
[1,8,7,2,3,6,4,5]=>[6,1,1]=>3360
[1,8,7,2,6,3,4,5]=>[7,1]=>5760
[8,2,7,3,6,1,4,5]=>[4,3,1]=>3360
[1,8,7,3,6,2,4,5]=>[4,3,1]=>3360
[1,8,2,7,6,3,4,5]=>[5,2,1]=>4032
[8,2,7,4,1,5,6,3]=>[6,1,1]=>3360
[8,2,1,7,5,6,3,4]=>[5,1,1,1]=>1344
[8,7,3,1,5,6,2,4]=>[3,2,1,1,1]=>1120
[2,8,7,3,5,6,1,4]=>[6,1,1]=>3360
[8,3,1,6,7,5,2,4]=>[8]=>5040
[8,5,2,1,6,7,4,3]=>[8]=>5040
[1,5,2,8,6,7,4,3]=>[7,1]=>5760
[1,2,8,6,7,5,3,4]=>[6,1,1]=>3360
[1,8,3,6,7,5,2,4]=>[6,1,1]=>3360
[8,2,3,6,7,5,1,4]=>[6,1,1]=>3360
[8,3,7,2,5,6,1,4]=>[6,1,1]=>3360
[8,1,3,7,5,6,2,4]=>[5,1,1,1]=>1344
[8,4,1,2,7,5,6,3]=>[3,3,2]=>1120
[8,1,4,2,6,7,5,3]=>[5,3]=>2688
[1,2,8,6,7,3,5,4]=>[4,2,1,1]=>2520
[8,1,2,7,3,6,4,5]=>[5,2,1]=>4032
[8,1,7,3,6,2,4,5]=>[5,3]=>2688
[8,1,7,2,6,3,4,5]=>[8]=>5040
[8,1,7,2,3,6,4,5]=>[7,1]=>5760
[8,1,3,7,2,5,6,4]=>[7,1]=>5760
[1,8,3,6,7,2,5,4]=>[4,2,1,1]=>2520
[1,7,8,2,3,6,5,4]=>[6,1,1]=>3360
[8,3,7,1,2,5,6,4]=>[5,3]=>2688
[8,7,1,2,3,6,4,5]=>[4,3,1]=>3360
[2,8,5,7,4,6,3,1]=>[4,3,1]=>3360
[3,1,8,5,7,4,2,6]=>[8]=>5040
[8,3,5,7,4,2,6,1]=>[6,2]=>3360
[8,3,6,2,4,5,7,1]=>[5,2,1]=>4032
[2,8,6,4,3,5,7,1]=>[3,3,1,1]=>1120
[2,6,8,3,5,4,7,1]=>[6,1,1]=>3360
[2,7,5,8,4,6,3,1]=>[7,1]=>5760
[8,4,2,7,6,1,3,5]=>[4,4]=>1260
[4,8,1,7,6,3,2,5]=>[8]=>5040
[4,1,7,6,2,3,5,8]=>[7,1]=>5760
[3,7,1,8,6,2,5,4]=>[4,2,2]=>1260
[3,1,7,6,4,5,2,8]=>[4,3,1]=>3360
[3,1,7,5,8,4,2,6]=>[4,4]=>1260
[3,1,6,8,7,5,2,4]=>[6,2]=>3360
[6,3,8,7,5,2,4,1]=>[5,2,1]=>4032
[7,3,5,8,4,2,6,1]=>[8]=>5040
[7,3,6,4,2,8,5,1]=>[7,1]=>5760
[7,8,3,6,2,5,4,1]=>[7,1]=>5760
[7,4,8,2,1,6,3,5]=>[5,2,1]=>4032
[8,7,4,6,3,2,5,1]=>[6,2]=>3360
[7,8,5,2,1,4,3,6]=>[4,4]=>1260
[7,5,2,3,1,4,8,6]=>[8]=>5040
[7,4,6,2,3,8,1,5]=>[4,2,2]=>1260
[6,4,2,5,8,3,7,1]=>[7,1]=>5760
[4,6,5,8,1,3,2,7]=>[8]=>5040
[4,7,1,5,3,8,2,6]=>[4,2,2]=>1260
[4,7,8,1,3,6,2,5]=>[3,2,2,1]=>1680
[5,7,1,3,4,6,2,8]=>[4,2,1,1]=>2520
[5,7,1,4,2,3,6,8]=>[6,1,1]=>3360
[5,8,1,3,2,4,6,7]=>[8]=>5040
[4,8,6,1,3,2,7,5]=>[5,2,1]=>4032
[8,4,6,2,1,3,7,5]=>[3,2,2,1]=>1680
[5,4,8,7,2,3,6,1]=>[8]=>5040
[5,4,8,7,3,1,2,6]=>[5,3]=>2688
[6,8,3,7,2,5,4,1]=>[5,2,1]=>4032
[5,4,6,8,2,3,7,1]=>[5,2,1]=>4032
[5,7,4,2,8,3,6,1]=>[5,3]=>2688
[6,4,7,2,1,8,3,5]=>[4,2,2]=>1260
[6,5,3,4,1,2,8,7]=>[4,2,1,1]=>2520
[6,8,5,4,1,3,2,7]=>[4,3,1]=>3360
[6,4,3,7,1,5,2,8]=>[3,3,1,1]=>1120
[9,8,7,6,5,2,3,1,4]=>[6,2,1]=>30240
[7,4,2,5,6,1,3,8]=>[7,1]=>5760
[6,4,2,8,1,5,7,3]=>[4,3,1]=>3360
[6,3,7,8,2,5,1,4]=>[6,2]=>3360
[7,3,5,6,4,2,1,8]=>[5,2,1]=>4032
[5,3,7,6,8,2,4,1]=>[5,3]=>2688
[4,8,6,7,5,3,2,1]=>[5,2,1]=>4032
[6,3,8,7,2,4,1,5]=>[4,4]=>1260
[5,3,8,7,2,6,4,1]=>[5,2,1]=>4032
[5,3,7,8,6,2,4,1]=>[8]=>5040
[5,7,6,4,8,2,1,3]=>[7,1]=>5760
[6,5,2,4,3,7,8,1]=>[4,3,1]=>3360
[5,4,6,2,8,7,1,3]=>[6,2]=>3360
[5,7,4,3,6,8,1,2]=>[6,2]=>3360
[5,7,3,8,6,2,4,1]=>[7,1]=>5760
[5,7,8,2,6,4,1,3]=>[6,2]=>3360
[3,6,8,5,7,1,4,2]=>[5,3]=>2688
[1,7,4,8,6,2,3,5]=>[7,1]=>5760
[3,6,2,5,7,8,1,4]=>[8]=>5040
[5,2,7,4,6,8,1,3]=>[6,1,1]=>3360
[5,3,6,7,1,8,4,2]=>[4,2,2]=>1260
[4,2,5,6,7,1,8,3]=>[4,3,1]=>3360
[8,1,3,6,7,2,4,5]=>[7,1]=>5760
[8,1,4,2,7,5,3,6]=>[8]=>5040
[6,1,3,8,2,7,4,5]=>[7,1]=>5760
[1,7,5,2,8,6,3,4]=>[6,1,1]=>3360
[1,5,8,4,2,6,3,7]=>[3,2,1,1,1]=>1120
[3,5,7,4,1,6,8,2]=>[6,1,1]=>3360
[3,5,7,1,2,6,4,8]=>[4,2,1,1]=>2520
[4,5,1,8,2,3,7,6]=>[5,2,1]=>4032
[4,7,1,8,2,6,3,5]=>[7,1]=>5760
[7,5,1,2,3,8,6,4]=>[8]=>5040
[7,8,4,5,1,3,2,6]=>[8]=>5040
[6,7,1,3,2,5,4,8]=>[7,1]=>5760
[6,7,1,4,3,5,2,8]=>[4,2,1,1]=>2520
[7,8,2,3,1,5,4,6]=>[8]=>5040
[7,8,2,4,3,5,1,6]=>[5,2,1]=>4032
[7,8,2,4,1,5,3,6]=>[7,1]=>5760
[1,4,2,6,5,7,3,8]=>[5,1,1,1]=>1344
[5,6,1,4,2,7,3,8]=>[6,1,1]=>3360
[6,7,2,4,1,5,3,8]=>[3,3,1,1]=>1120
[6,7,2,4,3,5,1,8]=>[6,1,1]=>3360
[6,7,2,3,1,5,4,8]=>[4,3,1]=>3360
[6,7,3,5,4,8,1,2]=>[5,2,1]=>4032
[2,4,1,6,5,7,3,8]=>[6,1,1]=>3360
[1,5,2,6,4,7,3,8]=>[6,1,1]=>3360
[2,5,1,6,4,7,3,8]=>[7,1]=>5760
[3,6,5,7,4,8,1,2]=>[5,3]=>2688
[5,6,2,4,3,7,1,8]=>[6,1,1]=>3360
[4,5,2,6,1,7,3,8]=>[7,1]=>5760
[4,5,1,6,3,7,2,8]=>[7,1]=>5760
[4,5,3,6,1,7,2,8]=>[6,1,1]=>3360
[5,6,3,4,1,7,2,8]=>[3,2,1,1,1]=>1120
[5,6,1,4,3,7,2,8]=>[3,3,1,1]=>1120
[5,6,1,3,2,7,4,8]=>[7,1]=>5760
[5,6,4,7,1,3,2,8]=>[5,2,1]=>4032
[6,7,4,5,1,3,2,8]=>[5,2,1]=>4032
[6,7,5,8,1,3,2,4]=>[4,2,2]=>1260
[4,5,1,3,2,7,6,8]=>[3,2,2,1]=>1680
[4,6,5,7,1,3,2,8]=>[7,1]=>5760
[4,6,1,3,2,7,5,8]=>[4,3,1]=>3360
[1,4,3,6,2,7,5,8]=>[5,1,1,1]=>1344
[3,4,1,6,5,7,2,8]=>[4,2,1,1]=>2520
[4,5,2,3,1,7,6,8]=>[5,2,1]=>4032
[4,5,3,7,6,8,1,2]=>[4,3,1]=>3360
[4,6,5,7,3,8,1,2]=>[3,3,2]=>1120
[4,6,5,7,2,3,1,8]=>[4,3,1]=>3360
[3,5,4,6,1,7,2,8]=>[7,1]=>5760
[3,5,1,6,4,7,2,8]=>[5,2,1]=>4032
[1,5,3,6,4,7,2,8]=>[5,1,1,1]=>1344
[1,5,3,6,2,7,4,8]=>[3,2,1,1,1]=>1120
[3,5,2,6,1,7,4,8]=>[4,3,1]=>3360
[3,5,2,6,4,7,1,8]=>[7,1]=>5760
[3,4,2,6,1,7,5,8]=>[7,1]=>5760
[4,6,2,3,1,7,5,8]=>[7,1]=>5760
[2,4,3,6,1,7,5,8]=>[6,1,1]=>3360
[2,5,3,6,4,7,1,8]=>[6,1,1]=>3360
[2,5,3,6,1,7,4,8]=>[3,3,1,1]=>1120
[3,6,2,7,5,4,8,1]=>[7,1]=>5760
[4,6,1,7,3,8,2,5]=>[8]=>5040
[5,2,6,7,4,3,8,1]=>[5,2,1]=>4032
[3,5,2,7,6,4,8,1]=>[8]=>5040
[1,5,7,2,8,3,6,4]=>[4,3,1]=>3360
[2,5,7,3,1,8,4,6]=>[3,3,2]=>1120
[2,1,5,6,8,4,3,7]=>[4,2,2]=>1260
[1,3,7,2,8,5,4,6]=>[4,3,1]=>3360
[4,6,2,7,1,8,3,5]=>[8]=>5040
[1,5,4,3,6,8,2,7]=>[5,2,1]=>4032
[1,6,4,5,7,8,3,2]=>[4,3,1]=>3360
[2,1,5,6,8,4,7,3]=>[3,2,2,1]=>1680
[2,1,5,6,8,7,3,4]=>[6,2]=>3360
[3,6,5,2,7,8,4,1]=>[8]=>5040
[6,2,4,7,5,8,3,1]=>[3,3,1,1]=>1120
[1,5,7,8,4,2,6,3]=>[7,1]=>5760
[3,7,4,1,8,6,2,5]=>[3,2,2,1]=>1680
[3,4,6,8,5,7,2,1]=>[7,1]=>5760
[4,2,5,7,3,1,8,6]=>[5,2,1]=>4032
[2,5,6,8,1,7,4,3]=>[5,3]=>2688
[4,5,6,1,8,7,3,2]=>[3,3,2]=>1120
[4,5,6,3,1,8,7,2]=>[7,1]=>5760
[4,3,6,2,1,7,5,8]=>[7,1]=>5760
[4,6,3,2,1,7,5,8]=>[6,1,1]=>3360
[4,3,5,7,6,1,8,2]=>[8]=>5040
[4,3,2,6,1,7,5,8]=>[5,2,1]=>4032
[5,3,2,1,6,4,7,8]=>[4,2,1,1]=>2520
[5,3,1,6,2,7,4,8]=>[4,3,1]=>3360
[5,1,6,3,2,7,4,8]=>[4,3,1]=>3360
[5,3,6,4,2,1,7,8]=>[5,1,1,1]=>1344
[5,3,2,6,4,1,7,8]=>[4,2,1,1]=>2520
[5,2,1,6,3,7,4,8]=>[3,3,1,1]=>1120
[5,2,6,3,1,7,4,8]=>[4,2,1,1]=>2520
[4,2,6,3,1,7,8,5]=>[7,1]=>5760
[3,6,2,1,7,4,5,8]=>[5,2,1]=>4032
[3,6,2,7,4,1,5,8]=>[4,3,1]=>3360
[2,4,7,1,3,6,5,8]=>[3,3,1,1]=>1120
[2,6,1,3,7,5,4,8]=>[7,1]=>5760
[5,1,6,2,7,4,3,8]=>[7,1]=>5760
[5,2,1,6,4,3,7,8]=>[5,1,1,1]=>1344
[5,4,2,1,6,3,7,8]=>[6,1,1]=>3360
[5,4,2,6,3,1,7,8]=>[6,1,1]=>3360
[5,4,1,6,2,7,3,8]=>[7,1]=>5760
[5,1,6,4,2,7,3,8]=>[3,3,1,1]=>1120
[2,6,1,5,4,3,7,8]=>[4,2,1,1]=>2520
[3,1,6,2,5,4,7,8]=>[5,1,1,1]=>1344
[5,1,6,4,3,2,7,8]=>[5,1,1,1]=>1344
[5,4,1,6,3,2,7,8]=>[3,3,1,1]=>1120
[5,4,3,1,6,2,7,8]=>[5,1,1,1]=>1344
[8,2,1,7,6,5,4,3,9]=>[3,2,2,1,1]=>7560
[7,3,1,6,5,4,8,2]=>[5,2,1]=>4032
[7,2,8,1,5,4,3,6]=>[6,1,1]=>3360
[4,2,7,6,5,8,1,3]=>[6,1,1]=>3360
[3,8,2,6,5,4,1,7]=>[5,2,1]=>4032
[3,2,8,7,6,5,4,1,9]=>[3,2,2,1,1]=>7560
[10,1,11,9,8,7,6,5,4,3,2]=>[5,2,2,2]=>166320
[9,2,1,8,7,6,5,4,3,10]=>[3,2,2,1,1,1]=>25200
[8,3,1,7,6,5,4,9,2]=>[5,2,2]=>9072
[8,2,9,1,6,5,4,3,7]=>[6,2,1]=>30240
[7,3,2,1,5,4,6,8]=>[4,2,1,1]=>2520
[7,2,8,6,1,4,3,5]=>[5,2,1]=>4032
[5,2,7,6,8,4,1,3]=>[5,2,1]=>4032
[4,2,8,7,6,5,9,1,3]=>[6,2,1]=>30240
[3,8,7,2,5,4,1,6]=>[4,3,1]=>3360
[3,9,2,7,6,5,4,1,8]=>[5,2,2]=>9072
[3,2,9,8,7,6,5,4,1,10]=>[3,2,2,1,1,1]=>25200
[2,11,10,9,8,7,6,5,4,1,3]=>[5,2,2,2]=>166320
[11,1,12,10,9,8,7,6,5,4,3,2]=>[5,2,2,2,1]=>1995840
[9,3,1,8,7,6,5,4,10,2]=>[5,2,2,1]=>90720
[9,2,10,1,7,6,5,4,3,8]=>[6,2,1,1]=>151200
[8,4,1,7,6,5,9,3,2]=>[4,3,2]=>15120
[8,3,2,1,6,5,4,7,9]=>[4,2,2,1]=>11340
[8,2,9,7,1,5,4,3,6]=>[6,2,1]=>30240
[7,5,1,6,8,4,3,2]=>[3,3,2]=>1120
[7,4,2,1,5,6,3,8]=>[5,1,1,1]=>1344
[7,2,8,6,5,1,3,4]=>[6,1,1]=>3360
[5,3,2,6,7,4,1,8]=>[3,2,2,1]=>1680
[5,2,8,7,6,9,4,1,3]=>[6,2,1]=>30240
[4,3,7,2,5,6,1,8]=>[5,1,1,1]=>1344
[4,3,2,7,6,5,8,1,9]=>[4,2,2,1]=>11340
[4,2,9,8,7,6,5,10,1,3]=>[6,2,1,1]=>151200
[3,9,8,2,6,5,4,1,7]=>[4,3,2]=>15120
[3,10,2,8,7,6,5,4,1,9]=>[5,2,2,1]=>90720
[2,12,11,10,9,8,7,6,5,4,1,3]=>[5,2,2,2,1]=>1995840
[6,7,1,4,3,2,5,8]=>[6,1,1]=>3360
[3,4,2,6,7,1,5,8]=>[5,2,1]=>4032
[3,7,1,6,5,2,4,8]=>[4,2,1,1]=>2520
[3,5,6,2,4,7,1,8]=>[4,3,1]=>3360
[3,5,8,7,2,4,6,1]=>[3,3,2]=>1120
[1,7,8,2,5,4,3,6]=>[6,1,1]=>3360
[8,7,2,5,4,3,6,1]=>[4,2,2]=>1260
[2,5,6,4,7,1,3,8]=>[6,1,1]=>3360
[4,7,1,6,3,5,2,8]=>[5,2,1]=>4032
[4,5,3,8,7,2,6,1]=>[4,3,1]=>3360
[1,4,5,3,7,8,2,6]=>[5,2,1]=>4032
[1,4,8,2,7,6,3,5]=>[4,2,1,1]=>2520
[4,7,3,5,1,8,6,2]=>[4,3,1]=>3360
[8,7,3,6,1,5,4,2]=>[7,1]=>5760
[2,5,8,7,4,6,1,3]=>[5,2,1]=>4032
[5,4,2,1,7,8,3,6]=>[6,2]=>3360
[4,7,8,3,5,2,1,6]=>[7,1]=>5760
[4,7,6,2,1,8,3,5]=>[8]=>5040
[1,4,6,7,3,5,8,2]=>[4,3,1]=>3360
[8,3,6,2,1,7,5,4]=>[8]=>5040
[8,3,7,6,4,2,1,5]=>[8]=>5040
[2,3,1,8,4,7,6,5]=>[3,3,2]=>1120
[2,7,4,8,6,5,1,3]=>[3,3,2]=>1120
[8,6,5,1,4,7,3,2]=>[8]=>5040
[8,5,4,1,7,3,6,2]=>[8]=>5040
[6,3,7,2,8,5,4,1]=>[4,4]=>1260
[1,6,3,8,2,7,5,4]=>[4,2,1,1]=>2520
[1,7,5,3,8,2,6,4]=>[4,3,1]=>3360
[6,2,7,4,1,8,5,3]=>[6,1,1]=>3360
[8,6,3,2,7,5,1,4]=>[7,1]=>5760
[2,7,5,1,3,8,6,4]=>[6,2]=>3360
[1,7,6,4,3,8,2,5]=>[4,2,1,1]=>2520
[3,7,2,4,8,6,5,1]=>[6,1,1]=>3360
[3,4,2,8,7,6,1,5]=>[7,1]=>5760
[5,1,4,3,2,7,8,6]=>[3,3,2]=>1120
[3,7,8,5,2,4,1,6]=>[8]=>5040
[3,7,6,2,4,1,8,5]=>[5,3]=>2688
[1,6,8,2,5,7,4,3]=>[4,2,1,1]=>2520
[6,7,2,5,8,4,3,1]=>[5,3]=>2688
[5,2,7,8,4,3,1,6]=>[7,1]=>5760
[5,3,1,7,8,4,2,6]=>[8]=>5040
[2,7,6,4,1,3,8,5]=>[5,2,1]=>4032
[4,1,7,6,3,2,8,5]=>[4,4]=>1260
[8,4,2,7,6,3,1,5]=>[8]=>5040
[6,3,1,7,5,2,8,4]=>[4,3,1]=>3360
[6,2,7,5,3,1,8,4]=>[5,2,1]=>4032
[1,5,8,2,7,4,6,3]=>[5,2,1]=>4032
[5,7,2,8,4,6,3,1]=>[4,3,1]=>3360
[5,7,3,1,8,4,6,2]=>[7,1]=>5760
[8,4,7,3,1,6,5,2]=>[7,1]=>5760
[2,6,8,5,7,4,1,3]=>[6,2]=>3360
[6,5,2,1,7,4,8,3]=>[5,3]=>2688
[5,7,4,6,2,1,8,3]=>[8]=>5040
[5,6,4,8,3,7,2,1]=>[5,3]=>2688
[6,7,1,8,3,4,2,5]=>[6,2]=>3360
[7,8,3,5,1,4,2,6]=>[7,1]=>5760
[5,6,2,7,1,8,3,4]=>[6,2]=>3360
[6,7,2,4,3,8,1,5]=>[7,1]=>5760
[2,4,3,8,6,7,1,5]=>[7,1]=>5760
[1,8,2,7,4,5,3,6]=>[7,1]=>5760
[2,5,4,8,3,6,1,7]=>[7,1]=>5760
[2,3,1,8,5,6,4,7]=>[3,3,1,1]=>1120
[3,8,5,6,4,7,1,2]=>[6,2]=>3360
[5,7,3,6,4,8,1,2]=>[7,1]=>5760
[5,7,2,3,1,6,4,8]=>[4,2,1,1]=>2520
[5,7,2,4,3,6,1,8]=>[5,1,1,1]=>1344
[4,6,2,7,1,5,3,8]=>[7,1]=>5760
[4,7,1,6,2,5,3,8]=>[7,1]=>5760
[4,7,1,5,3,6,2,8]=>[4,2,1,1]=>2520
[4,6,3,5,1,7,2,8]=>[3,3,1,1]=>1120
[6,7,3,5,1,4,2,8]=>[4,2,1,1]=>2520
[5,6,3,7,1,4,2,8]=>[4,2,1,1]=>2520
[5,7,1,6,3,4,2,8]=>[3,2,2,1]=>1680
[1,8,5,6,3,4,2,7]=>[3,2,2,1]=>1680
[1,8,5,6,4,7,2,3]=>[7,1]=>5760
[5,7,1,6,4,8,2,3]=>[6,2]=>3360
[4,6,5,8,1,7,2,3]=>[5,3]=>2688
[3,7,1,4,2,8,5,6]=>[3,2,2,1]=>1680
[3,5,1,4,2,8,6,7]=>[3,2,2,1]=>1680
[4,6,5,8,3,7,1,2]=>[6,2]=>3360
[4,6,5,8,2,3,1,7]=>[4,4]=>1260
[3,4,2,6,5,8,1,7]=>[7,1]=>5760
[3,5,4,6,2,8,1,7]=>[6,2]=>3360
[1,8,3,5,4,7,2,6]=>[4,2,1,1]=>2520
[3,4,2,7,1,8,5,6]=>[6,2]=>3360
[4,7,2,3,1,8,5,6]=>[6,2]=>3360
[2,4,3,8,1,7,5,6]=>[7,1]=>5760
[2,5,3,8,4,7,1,6]=>[7,1]=>5760
[2,6,3,8,1,7,4,5]=>[7,1]=>5760
[2,7,1,8,3,6,4,5]=>[7,1]=>5760
[4,5,1,8,7,6,2,3]=>[4,3,1]=>3360
[5,2,6,8,3,7,4,1]=>[7,1]=>5760
[3,1,6,8,7,4,5,2]=>[6,2]=>3360
[6,1,4,8,7,2,5,3]=>[3,3,2]=>1120
[6,1,8,4,7,3,5,2]=>[5,2,1]=>4032
[6,8,3,5,7,1,4,2]=>[3,2,2,1]=>1680
[4,6,7,8,2,5,3,1]=>[3,3,2]=>1120
[7,4,5,2,8,6,3,1]=>[5,2,1]=>4032
[6,8,2,5,3,7,4,1]=>[8]=>5040
[6,3,8,4,2,7,5,1]=>[7,1]=>5760
[3,4,7,5,8,6,2,1]=>[7,1]=>5760
[2,7,5,3,8,6,4,1]=>[7,1]=>5760
[5,6,2,8,3,7,4,1]=>[8]=>5040
[1,5,8,2,7,3,6,4]=>[7,1]=>5760
[6,8,5,3,7,2,4,1]=>[4,4]=>1260
[6,8,5,2,3,7,4,1]=>[6,2]=>3360
[7,5,3,8,2,6,4,1]=>[4,2,1,1]=>2520
[7,5,2,3,8,6,4,1]=>[7,1]=>5760
[6,7,3,4,8,5,2,1]=>[4,2,1,1]=>2520
[7,4,2,5,8,6,3,1]=>[7,1]=>5760
[7,4,5,8,1,6,3,2]=>[4,3,1]=>3360
[6,3,4,7,8,5,2,1]=>[4,4]=>1260
[6,1,2,7,4,5,8,3]=>[8]=>5040
[2,5,8,3,4,1,6,7]=>[8]=>5040
[11,1,2,3,4,5,6,7,8,9,12,10]=>[12]=>39916800
[5,6,2,7,4,3,8,1]=>[5,3]=>2688
[4,6,7,3,2,5,8,1]=>[5,3]=>2688
[2,6,1,8,4,5,3,7]=>[8]=>5040
[2,5,7,8,4,3,6,1]=>[5,3]=>2688
[2,12,1,3,4,5,6,7,8,9,10,11]=>[12]=>39916800
[3,4,5,7,8,6,1,2]=>[7,1]=>5760
[3,4,5,7,6,8,1,2]=>[8]=>5040
[3,4,5,6,8,7,1,2]=>[8]=>5040
[1,2,5,8,3,6,4,7]=>[3,2,1,1,1]=>1120
[1,2,5,8,3,4,7,6]=>[3,2,1,1,1]=>1120
[7,8,1,2,3,5,4,6]=>[8]=>5040
[1,2,5,7,3,6,8,4]=>[3,2,1,1,1]=>1120
[1,6,8,4,5,2,7,3]=>[2,2,1,1,1,1]=>210
[1,6,8,2,3,7,4,5]=>[4,3,1]=>3360
[1,4,5,7,6,2,8,3]=>[7,1]=>5760
[7,8,1,2,3,4,6,5]=>[8]=>5040
[7,8,1,2,3,6,4,5]=>[7,1]=>5760
[4,2,1,6,5,3,8,7]=>[4,2,1,1]=>2520
[6,8,2,1,4,3,7,5]=>[7,1]=>5760
[8,6,2,4,3,1,5,7]=>[7,1]=>5760
[4,6,5,2,8,3,7,1]=>[7,1]=>5760
[2,6,4,5,8,3,7,1]=>[7,1]=>5760
[8,4,2,6,3,5,1,7]=>[5,3]=>2688
[4,2,6,3,5,8,7,1]=>[5,1,1,1]=>1344
[6,2,4,3,8,5,7,1]=>[4,2,1,1]=>2520
[8,2,4,3,6,5,1,7]=>[3,2,2,1]=>1680
[2,6,8,7,4,5,1,3]=>[6,2]=>3360
[4,2,8,6,5,7,1,3]=>[4,2,1,1]=>2520
[8,2,6,4,5,1,3,7]=>[5,1,1,1]=>1344
[2,8,5,3,1,4,6,7]=>[8]=>5040
[2,7,4,8,3,5,1,6]=>[5,3]=>2688
[2,7,4,8,3,5,6,1]=>[8]=>5040
[7,2,8,4,3,5,1,6]=>[4,2,1,1]=>2520
[8,4,2,1,5,3,6,7]=>[7,1]=>5760
[8,5,1,4,2,3,6,7]=>[5,2,1]=>4032
[8,4,1,5,3,2,6,7]=>[8]=>5040
[6,7,3,8,4,2,5,1]=>[7,1]=>5760
[6,7,3,8,4,2,1,5]=>[4,3,1]=>3360
[7,1,8,4,3,5,2,6]=>[4,3,1]=>3360
[1,7,8,4,3,5,2,6]=>[4,2,1,1]=>2520
[7,1,4,8,3,5,2,6]=>[5,3]=>2688
[7,4,8,1,5,6,2,3]=>[4,2,1,1]=>2520
[7,1,8,4,3,5,6,2]=>[7,1]=>5760
[6,7,3,1,8,4,5,2]=>[4,3,1]=>3360
[6,7,3,8,4,5,2,1]=>[5,2,1]=>4032
[6,7,1,4,8,3,5,2]=>[4,3,1]=>3360
[6,7,4,1,3,8,2,5]=>[6,2]=>3360
[1,6,7,8,4,3,2,5]=>[4,3,1]=>3360
[7,2,1,8,4,5,3,6]=>[4,3,1]=>3360
[6,2,7,1,8,4,3,5]=>[3,2,2,1]=>1680
[6,2,7,8,4,3,1,5]=>[4,3,1]=>3360
[6,2,7,8,4,3,5,1]=>[7,1]=>5760
[2,6,7,4,8,3,5,1]=>[7,1]=>5760
[2,6,7,4,8,3,1,5]=>[5,2,1]=>4032
[7,8,1,3,6,2,4,5]=>[4,4]=>1260
[1,2,7,8,6,3,4,5]=>[6,1,1]=>3360
[2,6,7,1,8,5,3,4]=>[6,2]=>3360
[2,6,7,8,5,3,1,4]=>[5,2,1]=>4032
[2,6,7,8,5,3,4,1]=>[7,1]=>5760
[6,2,7,8,4,5,3,1]=>[5,2,1]=>4032
[7,2,1,8,4,5,6,3]=>[7,1]=>5760
[1,7,2,8,4,5,6,3]=>[7,1]=>5760
[3,7,8,1,5,6,2,4]=>[4,2,1,1]=>2520
[6,3,7,8,1,5,2,4]=>[3,3,2]=>1120
[6,7,1,2,8,5,3,4]=>[8]=>5040
[1,6,7,8,4,2,5,3]=>[5,2,1]=>4032
[3,1,2,7,6,5,8,4]=>[3,3,2]=>1120
[6,1,2,4,7,3,8,5]=>[4,3,1]=>3360
[1,7,5,3,6,4,8,2]=>[4,3,1]=>3360
[5,1,2,6,7,4,8,3]=>[6,2]=>3360
[4,1,5,7,3,2,6,8]=>[5,2,1]=>4032
[4,6,1,7,3,2,5,8]=>[5,2,1]=>4032
[4,6,1,8,3,2,5,7]=>[6,2]=>3360
[4,7,1,8,3,5,2,6]=>[6,2]=>3360
[4,1,7,8,6,2,3,5]=>[6,2]=>3360
[1,6,5,7,8,3,4,2]=>[5,2,1]=>4032
[1,6,5,8,7,3,4,2]=>[7,1]=>5760
[4,1,8,7,6,2,3,5]=>[8]=>5040
[4,8,1,7,3,5,2,6]=>[8]=>5040
[4,8,1,6,3,2,5,7]=>[8]=>5040
[4,7,1,6,3,2,5,8]=>[7,1]=>5760
[6,1,2,3,7,5,4,8]=>[7,1]=>5760
[6,8,1,5,3,7,2,4]=>[8]=>5040
[8,7,5,2,4,1,6,3]=>[8]=>5040
[1,5,7,3,4,8,6,2]=>[7,1]=>5760
[1,5,8,3,4,7,6,2]=>[5,2,1]=>4032
[7,8,5,2,4,1,6,3]=>[5,3]=>2688
[7,1,2,3,5,6,4,8]=>[5,1,1,1]=>1344
[8,1,2,3,5,6,4,7]=>[6,1,1]=>3360
[8,1,2,3,5,4,7,6]=>[6,1,1]=>3360
[7,1,8,4,6,3,2,5]=>[4,3,1]=>3360
[6,8,2,4,3,1,5,7]=>[5,2,1]=>4032
[6,7,2,4,3,1,5,8]=>[4,2,1,1]=>2520
[3,8,1,2,4,5,7,6]=>[5,2,1]=>4032
[3,7,1,8,6,4,2,5]=>[4,2,2]=>1260
[1,6,4,3,7,5,8,2]=>[5,2,1]=>4032
[3,1,2,6,7,5,8,4]=>[5,3]=>2688
[3,8,1,7,6,4,2,5]=>[6,2]=>3360
[7,6,2,4,3,1,5,8]=>[6,1,1]=>3360
[8,7,2,4,3,5,1,6]=>[7,1]=>5760
[8,1,7,4,6,3,2,5]=>[7,1]=>5760
[8,1,7,6,5,3,2,4]=>[7,1]=>5760
[1,5,7,3,4,6,8,2]=>[6,1,1]=>3360
[8,7,2,5,3,6,1,4]=>[7,1]=>5760
[7,1,2,3,5,4,8,6]=>[7,1]=>5760
[6,1,2,3,5,8,4,7]=>[7,1]=>5760
[6,1,2,3,5,7,4,8]=>[6,1,1]=>3360
[5,1,2,3,7,6,4,8]=>[6,1,1]=>3360
[5,1,2,3,8,6,4,7]=>[7,1]=>5760
[1,5,6,3,4,7,8,2]=>[7,1]=>5760
[8,6,5,2,4,7,1,3]=>[8]=>5040
[7,6,2,5,3,1,8,4]=>[8]=>5040
[7,4,5,2,3,8,6,1]=>[4,2,2]=>1260
[8,2,3,7,4,5,1,6]=>[6,1,1]=>3360
[8,4,7,3,2,5,1,6]=>[8]=>5040
[5,4,6,3,1,2,8,7]=>[4,2,2]=>1260
[4,6,2,3,1,5,8,7]=>[6,2]=>3360
[7,2,3,4,5,8,6,1]=>[4,1,1,1,1]=>420
[8,2,3,4,5,7,1,6]=>[4,1,1,1,1]=>420
[7,3,4,6,8,5,1,2]=>[6,2]=>3360
[4,7,3,2,8,6,1,5]=>[4,2,1,1]=>2520
[3,7,4,5,1,8,6,2]=>[4,4]=>1260
[3,8,2,6,7,4,5,1]=>[4,2,2]=>1260
[4,8,1,5,6,7,3,2]=>[6,2]=>3360
[5,8,2,4,6,7,1,3]=>[4,3,1]=>3360
[6,8,1,3,4,2,7,5]=>[7,1]=>5760
[5,8,2,4,3,1,7,6]=>[6,1,1]=>3360
[2,1,7,6,8,5,3,4]=>[4,2,2]=>1260
[3,7,6,1,8,5,2,4]=>[6,2]=>3360
[4,7,2,3,8,5,1,6]=>[5,3]=>2688
[7,1,3,6,4,8,5,2]=>[7,1]=>5760
[7,6,1,4,8,5,2,3]=>[7,1]=>5760
[6,2,3,7,8,5,4,1]=>[4,2,1,1]=>2520
[6,2,3,8,4,5,1,7]=>[6,1,1]=>3360
[7,2,3,6,8,4,1,5]=>[2,2,2,1,1]=>420
[8,2,3,5,7,1,4,6]=>[3,3,1,1]=>1120
[6,4,8,3,5,1,7,2]=>[4,2,1,1]=>2520
[5,4,8,3,6,7,1,2]=>[4,4]=>1260
[3,5,1,8,4,6,7,2]=>[4,2,1,1]=>2520
[3,6,1,8,4,5,2,7]=>[6,2]=>3360
[4,6,8,3,5,2,7,1]=>[4,2,1,1]=>2520
[5,7,8,3,2,4,1,6]=>[4,4]=>1260
[4,8,2,3,5,6,1,7]=>[6,1,1]=>3360
[6,8,2,3,1,4,5,7]=>[8]=>5040
[5,2,7,4,8,3,1,6]=>[6,1,1]=>3360
[3,7,8,2,1,4,6,5]=>[4,4]=>1260
[3,7,5,2,8,4,1,6]=>[8]=>5040
[8,3,7,4,2,6,1,5]=>[6,1,1]=>3360
[1,8,3,2,4,5,7,6]=>[5,1,1,1]=>1344
[8,7,4,2,1,6,3,5]=>[4,3,1]=>3360
[1,2,8,7,5,6,3,4]=>[4,1,1,1,1]=>420
[1,4,8,6,5,7,2,3]=>[4,2,1,1]=>2520
[5,2,6,3,8,1,4,7]=>[7,1]=>5760
[7,2,8,1,3,6,5,4]=>[6,1,1]=>3360
[5,3,8,4,1,2,7,6]=>[4,2,1,1]=>2520
[5,8,4,3,6,2,1,7]=>[6,2]=>3360
[1,8,2,4,7,6,5,3]=>[3,2,1,1,1]=>1120
[8,2,1,4,6,5,7,3]=>[3,2,1,1,1]=>1120
[6,1,5,2,4,7,8,3]=>[8]=>5040
[4,1,8,5,2,7,6,3]=>[4,2,2]=>1260
[4,1,8,2,3,7,5,6]=>[5,3]=>2688
[5,3,8,7,2,1,4,6]=>[6,2]=>3360
[6,7,3,5,1,4,8,2]=>[4,3,1]=>3360
[6,4,7,5,8,2,3,1]=>[6,2]=>3360
[5,7,8,4,2,6,3,1]=>[6,1,1]=>3360
[5,7,4,1,6,8,3,2]=>[8]=>5040
[5,8,4,6,1,7,3,2]=>[4,2,2]=>1260
[5,6,1,4,7,8,3,2]=>[4,3,1]=>3360
[5,3,6,7,4,8,2,1]=>[8]=>5040
[5,4,8,6,2,7,3,1]=>[8]=>5040
[7,4,8,5,6,2,1,3]=>[4,2,2]=>1260
[5,6,3,8,4,7,2,1]=>[4,3,1]=>3360
[5,6,3,8,2,7,4,1]=>[7,1]=>5760
[6,7,3,8,5,2,4,1]=>[6,1,1]=>3360
[6,4,7,2,5,3,8,1]=>[5,2,1]=>4032
[6,2,7,5,1,4,8,3]=>[4,3,1]=>3360
[3,5,7,8,4,6,2,1]=>[7,1]=>5760
[5,3,7,8,4,6,2,1]=>[4,3,1]=>3360
[5,7,8,2,4,6,3,1]=>[7,1]=>5760
[3,6,4,8,7,2,5,1]=>[4,2,2]=>1260
[3,5,4,8,2,7,6,1]=>[4,2,2]=>1260
[4,5,7,3,8,6,2,1]=>[7,1]=>5760
[3,5,6,8,4,7,2,1]=>[8]=>5040
[6,3,1,8,7,5,4,2]=>[8]=>5040
[5,4,8,1,7,6,3,2]=>[7,1]=>5760
[8,5,4,1,7,6,3,2]=>[7,1]=>5760
[1,8,2,5,6,3,4,7]=>[7,1]=>5760
[7,2,8,4,5,1,3,6]=>[5,1,1,1]=>1344
[1,3,7,5,6,2,4,8]=>[6,1,1]=>3360
[1,6,7,4,3,5,2,8]=>[5,1,1,1]=>1344
[1,8,5,2,3,7,4,6]=>[5,2,1]=>4032
[1,8,2,5,3,6,7,4]=>[5,1,1,1]=>1344
[2,6,8,4,3,5,7,1]=>[6,1,1]=>3360
[7,5,8,3,2,1,6,4]=>[3,3,2]=>1120
[7,2,8,4,1,5,6,3]=>[4,2,1,1]=>2520
[7,5,8,1,2,6,3,4]=>[5,2,1]=>4032
[1,6,7,4,3,2,8,5]=>[4,2,1,1]=>2520
[1,5,2,6,4,7,8,3]=>[7,1]=>5760
[1,5,4,6,2,3,7,8]=>[3,2,1,1,1]=>1120
[6,2,5,7,1,4,8,3]=>[7,1]=>5760
[6,5,4,3,8,1,7,2]=>[3,2,2,1]=>1680
[7,3,6,8,5,2,4,1]=>[4,3,1]=>3360
[2,7,8,3,6,5,1,4]=>[3,3,2]=>1120
[2,7,8,5,4,6,3,1]=>[5,2,1]=>4032
[2,6,5,8,3,4,1,7]=>[6,2]=>3360
[2,6,5,7,3,4,1,8]=>[5,2,1]=>4032
[6,2,5,7,4,1,3,8]=>[4,2,1,1]=>2520
[6,2,5,8,4,1,3,7]=>[5,2,1]=>4032
[2,7,8,4,6,1,3,5]=>[7,1]=>5760
[6,1,2,8,3,7,4,5]=>[8]=>5040
[6,1,2,8,5,4,7,3]=>[6,1,1]=>3360
[6,2,5,7,8,1,3,4]=>[5,2,1]=>4032
[1,5,4,2,6,7,3,8]=>[6,1,1]=>3360
[2,6,5,7,3,8,1,4]=>[6,2]=>3360
[1,6,2,7,5,8,4,3]=>[4,2,1,1]=>2520
[1,3,2,7,8,5,6,4]=>[5,2,1]=>4032
[1,6,2,4,8,7,3,5]=>[4,2,1,1]=>2520
[6,5,2,1,8,7,3,4]=>[8]=>5040
[2,6,5,3,7,8,4,1]=>[4,4]=>1260
[6,2,5,3,8,4,7,1]=>[6,1,1]=>3360
[6,5,2,3,8,7,1,4]=>[5,3]=>2688
[5,4,1,2,3,8,6,7]=>[3,3,2]=>1120
[5,1,4,2,3,7,8,6]=>[5,3]=>2688
[1,5,4,2,6,3,8,7]=>[5,2,1]=>4032
[5,1,6,3,8,2,7,4]=>[7,1]=>5760
[9,8,7,6,5,4,3,1,2,10]=>[4,2,2,1,1]=>56700
[8,7,6,5,4,2,1,3,9]=>[6,2,1]=>30240
[1,9,8,7,6,5,3,2,4]=>[6,2,1]=>30240
[1,8,7,6,2,5,4,3]=>[7,1]=>5760
[1,10,9,8,7,6,5,4,2,3]=>[4,2,2,1,1]=>56700
[2,1,9,8,7,6,5,4,3]=>[2,2,2,2,1]=>945
[1,2,9,8,7,6,5,4,3]=>[2,2,2,1,1,1]=>1260
[3,2,1,9,8,7,6,5,4]=>[2,2,2,2,1]=>945
[1,2,3,9,8,7,6,5,4]=>[2,2,2,1,1,1]=>1260
[4,3,2,1,9,8,7,6,5]=>[2,2,2,2,1]=>945
[1,2,3,4,9,8,7,6,5]=>[2,2,1,1,1,1,1]=>378
[1,2,3,4,5,9,8,7,6]=>[2,2,1,1,1,1,1]=>378
[1,2,3,5,4,7,6,9,8]=>[2,2,2,1,1,1]=>1260
[1,2,3,4,5,7,6,9,8]=>[2,2,1,1,1,1,1]=>378
[1,2,10,9,8,7,6,5,4,3]=>[2,2,2,2,1,1]=>4725
[3,2,1,10,9,8,7,6,5,4]=>[2,2,2,2,1,1]=>4725
[1,2,3,10,9,8,7,6,5,4]=>[2,2,2,1,1,1,1]=>3150
[1,2,3,4,10,9,8,7,6,5]=>[2,2,2,1,1,1,1]=>3150
[1,2,3,4,5,6,10,9,8,7]=>[2,2,1,1,1,1,1,1]=>630
[1,2,3,4,5,6,7,10,9,8]=>[2,1,1,1,1,1,1,1,1]=>45
[5,2,7,4,1,6,3,8]=>[2,2,1,1,1,1]=>210
[4,7,3,1,5,6,2,8]=>[2,2,1,1,1,1]=>210
[5,8,3,4,1,6,7,2]=>[2,2,1,1,1,1]=>210
[1,7,8,4,5,6,2,3]=>[2,2,1,1,1,1]=>210
[1,5,8,4,2,6,7,3]=>[2,2,1,1,1,1]=>210
[1,6,3,8,5,2,7,4]=>[2,2,1,1,1,1]=>210
[5,2,3,7,1,6,4,8]=>[2,2,1,1,1,1]=>210
[6,2,3,7,5,1,4,8]=>[2,2,1,1,1,1]=>210
[1,7,3,4,8,6,2,5]=>[2,2,1,1,1,1]=>210
[6,2,3,4,8,1,7,5]=>[2,2,1,1,1,1]=>210
[8,7,3,2,1,6,5,4]=>[6,1,1]=>3360
[8,7,6,3,1,5,2,4]=>[6,2]=>3360
[8,5,1,7,2,3,4,6]=>[4,2,2]=>1260
[9,8,7,6,5,2,1,4,3]=>[4,4,1]=>11340
[9,8,7,3,2,1,6,5,4]=>[6,3]=>20160
[9,8,7,6,3,1,5,2,4]=>[4,3,2]=>15120
[9,4,3,2,1,8,7,6,5]=>[3,2,2,1,1]=>7560
[9,8,4,3,1,7,6,2,5]=>[3,2,2,2]=>2520
[9,8,7,2,1,4,3,6,5]=>[4,3,2]=>15120
[9,8,7,4,1,6,2,3,5]=>[4,3,1,1]=>15120
[5,4,3,1,9,8,7,2,6]=>[7,1,1]=>25920
[9,5,2,1,8,4,3,7,6]=>[5,4]=>18144
[9,8,3,1,5,2,7,4,6]=>[6,1,1,1]=>10080
[6,3,1,9,5,2,8,4,7]=>[4,4,1]=>11340
[6,5,1,9,8,2,3,4,7]=>[9]=>40320
[9,2,1,4,3,6,5,8,7]=>[5,1,1,1,1]=>3024
[9,6,1,8,2,3,4,5,7]=>[9]=>40320
[5,1,7,2,9,3,4,6,8]=>[9]=>40320
[7,1,9,2,3,4,5,6,8]=>[9]=>40320
[10,9,8,7,6,5,2,1,4,3]=>[4,4,2]=>56700
[10,9,8,7,3,2,1,6,5,4]=>[6,4]=>151200
[10,9,8,7,6,3,1,5,2,4]=>[4,4,2]=>56700
[10,9,4,3,2,1,8,7,6,5]=>[6,2,2]=>75600
[10,9,8,4,3,1,7,6,2,5]=>[6,2,1,1]=>151200
[10,9,8,7,2,1,4,3,6,5]=>[6,2,2]=>75600
[10,9,8,7,4,1,6,2,3,5]=>[6,4]=>151200
[10,5,4,3,1,9,8,7,2,6]=>[6,2,2]=>75600
[10,9,5,2,1,8,4,3,7,6]=>[6,4]=>151200
[10,9,5,4,1,8,7,2,3,6]=>[8,1,1]=>226800
[10,9,8,3,1,5,2,7,4,6]=>[6,4]=>151200
[6,5,2,1,10,9,4,3,8,7]=>[10]=>362880
[6,5,4,1,10,9,8,2,3,7]=>[5,5]=>72576
[10,3,2,1,6,5,4,9,8,7]=>[4,2,2,2]=>18900
[10,6,5,1,9,8,2,3,4,7]=>[10]=>362880
[10,9,2,1,4,3,6,5,8,7]=>[10]=>362880
[10,9,6,1,8,2,3,4,5,7]=>[10]=>362880
[4,3,1,7,6,2,10,9,5,8]=>[10]=>362880
[7,2,1,10,4,3,6,5,9,8]=>[4,4,1,1]=>56700
[7,4,1,10,6,2,9,3,5,8]=>[10]=>362880
[7,6,1,10,9,2,3,4,5,8]=>[3,3,2,2]=>25200
[10,5,1,7,2,9,3,4,6,8]=>[6,2,2]=>75600
[10,7,1,9,2,3,4,5,6,8]=>[10]=>362880
[4,1,6,2,8,3,10,5,7,9]=>[3,3,2,2]=>25200
[6,1,8,2,10,3,4,5,7,9]=>[10]=>362880
[8,1,10,2,3,4,5,6,7,9]=>[5,5]=>72576
[2,4,8,5,3,7,1,6]=>[8]=>5040
[2,4,1,8,5,3,7,6]=>[6,1,1]=>3360
[2,4,8,6,3,1,7,5]=>[4,3,1]=>3360
[3,4,6,8,2,1,7,5]=>[4,3,1]=>3360
[3,4,1,5,8,2,7,6]=>[5,2,1]=>4032
[8,1,4,5,3,2,7,6]=>[4,3,1]=>3360
[3,4,1,5,2,8,7,6]=>[3,2,2,1]=>1680
[3,4,6,2,1,8,7,5]=>[5,2,1]=>4032
[3,5,6,2,1,7,8,4]=>[8]=>5040
[3,4,6,2,7,8,1,5]=>[6,2]=>3360
[8,1,4,6,3,7,2,5]=>[8]=>5040
[8,1,4,6,3,7,5,2]=>[5,3]=>2688
[3,5,6,2,1,7,4,8]=>[7,1]=>5760
[8,1,5,6,7,3,4,2]=>[5,3]=>2688
[8,1,5,6,7,3,2,4]=>[8]=>5040
[3,4,1,6,8,7,2,5]=>[4,2,2]=>1260
[3,5,6,1,8,7,2,4]=>[8]=>5040
[2,1,3,8,6,7,4,5]=>[5,2,1]=>4032
[8,1,3,2,6,7,5,4]=>[4,3,1]=>3360
[2,3,8,6,7,1,5,4]=>[6,2]=>3360
[2,4,1,8,6,7,5,3]=>[5,3]=>2688
[2,5,8,6,1,7,4,3]=>[3,3,2]=>1120
[3,5,6,1,8,7,4,2]=>[5,3]=>2688
[3,4,1,6,8,7,5,2]=>[6,2]=>3360
[3,4,6,8,7,1,5,2]=>[3,3,2]=>1120
[8,1,4,6,2,7,5,3]=>[8]=>5040
[3,5,1,6,7,8,4,2]=>[6,2]=>3360
[4,5,6,1,7,8,3,2]=>[6,2]=>3360
[4,5,6,1,7,3,8,2]=>[4,2,2]=>1260
[3,5,1,6,7,4,8,2]=>[4,2,2]=>1260
[8,1,5,6,7,4,2,3]=>[6,2]=>3360
[8,1,5,6,7,4,3,2]=>[3,3,2]=>1120
[3,5,1,6,7,4,2,8]=>[3,2,2,1]=>1680
[4,5,6,1,7,3,2,8]=>[3,2,2,1]=>1680
[6,5,8,7,4,3,1,2]=>[8]=>5040
[6,4,2,7,8,5,1,3]=>[8]=>5040
[6,1,4,8,7,5,2,3]=>[5,3]=>2688
[1,6,4,8,7,5,2,3]=>[4,3,1]=>3360
[1,8,6,2,4,7,3,5]=>[4,3,1]=>3360
[8,1,6,2,4,7,3,5]=>[5,3]=>2688
[7,6,2,1,4,8,3,5]=>[8]=>5040
[6,4,1,7,8,5,2,3]=>[5,3]=>2688
[7,6,1,2,4,8,3,5]=>[5,3]=>2688
[7,6,1,3,4,8,2,5]=>[8]=>5040
[8,1,6,3,4,7,2,5]=>[8]=>5040
[1,8,6,3,4,7,2,5]=>[7,1]=>5760
[1,7,2,5,4,8,3,6]=>[3,2,2,1]=>1680
[7,1,2,5,4,8,3,6]=>[4,2,2]=>1260
[2,7,1,5,4,8,3,6]=>[4,2,2]=>1260
[2,8,6,3,4,7,1,5]=>[8]=>5040
[2,8,6,1,4,7,3,5]=>[5,3]=>2688
[7,2,1,5,4,8,3,6]=>[3,2,2,1]=>1680
[1,2,7,5,4,8,3,6]=>[2,2,2,1,1]=>420
[3,2,7,5,4,8,1,6]=>[3,2,2,1]=>1680
[2,5,8,4,7,3,1,6]=>[4,3,1]=>3360
[2,3,7,5,4,8,1,6]=>[4,2,2]=>1260
[6,8,3,2,4,7,1,5]=>[4,3,1]=>3360
[3,7,2,5,4,8,1,6]=>[4,2,2]=>1260
[3,1,7,5,4,8,2,6]=>[4,2,2]=>1260
[1,3,7,5,4,8,2,6]=>[3,2,2,1]=>1680
[1,5,8,4,7,3,2,6]=>[3,3,1,1]=>1120
[5,1,8,4,7,3,2,6]=>[4,3,1]=>3360
[5,8,2,4,7,3,1,6]=>[4,3,1]=>3360
[6,8,4,3,7,5,1,2]=>[4,2,2]=>1260
[8,7,5,6,2,1,4,3]=>[8]=>5040
[8,5,2,4,7,3,1,6]=>[7,1]=>5760
[8,1,5,4,7,3,2,6]=>[7,1]=>5760
[1,8,5,4,7,3,2,6]=>[6,1,1]=>3360
[1,7,3,5,4,8,2,6]=>[2,2,2,1,1]=>420
[8,6,3,1,4,7,2,5]=>[4,3,1]=>3360
[8,6,4,2,7,5,1,3]=>[8]=>5040
[8,6,4,1,7,2,5,3]=>[4,2,2]=>1260
[5,3,7,4,6,8,2,1]=>[4,3,1]=>3360
[4,1,3,2,7,8,5,6]=>[3,2,2,1]=>1680
[1,4,3,2,7,8,5,6]=>[2,2,2,1,1]=>420
[2,4,3,1,7,8,5,6]=>[3,2,2,1]=>1680
[2,7,3,5,4,8,1,6]=>[3,2,2,1]=>1680
[2,8,5,4,7,3,1,6]=>[7,1]=>5760
[5,7,3,4,6,8,2,1]=>[4,2,1,1]=>2520
[8,2,5,4,7,3,1,6]=>[6,1,1]=>3360
[7,2,3,5,4,8,1,6]=>[2,2,2,1,1]=>420
[3,2,1,4,7,8,5,6]=>[2,2,2,1,1]=>420
[8,1,7,6,4,3,5,2]=>[5,3]=>2688
[8,6,4,5,2,7,1,3]=>[8]=>5040
[7,1,8,6,4,3,5,2]=>[8]=>5040
[7,4,2,5,1,6,3,8]=>[6,1,1]=>3360
[7,3,6,5,2,1,4,8]=>[7,1]=>5760
[8,3,6,5,2,1,7,4]=>[7,1]=>5760
[7,3,6,5,2,1,8,4]=>[8]=>5040
[7,5,8,6,4,2,1,3]=>[4,2,2]=>1260
[5,4,2,8,1,3,7,6]=>[5,2,1]=>4032
[5,8,2,6,4,1,3,7]=>[4,4]=>1260
[6,4,2,5,1,8,3,7]=>[8]=>5040
[6,3,5,2,1,4,7,8]=>[6,1,1]=>3360
[2,5,8,6,3,1,4,7]=>[8]=>5040
[2,3,5,8,1,4,7,6]=>[4,3,1]=>3360
[2,3,6,8,1,5,7,4]=>[5,2,1]=>4032
[6,3,8,5,2,7,1,4]=>[5,3]=>2688
[6,3,7,5,2,1,4,8]=>[5,2,1]=>4032
[2,5,7,6,3,1,4,8]=>[7,1]=>5760
[2,8,7,6,3,1,5,4]=>[5,3]=>2688
[2,5,8,7,6,3,1,4]=>[8]=>5040
[2,4,8,1,6,5,7,3]=>[3,2,2,1]=>1680
[2,8,7,3,6,1,4,5]=>[5,3]=>2688
[7,3,5,2,1,4,6,8]=>[7,1]=>5760
[8,4,2,5,1,3,7,6]=>[7,1]=>5760
[2,3,6,8,1,4,7,5]=>[7,1]=>5760
[2,7,8,6,3,1,4,5]=>[5,3]=>2688
[7,3,8,5,2,1,4,6]=>[8]=>5040
[2,3,6,1,8,4,7,5]=>[5,2,1]=>4032
[2,8,6,3,1,4,5,7]=>[5,3]=>2688
[8,3,5,2,1,4,6,7]=>[8]=>5040
[2,4,8,1,3,7,5,6]=>[5,3]=>2688
[2,5,8,1,7,3,6,4]=>[8]=>5040
[2,8,1,5,7,3,6,4]=>[8]=>5040
[3,8,6,1,4,7,5,2]=>[6,2]=>3360
[2,6,8,1,5,7,3,4]=>[7,1]=>5760
[2,7,1,5,8,3,4,6]=>[8]=>5040
[3,7,5,8,1,2,6,4]=>[3,3,2]=>1120
[7,3,6,1,2,8,4,5]=>[5,3]=>2688
[7,4,8,1,6,5,2,3]=>[4,2,2]=>1260
[7,4,5,8,6,1,2,3]=>[8]=>5040
[6,8,4,5,1,7,2,3]=>[8]=>5040
[5,1,8,7,6,2,3,4]=>[4,4]=>1260
[8,5,1,6,2,7,3,4]=>[6,2]=>3360
[4,5,1,8,7,2,3,6]=>[8]=>5040
[3,4,8,7,1,2,5,6]=>[8]=>5040
[6,4,8,7,1,2,5,3]=>[6,2]=>3360
[5,6,8,3,7,1,4,2]=>[8]=>5040
[6,4,7,1,2,8,5,3]=>[8]=>5040
[6,5,1,2,7,3,8,4]=>[5,3]=>2688
[6,5,1,8,2,7,3,4]=>[4,2,2]=>1260
[6,5,1,8,7,2,3,4]=>[6,2]=>3360
[6,5,1,7,2,8,3,4]=>[6,2]=>3360
[5,6,8,7,4,1,2,3]=>[6,2]=>3360
[6,8,5,7,4,1,2,3]=>[6,2]=>3360
[7,3,8,1,5,2,4,6]=>[4,3,1]=>3360
[4,1,7,5,3,6,2,8]=>[6,1,1]=>3360
[1,8,4,2,3,6,7,5]=>[5,1,1,1]=>1344
[2,5,8,3,4,6,7,1]=>[6,1,1]=>3360
[4,1,7,2,3,6,8,5]=>[4,3,1]=>3360
[4,6,2,1,5,7,8,3]=>[5,2,1]=>4032
[4,5,2,3,1,7,8,6]=>[5,3]=>2688
[3,2,6,7,4,1,8,5]=>[4,3,1]=>3360
[5,6,2,7,1,4,8,3]=>[6,2]=>3360
[6,2,3,8,1,7,4,5]=>[6,1,1]=>3360
[2,6,8,3,4,7,1,5]=>[4,4]=>1260
[4,6,2,7,5,1,3,8]=>[6,1,1]=>3360
[2,6,3,1,8,4,5,7]=>[4,3,1]=>3360
[2,4,3,7,8,1,5,6]=>[7,1]=>5760
[5,3,2,7,4,8,1,6]=>[4,2,2]=>1260
[5,1,2,7,6,8,4,3]=>[6,2]=>3360
[2,6,3,1,8,7,4,5]=>[5,2,1]=>4032
[3,5,6,4,7,8,1,2]=>[7,1]=>5760
[5,3,6,4,2,8,7,1]=>[6,1,1]=>3360
[5,4,2,3,7,8,6,1]=>[5,3]=>2688
[4,1,8,2,5,7,3,6]=>[4,3,1]=>3360
[3,1,8,4,7,2,5,6]=>[5,2,1]=>4032
[6,2,3,8,4,1,7,5]=>[3,2,1,1,1]=>1120
[2,6,4,1,5,3,8,7]=>[5,2,1]=>4032
[3,2,7,6,4,1,8,5]=>[7,1]=>5760
[2,5,4,1,7,6,8,3]=>[7,1]=>5760
[6,2,1,4,7,8,3,5]=>[6,1,1]=>3360
[2,6,5,1,7,8,3,4]=>[5,3]=>2688
[4,7,5,2,1,6,3,8]=>[6,1,1]=>3360
[4,2,3,7,8,1,6,5]=>[4,2,1,1]=>2520
[5,8,3,1,7,2,4,6]=>[4,3,1]=>3360
[6,8,3,1,5,2,4,7]=>[6,1,1]=>3360
[5,1,7,4,2,6,3,8]=>[3,2,1,1,1]=>1120
[6,8,3,2,5,1,7,4]=>[3,2,1,1,1]=>1120
[6,8,4,3,1,5,7,2]=>[3,2,2,1]=>1680
[6,8,4,2,1,5,7,3]=>[4,3,1]=>3360
[5,1,7,3,2,4,6,8]=>[4,3,1]=>3360
[5,2,1,8,3,6,7,4]=>[3,2,1,1,1]=>1120
[4,3,8,1,6,2,7,5]=>[5,2,1]=>4032
[4,2,1,8,5,7,3,6]=>[6,1,1]=>3360
[6,3,2,1,7,4,5,8]=>[3,2,2,1]=>1680
[6,4,2,1,7,5,3,8]=>[7,1]=>5760
[7,5,2,1,8,6,3,4]=>[7,1]=>5760
[5,3,2,7,6,1,4,8]=>[3,2,2,1]=>1680
[5,3,2,8,6,1,4,7]=>[3,3,2]=>1120
[6,3,2,8,7,1,4,5]=>[4,2,2]=>1260
[4,2,8,1,7,3,5,6]=>[3,2,2,1]=>1680
[4,3,8,7,2,1,5,6]=>[8]=>5040
[2,1,5,8,4,7,3,6]=>[6,2]=>3360
[4,3,1,6,2,7,5,8]=>[7,1]=>5760
[5,4,1,7,2,8,6,3]=>[8]=>5040
[5,4,2,1,6,7,3,8]=>[7,1]=>5760
[5,3,2,1,6,7,8,4]=>[6,2]=>3360
[8,6,1,4,5,7,2,3]=>[3,3,1,1]=>1120
[5,2,8,3,7,4,6,1]=>[7,1]=>5760
[6,2,8,5,4,7,3,1]=>[5,2,1]=>4032
[1,8,6,3,7,4,2,5]=>[4,3,1]=>3360
[1,8,6,5,7,2,3,4]=>[7,1]=>5760
[5,2,8,4,3,6,7,1]=>[4,1,1,1,1]=>420
[5,4,2,7,3,6,1,8]=>[6,1,1]=>3360
[5,4,2,8,3,6,1,7]=>[7,1]=>5760
[6,5,3,8,4,7,2,1]=>[7,1]=>5760
[5,2,8,4,3,7,1,6]=>[6,1,1]=>3360
[6,2,8,3,7,4,1,5]=>[7,1]=>5760
[5,4,2,7,3,1,8,6]=>[8]=>5040
[6,4,3,7,1,2,8,5]=>[7,1]=>5760
[6,4,3,8,1,2,7,5]=>[6,1,1]=>3360
[7,6,3,8,4,2,1,5]=>[3,2,2,1]=>1680
[7,2,8,5,1,6,3,4]=>[6,1,1]=>3360
[7,2,8,4,3,1,5,6]=>[6,1,1]=>3360
[7,5,3,8,4,2,6,1]=>[7,1]=>5760
[6,4,2,7,3,1,5,8]=>[5,2,1]=>4032
[7,6,4,8,2,3,5,1]=>[8]=>5040
[7,6,8,1,2,5,3,4]=>[5,3]=>2688
[5,3,1,7,8,4,6,2]=>[5,3]=>2688
[5,3,2,7,8,4,6,1]=>[3,3,2]=>1120
[5,4,1,6,3,8,7,2]=>[4,3,1]=>3360
[6,5,1,7,8,2,3,4]=>[8]=>5040
[6,3,1,7,8,4,2,5]=>[6,2]=>3360
[5,4,1,7,3,8,2,6]=>[3,3,2]=>1120
[6,3,2,7,8,4,1,5]=>[4,2,2]=>1260
[6,1,5,4,3,2,8,7]=>[3,2,2,1]=>1680
[8,7,6,1,3,5,2,4]=>[3,3,2]=>1120
[8,1,6,5,7,3,4,2]=>[3,3,2]=>1120
[8,4,1,5,7,6,2,3]=>[4,3,1]=>3360
[7,8,6,2,5,3,1,4]=>[3,2,2,1]=>1680
[6,1,3,5,2,8,4,7]=>[7,1]=>5760
[8,1,3,7,4,2,5,6]=>[4,3,1]=>3360
[4,3,8,7,5,2,1,6]=>[4,3,1]=>3360
[6,7,1,8,5,3,4,2]=>[4,3,1]=>3360
[2,7,6,4,8,3,5,1]=>[5,2,1]=>4032
[6,5,2,7,1,4,8,3]=>[8]=>5040
[7,4,6,1,3,2,8,5]=>[8]=>5040
[7,5,2,1,3,8,4,6]=>[3,3,2]=>1120
[8,4,7,6,3,1,5,2]=>[5,3]=>2688
[7,4,1,5,6,3,8,2]=>[8]=>5040
[3,4,7,5,6,1,8,2]=>[8]=>5040
[2,4,7,5,6,3,8,1]=>[8]=>5040
[5,4,1,7,6,2,8,3]=>[8]=>5040
[3,5,6,7,1,4,8,2]=>[8]=>5040
[2,7,6,1,3,4,8,5]=>[8]=>5040
[5,7,2,1,6,3,8,4]=>[8]=>5040
[4,7,2,5,6,3,8,1]=>[8]=>5040
[8,6,2,5,7,1,4,3]=>[5,3]=>2688
[2,7,4,5,3,8,1,6]=>[3,3,2]=>1120
[6,8,7,1,3,2,5,4]=>[5,3]=>2688
[2,8,6,5,7,1,4,3]=>[5,3]=>2688
[5,8,4,3,2,6,7,1]=>[4,2,1,1]=>2520
[1,8,5,6,2,4,7,3]=>[4,2,1,1]=>2520
[8,1,5,6,2,4,7,3]=>[5,2,1]=>4032
[6,4,8,1,3,2,7,5]=>[4,3,1]=>3360
[1,4,5,2,8,6,7,3]=>[3,2,1,1,1]=>1120
[2,3,1,7,8,6,4,5]=>[3,2,2,1]=>1680
[3,5,7,6,2,8,1,4]=>[3,3,2]=>1120
[4,5,6,1,2,8,7,3]=>[3,2,2,1]=>1680
[5,4,1,2,8,6,7,3]=>[4,2,1,1]=>2520
[8,4,5,2,1,6,7,3]=>[4,2,1,1]=>2520
[3,1,2,6,8,4,7,5]=>[3,2,2,1]=>1680
[5,1,3,2,7,8,4,6]=>[5,2,1]=>4032
[1,5,4,2,7,8,3,6]=>[5,2,1]=>4032
[4,6,7,8,3,1,5,2]=>[5,3]=>2688
[7,6,2,8,4,3,1,5]=>[3,3,2]=>1120
[5,2,8,6,3,4,7,1]=>[4,2,1,1]=>2520
[5,6,8,4,3,2,7,1]=>[4,2,1,1]=>2520
[5,3,8,1,7,2,4,6]=>[4,4]=>1260
[3,6,7,8,4,2,1,5]=>[3,3,2]=>1120
[6,5,1,8,4,3,7,2]=>[4,3,1]=>3360
[6,3,8,4,2,1,7,5]=>[4,2,1,1]=>2520
[2,5,8,3,1,6,7,4]=>[3,3,1,1]=>1120
[3,5,8,1,2,6,7,4]=>[4,2,1,1]=>2520
[3,2,8,1,5,6,7,4]=>[4,1,1,1,1]=>420
[1,5,8,3,2,6,7,4]=>[3,2,1,1,1]=>1120
[1,3,8,6,2,4,7,5]=>[4,2,1,1]=>2520
[3,2,7,8,4,6,1,5]=>[3,3,1,1]=>1120
[5,1,8,3,4,6,7,2]=>[6,1,1]=>3360
[4,8,7,2,1,6,3,5]=>[5,2,1]=>4032
[2,8,1,6,3,4,7,5]=>[5,2,1]=>4032
[8,3,4,2,1,6,5,7]=>[4,3,1]=>3360
[6,4,7,2,5,8,1,3]=>[5,2,1]=>4032
[8,4,5,2,6,3,1,7]=>[3,3,2]=>1120
[2,4,5,8,3,6,1,7]=>[5,2,1]=>4032
[3,5,8,1,2,6,4,7]=>[5,2,1]=>4032
[8,6,1,3,5,2,4,7]=>[5,2,1]=>4032
[8,5,1,2,6,4,3,7]=>[4,4]=>1260
[5,8,6,1,3,4,2,7]=>[5,3]=>2688
[5,8,4,6,1,3,2,7]=>[3,3,2]=>1120
[7,3,4,5,2,8,1,6]=>[4,2,2]=>1260
[5,7,4,3,6,1,8,2]=>[3,3,2]=>1120
[2,6,4,3,7,8,5,1]=>[4,2,2]=>1260
[7,4,1,8,3,2,5,6]=>[4,4]=>1260
[6,2,1,7,8,4,5,3]=>[7,1]=>5760
[7,6,3,1,5,4,8,2]=>[6,1,1]=>3360
[2,4,6,5,1,7,8,3]=>[4,4]=>1260
[1,4,7,5,6,8,2,3]=>[7,1]=>5760
[1,4,7,6,5,8,2,3]=>[6,1,1]=>3360
[3,7,5,2,4,6,8,1]=>[7,1]=>5760
[5,6,1,7,4,2,8,3]=>[6,2]=>3360
[3,7,4,8,1,2,6,5]=>[5,3]=>2688
[6,3,5,7,8,1,4,2]=>[4,2,2]=>1260
[3,6,5,7,1,8,4,2]=>[3,3,2]=>1120
[6,4,7,8,2,1,3,5]=>[4,2,2]=>1260
[6,7,3,8,4,1,2,5]=>[3,2,2,1]=>1680
[2,7,8,3,4,6,1,5]=>[4,3,1]=>3360
[7,5,8,4,1,3,2,6]=>[4,3,1]=>3360
[4,7,5,8,3,1,2,6]=>[4,2,2]=>1260
[3,6,7,4,8,1,2,5]=>[5,2,1]=>4032
[5,7,3,1,6,8,4,2]=>[7,1]=>5760
[2,7,3,1,8,6,4,5]=>[4,2,1,1]=>2520
[2,8,4,3,1,5,7,6]=>[5,2,1]=>4032
[4,8,1,2,3,5,7,6]=>[7,1]=>5760
[7,6,8,1,2,4,3,5]=>[8]=>5040
[7,6,8,5,1,3,2,4]=>[8]=>5040
[2,8,5,4,6,1,7,3]=>[6,1,1]=>3360
[8,4,5,2,7,6,1,3]=>[5,2,1]=>4032
[8,7,6,4,1,2,5,3]=>[7,1]=>5760
[6,7,1,3,5,2,8,4]=>[7,1]=>5760
[5,7,2,3,6,8,1,4]=>[8]=>5040
[8,5,3,2,7,6,1,4]=>[6,1,1]=>3360
[3,4,6,7,5,8,1,2]=>[7,1]=>5760
[3,4,5,7,6,1,8,2]=>[4,4]=>1260
[2,6,4,5,7,8,3,1]=>[4,4]=>1260
[3,8,5,1,6,2,7,4]=>[7,1]=>5760
[2,5,1,3,6,8,7,4]=>[7,1]=>5760
[5,4,6,1,3,7,8,2]=>[8]=>5040
[6,3,5,7,1,4,8,2]=>[8]=>5040
[7,3,4,6,8,1,5,2]=>[8]=>5040
[3,7,8,4,1,5,6,2]=>[7,1]=>5760
[8,7,5,4,2,1,6,3]=>[7,1]=>5760
[6,7,2,5,1,8,4,3]=>[8]=>5040
[3,6,1,2,5,8,4,7]=>[5,2,1]=>4032
[1,4,5,8,2,3,7,6]=>[6,1,1]=>3360
[1,2,6,4,5,8,3,7]=>[4,1,1,1,1]=>420
[1,5,2,4,6,8,3,7]=>[6,1,1]=>3360
[3,6,1,5,8,2,4,7]=>[4,2,2]=>1260
[2,6,5,1,4,8,3,7]=>[8]=>5040
[5,2,6,1,4,8,3,7]=>[4,3,1]=>3360
[2,5,1,8,4,7,3,6]=>[8]=>5040
[2,7,1,4,3,6,8,5]=>[6,1,1]=>3360
[1,3,7,5,8,2,4,6]=>[7,1]=>5760
[8,2,1,5,7,3,4,6]=>[4,3,1]=>3360
[2,5,4,8,1,3,7,6]=>[4,3,1]=>3360
[2,4,1,3,8,6,7,5]=>[4,2,1,1]=>2520
[8,4,3,7,1,2,6,5]=>[4,3,1]=>3360
[1,7,3,5,8,2,6,4]=>[3,3,1,1]=>1120
[1,8,4,2,6,7,3,5]=>[7,1]=>5760
[3,1,6,8,7,2,4,5]=>[4,4]=>1260
[7,2,1,6,8,3,4,5]=>[5,2,1]=>4032
[3,1,7,6,8,2,4,5]=>[6,2]=>3360
[4,1,7,2,6,8,3,5]=>[3,3,2]=>1120
[5,1,7,2,3,6,8,4]=>[7,1]=>5760
[7,2,1,6,3,5,8,4]=>[7,1]=>5760
[2,6,1,7,3,5,8,4]=>[5,3]=>2688
[7,1,2,5,3,6,8,4]=>[7,1]=>5760
[5,4,1,2,7,8,3,6]=>[4,2,2]=>1260
[8,1,3,2,4,6,7,5]=>[5,1,1,1]=>1344
[7,3,1,2,4,6,8,5]=>[7,1]=>5760
[1,8,3,4,7,2,5,6]=>[3,2,1,1,1]=>1120
[3,5,8,1,2,7,4,6]=>[6,2]=>3360
[3,6,8,1,2,4,7,5]=>[7,1]=>5760
[4,1,3,8,7,2,6,5]=>[7,1]=>5760
[1,3,7,4,8,2,6,5]=>[4,2,1,1]=>2520
[1,4,6,8,2,3,7,5]=>[4,2,1,1]=>2520
[3,5,8,1,7,2,4,6]=>[8]=>5040
[2,6,8,1,7,3,4,5]=>[8]=>5040
[6,1,5,8,2,3,7,4]=>[5,2,1]=>4032
[1,8,3,2,7,5,6,4]=>[3,3,1,1]=>1120
[3,1,7,2,8,5,6,4]=>[8]=>5040
[2,6,7,3,8,1,5,4]=>[5,3]=>2688
[8,4,1,7,3,6,2,5]=>[4,3,1]=>3360
[3,7,2,8,6,1,5,4]=>[6,2]=>3360
[6,2,3,8,7,1,5,4]=>[2,2,2,1,1]=>420
[5,1,7,8,4,2,6,3]=>[8]=>5040
[5,1,8,7,4,2,6,3]=>[6,2]=>3360
[4,7,2,8,3,6,5,1]=>[4,3,1]=>3360
[4,1,7,8,5,3,6,2]=>[4,3,1]=>3360
[5,1,7,4,8,3,6,2]=>[4,3,1]=>3360
[4,1,8,7,5,3,6,2]=>[7,1]=>5760
[4,8,2,7,3,6,5,1]=>[7,1]=>5760
[4,7,2,6,3,5,8,1]=>[8]=>5040
[6,8,2,4,3,7,5,1]=>[7,1]=>5760
[6,7,2,4,3,8,5,1]=>[4,3,1]=>3360
[6,8,2,7,3,5,4,1]=>[6,2]=>3360
[3,8,7,2,4,1,5,6]=>[8]=>5040
[3,7,8,2,4,1,5,6]=>[4,4]=>1260
[3,6,8,2,4,5,7,1]=>[4,3,1]=>3360
[3,6,7,2,4,5,8,1]=>[4,4]=>1260
[6,5,1,4,2,3,8,7]=>[3,2,2,1]=>1680
[8,6,1,7,2,5,4,3]=>[3,3,2]=>1120
[8,7,6,1,2,3,5,4]=>[3,3,2]=>1120
[5,4,3,1,6,2,8,7]=>[5,2,1]=>4032
[8,3,4,7,1,6,2,5]=>[4,3,1]=>3360
[6,3,4,1,8,5,2,7]=>[8]=>5040
[3,8,5,2,7,1,6,4]=>[5,3]=>2688
[2,8,6,7,5,3,4,1]=>[3,2,2,1]=>1680
[2,1,8,7,3,6,4,5]=>[3,2,2,1]=>1680
[3,6,5,8,2,4,7,1]=>[7,1]=>5760
[5,2,1,8,7,3,4,6]=>[7,1]=>5760
[6,5,2,7,4,3,8,1]=>[8]=>5040
[4,6,5,2,7,3,8,1]=>[8]=>5040
[6,2,7,1,8,3,5,4]=>[7,1]=>5760
[2,7,5,4,8,3,6,1]=>[7,1]=>5760
[8,7,5,1,2,6,4,3]=>[7,1]=>5760
[8,4,3,2,7,1,6,5]=>[5,2,1]=>4032
[7,1,6,2,3,8,5,4]=>[8]=>5040
[4,8,1,3,2,7,5,6]=>[5,3]=>2688
[3,8,1,4,7,5,2,6]=>[5,2,1]=>4032
[6,3,8,7,4,5,1,2]=>[5,3]=>2688
[6,1,4,8,5,2,3,7]=>[4,3,1]=>3360
[8,5,7,4,6,2,1,3]=>[4,3,1]=>3360
[4,6,7,8,2,3,5,1]=>[5,3]=>2688
[8,7,4,6,2,1,5,3]=>[5,3]=>2688
[7,6,1,3,5,2,8,4]=>[5,2,1]=>4032
[5,8,3,2,4,6,1,7]=>[6,1,1]=>3360
[8,2,6,5,3,1,7,4]=>[6,1,1]=>3360
[4,8,7,6,5,2,3,1]=>[5,2,1]=>4032
[2,1,8,6,4,3,7,5]=>[5,2,1]=>4032
[2,1,7,6,5,3,8,4]=>[5,2,1]=>4032
[2,7,6,1,3,5,8,4]=>[5,3]=>2688
[7,2,5,4,6,1,8,3]=>[6,1,1]=>3360
[4,7,6,1,2,5,8,3]=>[6,2]=>3360
[2,4,1,7,6,8,5,3]=>[8]=>5040
[3,4,1,7,8,5,6,2]=>[6,2]=>3360
[7,5,4,3,1,8,6,2]=>[6,2]=>3360
[8,5,6,2,7,3,1,4]=>[6,2]=>3360
[8,4,2,5,6,1,7,3]=>[7,1]=>5760
[6,3,5,4,1,7,8,2]=>[7,1]=>5760
[4,1,3,6,7,5,8,2]=>[7,1]=>5760
[1,7,2,4,5,8,3,6]=>[3,2,1,1,1]=>1120
[2,6,4,7,8,3,5,1]=>[8]=>5040
[1,2,6,4,7,8,3,5]=>[5,1,1,1]=>1344
[6,1,4,7,8,3,5,2]=>[8]=>5040
[3,6,4,7,8,1,5,2]=>[8]=>5040
[4,3,6,7,1,8,2,5]=>[8]=>5040
[1,3,6,4,7,2,8,5]=>[3,3,1,1]=>1120
[5,1,3,4,2,7,8,6]=>[3,3,1,1]=>1120
[5,4,2,1,3,7,8,6]=>[5,3]=>2688
[1,6,7,3,8,2,5,4]=>[5,2,1]=>4032
[6,1,4,7,8,5,2,3]=>[8]=>5040
[6,3,2,1,7,8,5,4]=>[4,2,2]=>1260
[8,6,5,1,3,2,4,7]=>[4,2,2]=>1260
[6,4,7,8,3,2,5,1]=>[5,3]=>2688
[3,8,4,7,1,2,5,6]=>[5,3]=>2688
[8,6,1,2,5,4,3,7]=>[4,3,1]=>3360
[4,8,6,1,5,3,2,7]=>[3,2,2,1]=>1680
[5,8,6,4,1,3,2,7]=>[3,2,2,1]=>1680
[8,3,6,4,5,2,1,7]=>[3,3,1,1]=>1120
[6,8,5,7,4,2,3,1]=>[4,4]=>1260
[2,3,8,7,1,6,4,5]=>[5,2,1]=>4032
[4,3,7,8,1,6,2,5]=>[4,3,1]=>3360
[3,5,8,7,4,1,2,6]=>[4,4]=>1260
[7,3,8,4,1,2,5,6]=>[4,3,1]=>3360
[4,8,1,2,7,3,5,6]=>[6,2]=>3360
[6,8,1,2,7,4,5,3]=>[6,2]=>3360
[5,6,8,4,1,3,7,2]=>[4,2,1,1]=>2520
[8,5,4,7,1,6,3,2]=>[4,3,1]=>3360
[2,5,8,7,3,6,4,1]=>[5,2,1]=>4032
[2,4,8,7,5,6,1,3]=>[4,2,1,1]=>2520
[3,7,4,8,5,6,2,1]=>[4,2,1,1]=>2520
[6,4,8,7,5,1,2,3]=>[3,2,2,1]=>1680
[3,8,5,2,4,6,7,1]=>[6,1,1]=>3360
[5,7,1,8,4,6,2,3]=>[5,2,1]=>4032
[6,3,8,7,2,1,4,5]=>[4,2,2]=>1260
[2,3,7,8,5,6,1,4]=>[4,2,1,1]=>2520
[3,7,6,8,5,1,2,4]=>[3,2,2,1]=>1680
[2,6,7,8,5,1,3,4]=>[3,2,2,1]=>1680
[2,4,7,8,1,6,3,5]=>[5,2,1]=>4032
[5,4,7,8,2,6,3,1]=>[5,2,1]=>4032
[2,8,3,4,1,5,7,6]=>[5,1,1,1]=>1344
[6,8,3,4,1,2,7,5]=>[5,1,1,1]=>1344
[6,8,7,1,5,2,3,4]=>[5,2,1]=>4032
[5,8,3,2,7,6,1,4]=>[3,3,1,1]=>1120
[2,5,3,1,8,6,7,4]=>[5,1,1,1]=>1344
[4,5,3,2,8,6,7,1]=>[5,1,1,1]=>1344
[3,5,8,6,1,4,7,2]=>[5,2,1]=>4032
[2,8,5,6,1,4,7,3]=>[5,2,1]=>4032
[4,8,6,1,5,2,7,3]=>[4,2,1,1]=>2520
[5,8,2,3,7,6,1,4]=>[4,3,1]=>3360
[4,6,8,5,3,2,7,1]=>[5,2,1]=>4032
[2,6,4,8,5,1,7,3]=>[3,3,1,1]=>1120
[7,6,4,8,5,2,1,3]=>[3,2,2,1]=>1680
[3,4,8,6,5,2,7,1]=>[3,3,1,1]=>1120
[3,4,8,7,5,6,2,1]=>[3,3,1,1]=>1120
[7,5,3,2,8,6,1,4]=>[4,2,1,1]=>2520
[2,5,1,3,8,6,7,4]=>[6,1,1]=>3360
[4,5,1,2,8,6,7,3]=>[6,1,1]=>3360
[5,4,8,1,3,6,7,2]=>[6,1,1]=>3360
[8,3,5,4,1,6,7,2]=>[5,1,1,1]=>1344
[7,3,4,8,5,6,1,2]=>[4,2,1,1]=>2520
[6,1,5,7,2,4,8,3]=>[8]=>5040
[7,4,5,1,2,3,8,6]=>[8]=>5040
[7,4,3,1,2,8,5,6]=>[5,2,1]=>4032
[8,4,7,6,2,1,5,3]=>[8]=>5040
[8,4,6,5,7,1,3,2]=>[8]=>5040
[7,2,1,4,5,8,3,6]=>[3,2,1,1,1]=>1120
[7,4,1,6,3,5,8,2]=>[8]=>5040
[3,5,7,6,4,1,8,2]=>[8]=>5040
[4,7,5,2,1,3,8,6]=>[8]=>5040
[5,7,2,3,6,4,8,1]=>[8]=>5040
[8,6,2,3,7,1,4,5]=>[8]=>5040
[5,7,2,4,8,3,6,1]=>[4,3,1]=>3360
[1,7,2,4,8,6,3,5]=>[3,2,1,1,1]=>1120
[7,6,1,5,4,8,3,2]=>[3,3,2]=>1120
[4,7,3,2,1,8,5,6]=>[5,2,1]=>4032
[3,1,7,2,5,8,4,6]=>[5,2,1]=>4032
[4,8,7,6,1,2,5,3]=>[8]=>5040
[7,8,6,1,3,2,5,4]=>[8]=>5040
[2,8,6,7,4,1,3,5]=>[8]=>5040
[5,8,6,4,2,3,1,7]=>[5,2,1]=>4032
[2,8,3,1,6,5,4,7]=>[5,2,1]=>4032
[3,8,1,2,5,7,4,6]=>[5,2,1]=>4032
[6,8,5,4,2,7,3,1]=>[7,1]=>5760
[6,8,3,1,2,4,5,7]=>[4,3,1]=>3360
[4,6,8,7,3,1,5,2]=>[8]=>5040
[6,5,3,7,8,4,1,2]=>[4,3,1]=>3360
[4,1,3,8,7,5,6,2]=>[4,3,1]=>3360
[6,2,7,4,8,1,3,5]=>[2,2,2,1,1]=>420
[8,4,5,2,1,6,3,7]=>[5,2,1]=>4032
[4,3,2,6,8,1,7,5]=>[3,2,2,1]=>1680
[7,1,5,6,3,8,2,4]=>[3,3,2]=>1120
[5,1,2,4,7,8,3,6]=>[5,2,1]=>4032
[3,5,4,2,8,1,6,7]=>[8]=>5040
[5,1,3,8,4,2,7,6]=>[6,1,1]=>3360
[6,2,8,7,3,5,4,1]=>[5,2,1]=>4032
[7,1,8,4,3,6,5,2]=>[6,1,1]=>3360
[3,6,8,7,4,1,2,5]=>[8]=>5040
[5,6,8,1,7,3,2,4]=>[8]=>5040
[3,1,6,8,7,4,2,5]=>[8]=>5040
[7,4,6,8,2,1,5,3]=>[8]=>5040
[6,5,8,4,3,1,2,7]=>[5,2,1]=>4032
[2,5,8,3,6,7,4,1]=>[8]=>5040
[8,5,1,3,7,4,6,2]=>[8]=>5040
[1,5,8,3,7,4,2,6]=>[4,3,1]=>3360
[3,8,2,7,1,5,6,4]=>[8]=>5040
[5,8,2,3,6,4,1,7]=>[8]=>5040
[6,8,2,3,4,7,5,1]=>[8]=>5040
[7,5,1,8,4,2,6,3]=>[8]=>5040
[3,6,8,5,2,7,4,1]=>[5,3]=>2688
[2,1,6,5,4,8,3,7]=>[4,2,2]=>1260
[2,1,7,8,4,6,5,3]=>[5,2,1]=>4032
[2,1,7,4,3,5,8,6]=>[5,2,1]=>4032
[7,5,2,8,4,6,3,1]=>[7,1]=>5760
[7,8,2,4,3,1,5,6]=>[7,1]=>5760
[7,6,3,8,1,5,4,2]=>[7,1]=>5760
[7,2,4,1,6,3,8,5]=>[7,1]=>5760
[8,4,3,1,7,5,2,6]=>[7,1]=>5760
[7,3,1,4,6,8,5,2]=>[7,1]=>5760
[4,3,8,7,1,6,5,2]=>[4,3,1]=>3360
[5,2,4,3,6,8,1,7]=>[5,2,1]=>4032
[3,8,6,5,4,1,2,7]=>[3,3,2]=>1120
[4,7,5,6,3,8,2,1]=>[4,2,2]=>1260
[5,8,2,7,3,4,6,1]=>[5,3]=>2688
[6,7,2,4,5,3,8,1]=>[6,1,1]=>3360
[6,3,2,1,4,8,5,7]=>[6,2]=>3360
[6,2,3,1,4,7,8,5]=>[6,1,1]=>3360
[5,2,1,3,6,4,8,7]=>[5,2,1]=>4032
[7,1,8,3,5,4,6,2]=>[7,1]=>5760
[7,1,2,4,8,5,6,3]=>[7,1]=>5760
[7,2,1,3,4,5,8,6]=>[7,1]=>5760
[8,7,3,5,4,2,1,6]=>[5,2,1]=>4032
[5,1,6,4,3,2,8,7]=>[5,2,1]=>4032
[8,3,7,1,4,6,5,2]=>[7,1]=>5760
[2,8,3,6,4,7,5,1]=>[4,3,1]=>3360
[6,2,1,7,5,8,3,4]=>[6,1,1]=>3360
[6,3,8,7,5,2,1,4]=>[7,1]=>5760
[6,7,2,1,5,8,4,3]=>[7,1]=>5760
[9,1,8,7,6,5,4,3,2]=>[3,2,2,2]=>2520
[7,6,8,1,5,4,3,2]=>[7,1]=>5760
[7,1,9,8,6,5,4,3,2]=>[7,2]=>25920
[6,1,9,8,7,5,4,3,2]=>[9]=>40320
[5,4,8,7,6,1,3,2]=>[5,3]=>2688
[5,1,9,8,7,6,4,3,2]=>[8,1]=>45360
[4,1,9,8,7,6,5,3,2]=>[6,2,1]=>30240
[3,1,9,8,7,6,5,4,2]=>[4,2,2,1]=>11340
[10,1,9,8,7,6,5,4,3,2]=>[3,2,2,2,1]=>25200
[9,8,1,7,6,5,4,3,2]=>[5,2,2]=>9072
[7,6,1,8,5,4,3,2]=>[4,3,1]=>3360
[8,7,9,1,6,5,4,3,2]=>[7,2]=>25920
[8,1,10,9,7,6,5,4,3,2]=>[7,2,1]=>259200
[6,5,8,1,7,4,3,2]=>[5,3]=>2688
[7,6,9,8,1,5,4,3,2]=>[9]=>40320
[7,1,10,9,8,6,5,4,3,2]=>[9,1]=>403200
[6,5,9,8,7,1,4,3,2]=>[7,2]=>25920
[6,1,10,9,8,7,5,4,3,2]=>[10]=>362880
[6,5,8,7,4,1,3,2]=>[6,2]=>3360
[5,4,9,8,7,6,1,3,2]=>[5,3,1]=>24192
[5,1,10,9,8,7,6,4,3,2]=>[8,2]=>226800
[4,3,9,8,7,6,5,1,2]=>[3,3,2,1]=>10080
[4,1,10,9,8,7,6,5,3,2]=>[6,2,2]=>75600
[3,2,9,8,7,6,5,4,1]=>[3,2,2,1,1]=>7560
[3,1,10,9,8,7,6,5,4,2]=>[4,2,2,2]=>18900
[1,6,4,8,3,2,5,7]=>[5,2,1]=>4032
[1,8,3,5,6,2,4,7]=>[6,1,1]=>3360
[1,4,8,5,6,2,3,7]=>[4,3,1]=>3360
[1,2,8,5,3,7,4,6]=>[6,1,1]=>3360
[6,1,4,8,2,3,5,7]=>[8]=>5040
[8,7,2,5,6,1,4,3]=>[8]=>5040
[1,8,2,5,4,7,3,6]=>[5,2,1]=>4032
[5,7,4,1,2,3,8,6]=>[8]=>5040
[1,7,4,2,5,3,8,6]=>[6,1,1]=>3360
[6,7,4,2,1,3,8,5]=>[8]=>5040
[6,4,3,8,5,7,1,2]=>[3,3,1,1]=>1120
[7,4,3,6,2,1,5,8]=>[6,1,1]=>3360
[7,2,5,3,4,1,6,8]=>[3,3,1,1]=>1120
[8,3,7,4,5,6,1,2]=>[5,1,1,1]=>1344
[2,7,4,3,1,5,6,8]=>[5,2,1]=>4032
[6,8,4,2,3,1,5,7]=>[6,2]=>3360
[3,7,5,2,4,1,6,8]=>[7,1]=>5760
[7,1,3,2,8,4,5,6]=>[7,1]=>5760
[2,1,7,4,8,3,5,6]=>[5,2,1]=>4032
[5,2,8,6,1,3,4,7]=>[5,2,1]=>4032
[2,8,3,1,4,5,6,7]=>[7,1]=>5760
[7,4,8,2,3,1,5,6]=>[6,2]=>3360
[4,2,7,3,1,5,6,8]=>[6,1,1]=>3360
[8,3,7,2,1,4,5,6]=>[8]=>5040
[6,5,2,4,7,1,3,8]=>[4,2,1,1]=>2520
[6,5,7,4,1,8,2,3]=>[7,1]=>5760
[7,6,4,5,1,8,2,3]=>[8]=>5040
[8,6,4,1,3,7,2,5]=>[5,3]=>2688
[6,4,3,1,8,2,5,7]=>[4,3,1]=>3360
[7,4,1,2,8,3,5,6]=>[6,2]=>3360
[4,8,1,3,5,7,2,6]=>[4,3,1]=>3360
[7,8,4,1,3,6,2,5]=>[7,1]=>5760
[6,5,8,1,3,7,2,4]=>[8]=>5040
[5,3,6,1,8,2,4,7]=>[5,3]=>2688
[4,7,3,1,8,2,5,6]=>[5,2,1]=>4032
[8,3,1,7,2,4,5,6]=>[8]=>5040
[2,8,1,4,7,3,5,6]=>[5,2,1]=>4032
[4,1,5,8,3,7,6,2]=>[4,2,2]=>1260
[4,5,1,8,2,7,6,3]=>[4,2,2]=>1260
[4,5,2,1,8,7,6,3]=>[4,2,2]=>1260
[4,8,6,3,7,5,1,2]=>[6,2]=>3360
[5,6,2,7,4,1,8,3]=>[8]=>5040
[5,6,7,2,3,1,8,4]=>[8]=>5040
[5,1,6,7,8,3,4,2]=>[4,2,2]=>1260
[4,1,6,8,7,3,5,2]=>[4,2,2]=>1260
[4,1,6,8,7,5,3,2]=>[4,4]=>1260
[4,6,8,1,7,5,2,3]=>[4,2,2]=>1260
[5,6,7,1,8,3,2,4]=>[4,4]=>1260
[5,6,7,3,8,1,2,4]=>[8]=>5040
[5,6,7,3,8,2,1,4]=>[6,2]=>3360
[7,4,6,2,3,5,1,8]=>[3,2,2,1]=>1680
[1,4,8,6,3,2,5,7]=>[4,3,1]=>3360
[7,4,1,6,3,8,5,2]=>[4,4]=>1260
[7,6,3,1,5,8,4,2]=>[3,3,1,1]=>1120
[6,4,2,5,7,3,1,8]=>[7,1]=>5760
[4,2,5,7,6,3,1,8]=>[3,3,1,1]=>1120
[7,4,5,6,1,8,3,2]=>[4,4]=>1260
[4,1,5,8,6,3,2,7]=>[5,3]=>2688
[3,2,7,6,1,8,5,4]=>[4,3,1]=>3360
[4,7,5,1,6,8,2,3]=>[4,2,2]=>1260
[8,6,5,1,2,7,4,3]=>[8]=>5040
[3,2,5,1,4,8,7,6]=>[4,2,1,1]=>2520
[8,5,4,1,3,2,7,6]=>[7,1]=>5760
[1,4,2,3,6,8,7,5]=>[3,3,1,1]=>1120
[5,4,8,3,7,1,6,2]=>[4,4]=>1260
[4,7,1,8,2,5,3,6]=>[8]=>5040
[6,4,1,8,5,3,7,2]=>[3,3,1,1]=>1120
[8,4,6,1,3,5,2,7]=>[5,3]=>2688
[3,2,5,4,7,8,1,6]=>[4,2,1,1]=>2520
[5,2,4,3,7,8,1,6]=>[3,2,2,1]=>1680
[8,1,6,7,2,5,3,4]=>[8]=>5040
[3,1,7,6,5,8,2,4]=>[4,3,1]=>3360
[1,2,7,5,6,8,3,4]=>[4,2,1,1]=>2520
[6,1,4,7,2,8,3,5]=>[5,3]=>2688
[3,2,1,7,6,8,4,5]=>[3,2,2,1]=>1680
[3,2,8,6,4,7,1,5]=>[7,1]=>5760
[7,8,4,6,3,2,1,5]=>[6,2]=>3360
[1,8,6,5,3,7,2,4]=>[7,1]=>5760
[8,2,5,3,6,7,1,4]=>[7,1]=>5760
[3,8,5,2,7,6,1,4]=>[4,3,1]=>3360
[4,7,5,3,1,8,6,2]=>[4,4]=>1260
[4,5,3,6,8,1,7,2]=>[3,3,1,1]=>1120
[3,5,2,6,1,8,7,4]=>[4,3,1]=>3360
[1,6,3,5,7,2,8,4]=>[4,2,1,1]=>2520
[1,5,4,6,7,8,2,3]=>[4,3,1]=>3360
[8,4,6,5,7,2,1,3]=>[8]=>5040
[7,4,5,2,6,8,1,3]=>[4,2,2]=>1260
[5,4,2,6,8,7,1,3]=>[8]=>5040
[6,5,1,4,3,2,8,7]=>[5,2,1]=>4032
[3,6,4,5,2,1,8,7]=>[6,2]=>3360
[7,5,4,2,3,8,1,6]=>[4,2,2]=>1260
[7,8,1,3,5,6,2,4]=>[6,1,1]=>3360
[3,1,7,8,5,2,6,4]=>[5,2,1]=>4032
[1,3,7,5,8,2,6,4]=>[4,3,1]=>3360
[3,1,7,5,8,2,6,4]=>[5,3]=>2688
[3,5,7,1,8,4,6,2]=>[5,3]=>2688
[3,5,7,8,1,4,6,2]=>[8]=>5040
[5,3,7,1,8,4,6,2]=>[8]=>5040
[3,6,2,1,4,5,8,7]=>[6,2]=>3360
[4,6,2,5,1,3,8,7]=>[3,3,2]=>1120
[6,4,2,5,1,3,8,7]=>[6,2]=>3360
[8,6,1,7,3,2,4,5]=>[4,2,2]=>1260
[2,5,8,1,7,3,4,6]=>[5,3]=>2688
[6,8,2,7,3,1,4,5]=>[4,2,2]=>1260
[6,8,2,3,7,1,4,5]=>[6,2]=>3360
[8,6,2,7,4,5,1,3]=>[8]=>5040
[5,2,8,1,7,3,4,6]=>[4,3,1]=>3360
[4,2,3,8,1,5,6,7]=>[6,1,1]=>3360
[5,2,8,3,7,1,4,6]=>[7,1]=>5760
[5,2,8,4,6,1,3,7]=>[3,3,1,1]=>1120
[2,1,5,8,4,3,6,7]=>[6,2]=>3360
[5,8,3,2,7,1,4,6]=>[7,1]=>5760
[4,1,3,8,2,5,6,7]=>[7,1]=>5760
[3,5,8,2,7,1,4,6]=>[4,4]=>1260
[4,5,8,2,6,1,3,7]=>[5,3]=>2688
[2,6,8,3,7,1,4,5]=>[5,3]=>2688
[5,1,8,3,7,2,4,6]=>[8]=>5040
[5,1,8,4,6,2,3,7]=>[4,3,1]=>3360
[5,8,4,1,6,2,3,7]=>[8]=>5040
[4,5,8,1,6,2,3,7]=>[3,3,2]=>1120
[5,4,8,1,6,2,3,7]=>[5,3]=>2688
[4,8,5,1,6,2,3,7]=>[6,2]=>3360
[2,1,5,4,8,3,6,7]=>[5,2,1]=>4032
[2,4,3,8,1,5,6,7]=>[7,1]=>5760
[3,1,8,4,2,5,6,7]=>[7,1]=>5760
[3,8,4,2,1,5,6,7]=>[8]=>5040
[2,3,8,4,1,5,6,7]=>[7,1]=>5760
[3,4,2,8,1,5,6,7]=>[8]=>5040
[3,8,5,2,7,1,4,6]=>[8]=>5040
[4,8,5,2,6,1,3,7]=>[8]=>5040
[2,1,4,8,5,3,6,7]=>[5,2,1]=>4032
[3,2,8,4,1,5,6,7]=>[6,1,1]=>3360
[2,8,4,3,1,5,6,7]=>[6,2]=>3360
[5,7,4,3,8,2,6,1]=>[3,3,2]=>1120
[3,8,4,2,6,7,5,1]=>[5,3]=>2688
[6,1,7,5,2,8,4,3]=>[8]=>5040
[2,6,7,5,3,8,4,1]=>[4,4]=>1260
[6,7,4,8,2,5,3,1]=>[8]=>5040
[3,8,4,2,1,6,7,5]=>[6,1,1]=>3360
[6,7,5,8,1,2,4,3]=>[8]=>5040
[3,4,8,1,2,5,7,6]=>[7,1]=>5760
[6,1,3,4,8,2,5,7]=>[3,3,1,1]=>1120
[6,2,3,4,8,1,5,7]=>[3,2,1,1,1]=>1120
[6,7,4,8,2,3,5,1]=>[5,3]=>2688
[2,6,7,5,1,3,8,4]=>[8]=>5040
[6,7,4,8,1,3,2,5]=>[6,2]=>3360
[6,7,5,8,4,1,3,2]=>[6,2]=>3360
[6,7,4,8,2,1,3,5]=>[6,2]=>3360
[1,4,3,6,5,8,2,7]=>[5,1,1,1]=>1344
[6,7,8,2,3,5,4,1]=>[5,3]=>2688
[5,8,6,2,3,7,4,1]=>[8]=>5040
[1,8,3,4,7,6,2,5]=>[4,1,1,1,1]=>420
[8,7,2,3,6,5,4,1]=>[4,2,2]=>1260
[3,8,1,7,5,2,6,4]=>[5,2,1]=>4032
[4,8,1,6,7,2,5,3]=>[6,2]=>3360
[2,1,3,8,4,6,5,7]=>[4,2,1,1]=>2520
[1,3,2,8,5,4,6,7]=>[4,2,1,1]=>2520
[8,3,1,5,7,2,6,4]=>[8]=>5040
[1,5,6,8,7,4,2,3]=>[4,3,1]=>3360
[2,4,8,5,7,3,6,1]=>[8]=>5040
[4,2,8,6,7,3,5,1]=>[5,2,1]=>4032
[3,2,8,7,5,4,6,1]=>[3,3,1,1]=>1120
[3,1,8,7,5,6,2,4]=>[6,1,1]=>3360
[5,1,7,8,6,4,2,3]=>[8]=>5040
[7,8,3,2,6,1,4,5]=>[7,1]=>5760
[3,4,8,2,6,1,7,5]=>[5,2,1]=>4032
[7,8,4,1,5,6,3,2]=>[4,2,1,1]=>2520
[7,8,1,4,5,6,3,2]=>[3,2,1,1,1]=>1120
[7,8,1,2,6,3,4,5]=>[8]=>5040
[7,8,5,1,4,6,3,2]=>[5,2,1]=>4032
[7,8,4,5,1,6,3,2]=>[5,2,1]=>4032
[5,3,8,4,1,6,7,2]=>[3,2,1,1,1]=>1120
[6,2,4,8,1,5,3,7]=>[4,3,1]=>3360
[3,4,8,5,1,6,7,2]=>[6,1,1]=>3360
[3,5,8,1,4,6,7,2]=>[6,1,1]=>3360
[1,4,8,2,6,3,7,5]=>[4,2,1,1]=>2520
[5,3,8,1,4,6,7,2]=>[3,3,1,1]=>1120
[4,2,6,8,1,5,3,7]=>[7,1]=>5760
[7,4,2,8,1,5,3,6]=>[8]=>5040
[6,1,7,5,8,4,3,2]=>[6,2]=>3360
[6,2,1,8,4,5,3,7]=>[7,1]=>5760
[1,2,7,8,5,3,4,6]=>[5,1,1,1]=>1344
[6,3,7,8,5,4,1,2]=>[7,1]=>5760
[6,1,5,7,8,4,3,2]=>[8]=>5040
[1,7,5,6,8,4,3,2]=>[5,2,1]=>4032
[3,1,8,4,5,6,7,2]=>[4,1,1,1,1]=>420
[2,1,4,8,6,5,3,7]=>[4,2,2]=>1260
[2,4,1,8,6,5,3,7]=>[6,2]=>3360
[4,2,1,8,6,5,3,7]=>[5,2,1]=>4032
[3,2,7,8,5,1,4,6]=>[6,1,1]=>3360
[2,3,7,8,5,1,4,6]=>[7,1]=>5760
[2,7,3,8,5,1,4,6]=>[6,1,1]=>3360
[3,6,2,8,5,1,4,7]=>[4,3,1]=>3360
[4,1,2,8,7,5,3,6]=>[8]=>5040
[1,4,2,8,7,5,3,6]=>[7,1]=>5760
[7,3,6,8,5,4,1,2]=>[5,2,1]=>4032
[7,2,1,8,5,3,4,6]=>[6,1,1]=>3360
[1,2,6,8,4,5,3,7]=>[6,1,1]=>3360
[7,1,6,5,8,4,3,2]=>[8]=>5040
[6,5,7,1,8,4,3,2]=>[3,3,2]=>1120
[5,7,6,1,8,4,3,2]=>[8]=>5040
[6,7,1,5,8,4,3,2]=>[8]=>5040
[6,7,3,8,5,4,1,2]=>[6,1,1]=>3360
[7,1,2,8,4,5,3,6]=>[4,4]=>1260
[7,6,1,5,8,4,3,2]=>[5,3]=>2688
[7,5,6,1,8,4,3,2]=>[5,3]=>2688
[7,1,6,5,3,2,4,8]=>[7,1]=>5760
[1,8,7,5,3,2,4,6]=>[4,3,1]=>3360
[1,8,7,4,2,5,3,6]=>[4,2,1,1]=>2520
[8,7,4,2,5,3,6,1]=>[5,2,1]=>4032
[7,1,6,4,2,5,3,8]=>[6,1,1]=>3360
[2,6,5,4,7,1,3,8]=>[3,3,1,1]=>1120
[7,1,5,3,6,4,2,8]=>[4,3,1]=>3360
[5,3,7,1,6,4,2,8]=>[4,3,1]=>3360
[5,3,6,4,2,7,1,8]=>[6,1,1]=>3360
[1,5,3,8,7,4,2,6]=>[3,3,1,1]=>1120
[7,4,2,8,6,3,5,1]=>[8]=>5040
[5,3,6,1,8,7,4,2]=>[8]=>5040
[6,1,5,3,8,7,4,2]=>[8]=>5040
[2,8,7,5,4,6,1,3]=>[5,2,1]=>4032
[2,3,1,8,7,5,4,6]=>[5,3]=>2688
[5,3,8,7,4,2,1,6]=>[4,4]=>1260
[7,4,2,1,8,6,3,5]=>[5,2,1]=>4032
[8,6,3,5,7,4,2,1]=>[5,2,1]=>4032
[1,8,6,3,5,7,4,2]=>[4,2,1,1]=>2520
[6,3,8,5,2,1,7,4]=>[5,2,1]=>4032
[8,6,3,7,4,2,1,5]=>[5,2,1]=>4032
[2,8,6,4,7,5,1,3]=>[7,1]=>5760
[5,1,8,6,3,7,4,2]=>[5,3]=>2688
[6,3,7,4,1,8,5,2]=>[7,1]=>5760
[8,5,2,6,3,7,4,1]=>[3,3,2]=>1120
[6,1,8,7,4,2,5,3]=>[3,3,2]=>1120
[8,6,3,7,4,2,5,1]=>[3,2,2,1]=>1680
[1,8,6,3,2,4,7,5]=>[3,3,1,1]=>1120
[8,6,3,2,4,7,5,1]=>[5,2,1]=>4032
[7,5,1,8,6,3,2,4]=>[6,2]=>3360
[6,1,8,7,5,3,2,4]=>[7,1]=>5760
[4,3,2,8,7,6,1,5]=>[5,2,1]=>4032
[2,4,5,1,3,8,7,6]=>[3,2,2,1]=>1680
[7,5,8,6,3,2,4,1]=>[8]=>5040
[1,7,5,8,6,3,2,4]=>[3,2,2,1]=>1680
[1,7,4,2,5,8,6,3]=>[6,1,1]=>3360
[8,6,3,1,7,4,2,5]=>[7,1]=>5760
[8,7,4,2,5,3,1,6]=>[7,1]=>5760
[5,3,1,8,7,4,2,6]=>[5,3]=>2688
[4,1,8,7,5,3,2,6]=>[4,3,1]=>3360
[2,8,6,4,1,3,7,5]=>[4,2,1,1]=>2520
[4,1,8,6,3,2,7,5]=>[4,3,1]=>3360
[7,4,2,8,6,3,1,5]=>[6,2]=>3360
[6,3,1,8,5,2,7,4]=>[4,2,1,1]=>2520
[8,5,2,6,3,1,7,4]=>[4,3,1]=>3360
[7,4,8,5,2,6,3,1]=>[4,3,1]=>3360
[1,8,5,2,7,4,6,3]=>[7,1]=>5760
[8,5,2,7,4,6,3,1]=>[5,2,1]=>4032
[7,4,6,3,1,8,5,2]=>[5,3]=>2688
[6,3,1,7,4,8,5,2]=>[5,3]=>2688
[8,6,3,1,5,7,4,2]=>[6,1,1]=>3360
[4,1,7,5,8,6,3,2]=>[5,2,1]=>4032
[2,3,1,7,5,8,6,4]=>[4,3,1]=>3360
[7,4,8,5,2,1,6,3]=>[3,3,2]=>1120
[8,5,2,1,7,4,6,3]=>[8]=>5040
[1,7,4,6,3,8,5,2]=>[7,1]=>5760
[4,1,8,5,7,3,2,6]=>[5,3]=>2688
[2,1,5,7,8,4,3,6]=>[6,2]=>3360
[5,1,7,4,8,3,2,6]=>[7,1]=>5760
[4,7,2,8,3,6,1,5]=>[7,1]=>5760
[4,6,2,7,3,1,8,5]=>[8]=>5040
[6,2,8,4,1,7,3,5]=>[6,1,1]=>3360
[6,3,4,8,1,7,2,5]=>[8]=>5040
[1,8,5,4,2,3,7,6]=>[5,1,1,1]=>1344
[3,5,4,8,1,2,7,6]=>[7,1]=>5760
[5,6,3,8,7,1,2,4]=>[5,2,1]=>4032
[2,6,8,4,1,7,3,5]=>[7,1]=>5760
[1,8,7,4,2,6,3,5]=>[3,2,1,1,1]=>1120
[6,3,5,8,7,1,2,4]=>[4,2,2]=>1260
[5,2,8,6,7,1,3,4]=>[7,1]=>5760
[6,2,8,7,5,1,3,4]=>[4,2,1,1]=>2520
[1,8,5,7,6,2,3,4]=>[7,1]=>5760
[3,6,7,8,5,1,2,4]=>[5,2,1]=>4032
[1,8,6,7,5,2,3,4]=>[6,1,1]=>3360
[5,7,6,4,8,1,2,3]=>[5,2,1]=>4032
[6,3,8,7,5,1,2,4]=>[5,2,1]=>4032
[2,8,7,4,1,3,5,6]=>[7,1]=>5760
[5,4,8,7,1,3,2,6]=>[3,3,2]=>1120
[4,8,6,1,3,2,5,7]=>[6,2]=>3360
[5,4,2,7,6,8,1,3]=>[8]=>5040
[2,8,7,1,4,5,3,6]=>[6,2]=>3360
[4,2,1,8,7,3,5,6]=>[5,2,1]=>4032
[5,1,6,3,2,8,7,4]=>[4,3,1]=>3360
[4,6,1,8,7,3,2,5]=>[8]=>5040
[8,7,2,3,5,4,1,6]=>[7,1]=>5760
[5,3,1,4,8,7,2,6]=>[7,1]=>5760
[4,3,5,2,8,7,1,6]=>[8]=>5040
[3,4,2,8,6,1,5,7]=>[8]=>5040
[3,7,6,8,1,5,2,4]=>[4,2,2]=>1260
[8,1,4,2,3,6,7,5]=>[6,1,1]=>3360
[3,7,2,1,8,6,4,5]=>[5,2,1]=>4032
[2,8,6,1,7,3,5,4]=>[4,2,2]=>1260
[1,7,6,3,5,8,2,4]=>[4,2,1,1]=>2520
[3,7,5,1,6,8,2,4]=>[6,2]=>3360
[3,6,5,8,1,4,7,2]=>[4,3,1]=>3360
[8,1,5,6,4,7,2,3]=>[8]=>5040
[3,6,7,4,1,8,2,5]=>[7,1]=>5760
[1,7,4,6,8,2,5,3]=>[7,1]=>5760
[7,5,8,2,6,3,1,4]=>[6,2]=>3360
[2,7,1,6,5,4,8,3]=>[5,2,1]=>4032
[7,3,2,6,1,8,5,4]=>[3,3,2]=>1120
[6,4,7,2,3,1,8,5]=>[4,2,2]=>1260
[5,3,1,8,4,6,2,7]=>[7,1]=>5760
[3,8,1,6,7,4,2,5]=>[4,2,2]=>1260
[2,7,4,3,6,8,1,5]=>[3,3,2]=>1120
[2,8,4,6,1,5,3,7]=>[8]=>5040
[8,4,1,6,3,2,5,7]=>[5,3]=>2688
[4,7,3,8,5,2,1,6]=>[6,1,1]=>3360
[3,1,7,4,8,5,2,6]=>[4,3,1]=>3360
[7,4,1,6,3,2,8,5]=>[5,3]=>2688
[3,8,6,2,7,4,1,5]=>[8]=>5040
[7,3,1,4,5,2,8,6]=>[6,1,1]=>3360
[6,1,4,8,5,3,2,7]=>[7,1]=>5760
[8,1,2,4,6,7,5,3]=>[4,3,1]=>3360
[8,1,3,6,7,5,4,2]=>[4,3,1]=>3360
[7,5,2,3,8,6,1,4]=>[5,2,1]=>4032
[8,6,2,4,1,3,7,5]=>[3,3,1,1]=>1120
[4,7,5,1,8,6,3,2]=>[5,2,1]=>4032
[4,7,3,2,8,5,6,1]=>[7,1]=>5760
[8,4,5,7,6,1,3,2]=>[8]=>5040
[7,5,8,4,2,3,6,1]=>[5,2,1]=>4032
[3,8,4,6,1,7,5,2]=>[6,2]=>3360
[3,7,4,6,5,2,8,1]=>[7,1]=>5760
[4,2,7,6,1,5,8,3]=>[4,3,1]=>3360
[8,3,1,4,5,7,6,2]=>[4,2,1,1]=>2520
[3,5,1,6,8,4,7,2]=>[3,2,2,1]=>1680
[6,1,5,7,3,8,4,2]=>[4,2,2]=>1260
[5,8,4,7,3,2,6,1]=>[8]=>5040
[7,2,6,5,8,4,1,3]=>[5,2,1]=>4032
[8,3,2,5,1,6,7,4]=>[4,2,1,1]=>2520
[2,6,8,3,7,4,1,5]=>[8]=>5040
[8,1,5,6,4,7,3,2]=>[5,3]=>2688
[2,5,8,1,6,4,7,3]=>[5,2,1]=>4032
[7,4,1,8,3,2,6,5]=>[8]=>5040
[8,3,7,4,2,1,6,5]=>[7,1]=>5760
[5,2,6,8,3,1,7,4]=>[4,2,1,1]=>2520
[3,6,5,8,4,1,7,2]=>[7,1]=>5760
[7,3,6,1,8,4,5,2]=>[8]=>5040
[8,2,7,3,4,6,5,1]=>[4,2,1,1]=>2520
[7,3,8,2,5,6,4,1]=>[6,1,1]=>3360
[5,7,3,1,6,4,8,2]=>[4,3,1]=>3360
[6,1,3,2,4,8,7,5]=>[6,1,1]=>3360
[8,7,4,2,3,6,1,5]=>[7,1]=>5760
[8,7,1,5,4,2,3,6]=>[6,2]=>3360
[3,7,1,5,2,8,6,4]=>[6,2]=>3360
[8,7,2,5,4,1,3,6]=>[3,3,2]=>1120
[8,7,2,5,3,1,4,6]=>[5,3]=>2688
[5,2,8,7,1,4,3,6]=>[5,2,1]=>4032
[7,1,8,6,2,4,3,5]=>[6,2]=>3360
[8,1,6,2,7,5,3,4]=>[4,4]=>1260
[7,1,6,2,8,5,3,4]=>[8]=>5040
[6,3,4,1,7,2,8,5]=>[5,3]=>2688
[7,2,4,3,5,1,8,6]=>[4,2,1,1]=>2520
[5,1,7,2,3,8,6,4]=>[8]=>5040
[8,2,3,5,1,7,6,4]=>[4,2,1,1]=>2520
[7,6,3,1,4,8,2,5]=>[7,1]=>5760
[6,1,8,2,7,5,3,4]=>[8]=>5040
[7,2,8,1,6,5,3,4]=>[5,2,1]=>4032
[7,2,6,4,3,8,1,5]=>[4,2,1,1]=>2520
[5,1,7,4,3,8,2,6]=>[5,2,1]=>4032
[5,3,1,7,4,8,2,6]=>[6,2]=>3360
[7,4,8,2,1,5,3,6]=>[6,2]=>3360
[8,2,4,1,6,3,7,5]=>[6,1,1]=>3360
[8,2,7,5,1,6,4,3]=>[6,1,1]=>3360
[6,1,7,3,2,8,5,4]=>[8]=>5040
[4,7,2,1,6,3,8,5]=>[6,2]=>3360
[6,2,1,5,3,8,4,7]=>[7,1]=>5760
[5,3,1,6,2,8,4,7]=>[4,4]=>1260
[6,1,5,2,8,4,3,7]=>[4,4]=>1260
[7,4,3,8,1,5,2,6]=>[7,1]=>5760
[7,4,8,1,5,3,2,6]=>[4,3,1]=>3360
[6,1,5,3,2,8,4,7]=>[8]=>5040
[6,3,2,8,4,1,5,7]=>[4,2,2]=>1260
[7,3,4,2,8,5,1,6]=>[3,3,2]=>1120
[7,1,6,3,4,2,8,5]=>[8]=>5040
[8,5,1,3,7,4,2,6]=>[5,3]=>2688
[3,8,6,1,5,2,7,4]=>[6,1,1]=>3360
[8,6,1,3,7,5,2,4]=>[4,4]=>1260
[4,8,5,6,1,7,3,2]=>[6,2]=>3360
[6,7,1,3,8,5,2,4]=>[6,2]=>3360
[3,6,7,1,5,2,8,4]=>[5,2,1]=>4032
[7,1,3,8,4,2,6,5]=>[4,3,1]=>3360
[5,6,2,7,1,3,8,4]=>[3,3,2]=>1120
[5,6,2,8,1,3,7,4]=>[3,2,2,1]=>1680
[6,1,8,3,7,5,2,4]=>[5,3]=>2688
[7,4,2,1,5,8,3,6]=>[5,2,1]=>4032
[7,4,1,5,8,3,2,6]=>[8]=>5040
[7,3,2,6,4,8,1,5]=>[4,2,2]=>1260
[6,4,2,7,3,8,1,5]=>[8]=>5040
[5,1,8,3,7,4,2,6]=>[4,4]=>1260
[7,4,8,3,1,5,2,6]=>[8]=>5040
[5,2,1,7,4,8,3,6]=>[5,2,1]=>4032
[6,1,8,4,5,2,7,3]=>[3,2,1,1,1]=>1120
[7,1,6,4,5,2,8,3]=>[6,1,1]=>3360
[3,5,2,7,1,6,8,4]=>[4,3,1]=>3360
[4,5,7,3,1,6,8,2]=>[7,1]=>5760
[4,5,7,2,8,6,1,3]=>[7,1]=>5760
[3,5,1,7,2,6,8,4]=>[3,2,2,1]=>1680
[4,5,7,2,8,1,3,6]=>[6,2]=>3360
[4,6,7,2,1,5,8,3]=>[5,3]=>2688
[4,6,7,1,3,8,5,2]=>[3,3,2]=>1120
[3,6,1,5,7,8,4,2]=>[3,3,2]=>1120
[4,6,7,1,5,8,3,2]=>[3,2,2,1]=>1680
[6,1,3,7,4,8,5,2]=>[4,3,1]=>3360
[4,1,5,2,7,6,3,8]=>[3,3,1,1]=>1120
[7,5,1,4,2,8,6,3]=>[5,2,1]=>4032
[7,5,4,1,3,8,6,2]=>[8]=>5040
[7,4,3,2,8,1,6,5]=>[3,2,2,1]=>1680
[2,7,5,3,8,1,4,6]=>[8]=>5040
[1,8,5,3,6,4,2,7]=>[4,3,1]=>3360
[8,6,3,2,7,5,4,1]=>[5,2,1]=>4032
[8,5,7,4,3,6,2,1]=>[4,2,1,1]=>2520
[2,8,5,6,1,4,3,7]=>[6,2]=>3360
[6,5,8,1,4,2,7,3]=>[5,2,1]=>4032
[6,5,8,4,1,3,7,2]=>[6,1,1]=>3360
[5,4,8,3,2,1,7,6]=>[7,1]=>5760
[5,7,4,8,1,3,6,2]=>[6,2]=>3360
[7,1,8,6,2,5,3,4]=>[8]=>5040
[2,8,7,1,6,3,5,4]=>[4,4]=>1260
[3,7,6,1,5,4,2,8]=>[4,2,1,1]=>2520
[5,8,7,2,6,1,4,3]=>[5,3]=>2688
[7,3,8,6,5,1,2,4]=>[7,1]=>5760
[8,7,3,6,4,2,1,5]=>[7,1]=>5760
[6,1,4,2,5,3,7,8]=>[5,1,1,1]=>1344
[1,3,7,5,4,2,8,6]=>[5,2,1]=>4032
[6,1,3,5,4,2,7,8]=>[3,2,1,1,1]=>1120
[6,1,2,5,4,7,3,8]=>[5,2,1]=>4032
[5,1,6,3,4,7,8,2]=>[8]=>5040
[5,2,6,3,4,7,1,8]=>[6,1,1]=>3360
[3,4,7,5,8,6,1,2]=>[4,3,1]=>3360
[2,4,7,1,5,3,8,6]=>[4,3,1]=>3360
[2,3,6,7,4,8,1,5]=>[8]=>5040
[1,3,6,7,4,8,5,2]=>[4,3,1]=>3360
[2,7,6,5,3,1,8,4]=>[8]=>5040
[5,2,6,1,4,7,8,3]=>[4,3,1]=>3360
[4,7,6,5,2,1,8,3]=>[8]=>5040
[5,3,6,2,4,1,7,8]=>[6,1,1]=>3360
[5,7,4,2,1,3,6,8]=>[5,2,1]=>4032
[6,3,1,5,4,7,8,2]=>[6,2]=>3360
[5,3,6,1,4,2,7,8]=>[3,3,1,1]=>1120
[1,7,4,2,6,3,8,5]=>[7,1]=>5760
[5,7,4,1,2,3,6,8]=>[7,1]=>5760
[6,4,1,2,5,3,7,8]=>[3,2,1,1,1]=>1120
[4,7,6,3,8,5,1,2]=>[8]=>5040
[3,7,6,5,2,8,1,4]=>[8]=>5040
[3,7,6,5,1,2,8,4]=>[8]=>5040
[4,7,2,6,1,3,8,5]=>[8]=>5040
[2,7,1,6,8,3,5,4]=>[8]=>5040
[2,7,6,5,8,1,4,3]=>[8]=>5040
[9,1,2,3,4,5,6,8,7]=>[8,1]=>45360
[10,1,2,3,4,5,6,7,9,8]=>[9,1]=>403200
[9,1,2,3,4,5,7,8,6]=>[7,1,1]=>25920
[2,3,4,5,6,9,7,8,1]=>[7,1,1]=>25920
[2,3,4,5,6,7,8,10,9,1]=>[9,1]=>403200
[5,2,8,7,6,4,3,1]=>[7,1]=>5760
[8,2,7,6,1,5,4,3]=>[7,1]=>5760
[8,4,1,7,6,5,3,2]=>[6,2]=>3360
[4,5,6,2,3,8,1,7]=>[8]=>5040
[4,5,3,2,7,8,1,6]=>[5,2,1]=>4032
[6,5,7,3,8,4,2,1]=>[8]=>5040
[6,8,7,2,4,3,5,1]=>[8]=>5040
[3,2,7,4,5,8,1,6]=>[3,2,1,1,1]=>1120
[6,8,1,5,2,4,3,7]=>[8]=>5040
[8,3,4,6,1,5,2,7]=>[8]=>5040
[2,3,4,7,5,8,1,6]=>[5,2,1]=>4032
[6,3,4,7,8,2,5,1]=>[8]=>5040
[5,3,7,4,8,6,1,2]=>[6,1,1]=>3360
[8,3,6,4,1,7,2,5]=>[4,3,1]=>3360
[1,3,7,4,8,6,2,5]=>[3,2,1,1,1]=>1120
[3,7,8,5,4,1,2,6]=>[4,2,2]=>1260
[5,4,3,1,7,8,2,6]=>[5,2,1]=>4032
[5,7,6,2,8,4,1,3]=>[8]=>5040
[6,1,7,5,8,3,4,2]=>[8]=>5040
[7,5,6,4,1,3,8,2]=>[5,2,1]=>4032
[1,5,6,8,4,7,3,2]=>[4,3,1]=>3360
[4,1,3,7,6,5,8,2]=>[5,2,1]=>4032
[3,4,1,7,5,8,6,2]=>[5,2,1]=>4032
[8,5,7,4,3,1,6,2]=>[7,1]=>5760
[6,8,5,1,7,2,4,3]=>[8]=>5040
[8,2,4,1,3,7,6,5]=>[5,2,1]=>4032
[7,8,3,6,2,1,4,5]=>[4,3,1]=>3360
[8,1,7,4,2,3,6,5]=>[4,3,1]=>3360
[1,8,7,2,3,5,6,4]=>[4,3,1]=>3360
[2,8,3,1,6,7,5,4]=>[4,3,1]=>3360
[8,2,3,1,5,7,6,4]=>[3,2,1,1,1]=>1120
[3,8,4,1,2,7,6,5]=>[3,3,2]=>1120
[5,4,7,2,3,6,8,1]=>[5,2,1]=>4032
[6,3,2,1,8,4,7,5]=>[3,2,2,1]=>1680
[2,3,7,4,1,8,5,6]=>[5,2,1]=>4032
[6,4,1,3,2,7,8,5]=>[8]=>5040
[2,7,8,5,1,3,6,4]=>[8]=>5040
[8,2,5,6,7,1,3,4]=>[4,3,1]=>3360
[2,8,5,4,7,6,1,3]=>[6,1,1]=>3360
[6,7,1,5,8,2,4,3]=>[8]=>5040
[4,8,7,6,2,3,5,1]=>[8]=>5040
[7,8,1,5,3,2,6,4]=>[8]=>5040
[6,5,7,3,8,2,1,4]=>[8]=>5040
[8,1,4,7,2,5,6,3]=>[8]=>5040
[7,3,4,6,1,5,8,2]=>[8]=>5040
[8,3,4,5,7,1,6,2]=>[8]=>5040
[4,2,6,8,3,1,5,7]=>[7,1]=>5760
[3,7,6,2,4,5,1,8]=>[7,1]=>5760
[2,3,6,5,8,1,4,7]=>[4,4]=>1260
[2,3,5,8,6,1,4,7]=>[5,3]=>2688
[4,2,3,8,6,1,5,7]=>[6,1,1]=>3360
[6,4,1,2,8,3,5,7]=>[3,3,2]=>1120
[1,2,3,7,4,6,8,5]=>[4,1,1,1,1]=>420
[3,2,7,1,4,5,8,6]=>[7,1]=>5760
[2,1,5,3,8,7,4,6]=>[6,2]=>3360
[5,8,3,2,4,1,6,7]=>[7,1]=>5760
[4,2,7,1,8,3,5,6]=>[5,2,1]=>4032
[4,1,8,2,7,3,5,6]=>[3,3,2]=>1120
[1,2,7,5,3,8,4,6]=>[4,2,1,1]=>2520
[3,2,7,1,4,8,5,6]=>[5,2,1]=>4032
[1,2,3,7,6,8,4,5]=>[3,2,1,1,1]=>1120
[1,2,3,6,8,7,4,5]=>[3,2,1,1,1]=>1120
[1,2,3,7,8,4,6,5]=>[3,2,1,1,1]=>1120
[1,2,3,6,8,4,7,5]=>[2,2,1,1,1,1]=>210
[1,2,3,7,8,6,4,5]=>[2,2,1,1,1,1]=>210
[6,2,8,3,7,5,1,4]=>[4,3,1]=>3360
[4,2,8,3,7,5,6,1]=>[4,3,1]=>3360
[7,3,4,8,6,5,1,2]=>[4,2,2]=>1260
[5,3,4,8,7,2,6,1]=>[8]=>5040
[4,3,5,8,7,2,6,1]=>[5,3]=>2688
[4,6,3,8,5,7,2,1]=>[3,3,1,1]=>1120
[7,5,3,8,6,2,4,1]=>[4,3,1]=>3360
[2,6,8,3,7,4,5,1]=>[6,2]=>3360
[1,8,4,3,7,5,6,2]=>[3,2,2,1]=>1680
[2,5,8,3,7,4,6,1]=>[8]=>5040
[7,4,3,8,6,2,5,1]=>[7,1]=>5760
[3,5,4,8,7,2,6,1]=>[4,4]=>1260
[4,5,3,8,6,7,2,1]=>[4,3,1]=>3360
[3,6,7,8,4,5,2,1]=>[8]=>5040
[2,6,8,5,4,7,3,1]=>[6,2]=>3360
[1,8,5,6,4,7,3,2]=>[5,2,1]=>4032
[2,5,8,6,4,7,3,1]=>[8]=>5040
[7,4,6,5,8,3,2,1]=>[6,2]=>3360
[6,3,7,8,4,5,2,1]=>[5,3]=>2688
[4,3,7,8,5,6,2,1]=>[3,3,1,1]=>1120
[5,2,8,6,4,7,3,1]=>[7,1]=>5760
[4,2,8,6,5,7,3,1]=>[6,1,1]=>3360
[3,2,8,6,7,4,5,1]=>[3,2,2,1]=>1680
[2,3,8,7,5,4,6,1]=>[4,3,1]=>3360
[1,8,2,7,4,5,6,3]=>[4,3,1]=>3360
[7,2,8,6,3,4,5,1]=>[5,2,1]=>4032
[6,2,8,4,5,7,3,1]=>[5,1,1,1]=>1344
[5,2,8,4,6,7,3,1]=>[6,1,1]=>3360
[4,2,8,5,6,7,3,1]=>[7,1]=>5760
[4,3,6,8,5,7,2,1]=>[4,3,1]=>3360
[3,4,6,8,7,2,5,1]=>[6,2]=>3360
[7,3,5,8,6,2,4,1]=>[4,4]=>1260
[1,8,3,5,7,4,6,2]=>[4,2,1,1]=>2520
[2,7,8,4,5,6,3,1]=>[5,1,1,1]=>1344
[3,7,5,8,4,6,2,1]=>[5,2,1]=>4032
[5,7,4,6,8,3,2,1]=>[3,3,2]=>1120
[3,6,5,8,4,7,2,1]=>[5,3]=>2688
[2,6,8,4,5,7,3,1]=>[6,1,1]=>3360
[4,2,7,1,3,8,5,6]=>[3,2,2,1]=>1680
[5,3,6,1,7,2,4,8]=>[4,3,1]=>3360
[7,5,1,2,4,8,6,3]=>[5,3]=>2688
[4,7,5,2,8,1,3,6]=>[8]=>5040
[8,5,7,1,2,4,6,3]=>[6,2]=>3360
[3,8,5,6,1,2,4,7]=>[5,3]=>2688
[3,7,2,4,8,1,6,5]=>[5,2,1]=>4032
[5,1,2,8,6,3,4,7]=>[5,3]=>2688
[6,1,7,5,2,3,4,8]=>[7,1]=>5760
[6,8,1,3,7,4,5,2]=>[4,2,2]=>1260
[4,7,8,2,5,1,3,6]=>[7,1]=>5760
[3,8,7,1,2,4,6,5]=>[5,3]=>2688
[4,8,7,1,2,3,6,5]=>[3,3,2]=>1120
[5,8,7,1,2,4,6,3]=>[8]=>5040
[7,8,4,1,2,5,3,6]=>[4,4]=>1260
[7,8,1,2,6,5,3,4]=>[3,3,2]=>1120
[1,4,8,2,7,5,3,6]=>[5,2,1]=>4032
[6,1,3,4,7,2,5,8]=>[3,2,1,1,1]=>1120
[7,8,2,1,6,3,5,4]=>[8]=>5040
[6,1,2,7,5,4,3,8]=>[6,1,1]=>3360
[1,2,8,7,5,4,3,6]=>[5,1,1,1]=>1344
[5,1,7,3,6,4,8,2]=>[8]=>5040
[6,2,1,5,7,4,3,8]=>[6,1,1]=>3360
[6,2,3,7,4,1,5,8]=>[3,2,1,1,1]=>1120
[3,4,8,7,5,6,1,2]=>[6,1,1]=>3360
[2,3,8,7,4,1,5,6]=>[5,3]=>2688
[2,7,3,8,6,4,1,5]=>[4,3,1]=>3360
[1,8,3,7,6,4,5,2]=>[4,2,1,1]=>2520
[5,2,7,1,4,6,8,3]=>[3,3,1,1]=>1120
[4,6,7,5,2,1,8,3]=>[5,3]=>2688
[6,3,1,4,5,7,8,2]=>[6,1,1]=>3360
[5,3,1,4,6,2,7,8]=>[5,1,1,1]=>1344
[5,1,2,4,7,6,8,3]=>[6,1,1]=>3360
[5,7,4,1,2,6,3,8]=>[6,1,1]=>3360
[4,8,1,2,6,7,3,5]=>[8]=>5040
[4,1,7,8,2,6,3,5]=>[5,2,1]=>4032
[1,2,8,7,6,5,3,4]=>[4,2,1,1]=>2520
[3,1,2,4,6,8,7,5]=>[3,3,1,1]=>1120
[3,1,8,4,5,7,6,2]=>[4,2,1,1]=>2520
[3,2,8,5,4,7,1,6]=>[5,2,1]=>4032
[4,2,8,1,5,3,7,6]=>[3,2,1,1,1]=>1120
[4,3,8,5,7,6,1,2]=>[4,3,1]=>3360
[4,8,2,1,6,3,7,5]=>[5,2,1]=>4032
[3,8,6,5,2,7,1,4]=>[4,4]=>1260
[3,8,5,6,1,7,4,2]=>[3,3,2]=>1120
[3,5,7,8,1,2,6,4]=>[6,2]=>3360
[3,7,8,5,2,1,6,4]=>[8]=>5040
[3,7,2,8,4,1,6,5]=>[5,3]=>2688
[2,8,1,7,4,6,5,3]=>[4,3,1]=>3360
[2,8,7,5,1,6,4,3]=>[7,1]=>5760
[2,8,6,7,5,1,4,3]=>[5,2,1]=>4032
[8,2,4,1,7,3,5,6]=>[5,2,1]=>4032
[3,6,1,4,2,8,7,5]=>[4,2,1,1]=>2520
[6,1,7,4,3,8,2,5]=>[7,1]=>5760
[4,8,2,3,1,5,7,6]=>[7,1]=>5760
[2,7,4,1,8,3,5,6]=>[8]=>5040
[1,7,8,4,2,3,6,5]=>[6,1,1]=>3360
[4,7,1,3,8,2,6,5]=>[3,3,2]=>1120
[8,7,1,3,4,2,6,5]=>[5,3]=>2688
[2,4,3,7,5,8,1,6]=>[4,2,1,1]=>2520
[6,4,1,3,7,2,8,5]=>[5,3]=>2688
[8,1,4,3,6,2,7,5]=>[5,2,1]=>4032
[7,2,5,8,4,3,1,6]=>[5,2,1]=>4032
[6,1,8,3,4,2,7,5]=>[4,3,1]=>3360
[7,3,8,1,2,6,4,5]=>[4,3,1]=>3360
[5,3,1,8,4,7,2,6]=>[8]=>5040
[4,3,8,1,5,7,2,6]=>[5,2,1]=>4032
[7,3,6,4,5,8,2,1]=>[6,1,1]=>3360
[8,7,2,4,5,1,6,3]=>[6,1,1]=>3360
[7,1,5,4,8,6,3,2]=>[6,1,1]=>3360
[2,1,8,7,5,3,6,4]=>[5,2,1]=>4032
[5,8,3,7,4,1,6,2]=>[5,2,1]=>4032
[5,7,1,4,8,6,3,2]=>[6,1,1]=>3360
[5,3,7,4,8,6,2,1]=>[3,3,1,1]=>1120
[6,5,3,7,4,8,2,1]=>[4,3,1]=>3360
[7,5,8,4,1,6,3,2]=>[6,1,1]=>3360
[2,7,8,4,5,1,6,3]=>[4,2,1,1]=>2520
[5,7,3,8,4,1,6,2]=>[7,1]=>5760
[5,6,3,8,1,4,7,2]=>[4,2,1,1]=>2520
[3,7,8,4,1,6,5,2]=>[6,1,1]=>3360
[8,7,3,1,5,4,2,6]=>[4,2,1,1]=>2520
[3,6,2,1,5,4,8,7]=>[5,2,1]=>4032
[5,4,2,6,1,3,8,7]=>[4,2,2]=>1260
[3,2,6,5,1,4,8,7]=>[5,2,1]=>4032
[2,5,8,1,7,4,3,6]=>[8]=>5040
[6,8,2,7,4,3,1,5]=>[8]=>5040
[6,8,2,3,7,5,1,4]=>[4,4]=>1260
[7,6,2,5,4,8,1,3]=>[4,2,2]=>1260
[2,6,5,1,8,4,3,7]=>[4,4]=>1260
[4,2,7,3,1,8,5,6]=>[5,2,1]=>4032
[4,2,3,7,1,5,8,6]=>[6,1,1]=>3360
[5,2,7,3,8,6,1,4]=>[6,1,1]=>3360
[2,1,5,8,4,3,7,6]=>[5,2,1]=>4032
[5,8,4,2,6,7,1,3]=>[4,4]=>1260
[3,2,4,8,1,5,7,6]=>[6,1,1]=>3360
[2,4,8,3,1,7,5,6]=>[8]=>5040
[4,8,3,2,1,7,6,5]=>[5,2,1]=>4032
[4,1,3,7,2,6,8,5]=>[6,1,1]=>3360
[3,4,8,2,1,6,5,7]=>[5,2,1]=>4032
[6,8,3,7,2,1,5,4]=>[5,2,1]=>4032
[3,5,8,1,7,2,6,4]=>[4,4]=>1260
[5,1,7,4,6,8,3,2]=>[5,2,1]=>4032
[7,6,4,8,1,5,3,2]=>[8]=>5040
[5,3,7,1,8,2,6,4]=>[4,4]=>1260
[2,7,6,3,8,1,4,5]=>[6,2]=>3360
[2,1,7,6,4,8,3,5]=>[4,2,2]=>1260
[2,1,5,4,8,7,3,6]=>[5,2,1]=>4032
[5,4,8,7,2,6,1,3]=>[5,2,1]=>4032
[2,4,3,8,7,1,5,6]=>[5,2,1]=>4032
[3,4,1,8,6,2,7,5]=>[5,2,1]=>4032
[3,8,5,4,2,1,7,6]=>[6,1,1]=>3360
[4,8,6,5,2,7,1,3]=>[8]=>5040
[3,2,8,7,5,4,1,6]=>[6,1,1]=>3360
[2,8,6,5,4,3,1,7]=>[4,2,2]=>1260
[5,4,2,6,3,1,8,7]=>[6,2]=>3360
[7,3,6,5,2,8,4,1]=>[8]=>5040
[7,6,2,3,4,8,5,1]=>[8]=>5040
[8,7,5,3,1,4,2,6]=>[6,2]=>3360
[7,1,5,3,8,4,6,2]=>[8]=>5040
[3,7,6,4,2,8,5,1]=>[4,3,1]=>3360
[2,1,8,7,4,3,5,6]=>[3,3,2]=>1120
[3,8,7,4,2,1,5,6]=>[7,1]=>5760
[8,5,2,6,1,7,3,4]=>[8]=>5040
[5,4,2,6,8,3,7,1]=>[4,3,1]=>3360
[6,5,2,8,1,4,3,7]=>[8]=>5040
[3,4,8,1,5,2,7,6]=>[6,1,1]=>3360
[4,8,1,2,5,3,6,7]=>[7,1]=>5760
[2,3,4,6,5,7,8,9,10,1]=>[9,1]=>403200
[5,8,7,4,6,3,2,1]=>[7,1]=>5760
[4,8,7,6,3,5,2,1]=>[8]=>5040
[3,8,7,6,5,2,4,1]=>[7,1]=>5760
[7,9,6,8,5,4,3,2,1]=>[8,1]=>45360
[5,8,4,7,6,3,2,1]=>[8]=>5040
[6,9,8,5,7,4,3,2,1]=>[9]=>40320
[6,8,5,4,7,3,2,1]=>[7,1]=>5760
[5,9,8,7,4,6,3,2,1]=>[8,1]=>45360
[3,8,7,6,2,5,4,1]=>[8]=>5040
[4,9,8,7,6,3,5,2,1]=>[9]=>40320
[4,8,7,6,3,2,5,1]=>[5,3]=>2688
[3,9,8,7,6,5,2,4,1]=>[7,2]=>25920
[3,8,7,6,5,2,1,4]=>[4,3,1]=>3360
[9,7,10,5,8,3,6,2,4,1]=>[10]=>362880
[3,5,2,4,7,6,1,8]=>[5,1,1,1]=>1344
[3,5,4,7,2,6,1,8]=>[4,2,1,1]=>2520
[3,5,4,7,6,1,2,8]=>[7,1]=>5760
[3,5,4,7,6,1,8,2]=>[8]=>5040
[3,5,7,4,6,1,8,2]=>[7,1]=>5760
[3,5,7,4,6,1,2,8]=>[6,1,1]=>3360
[3,5,7,4,6,2,1,8]=>[3,3,1,1]=>1120
[3,2,5,7,4,6,1,8]=>[5,1,1,1]=>1344
[3,5,2,7,6,4,1,8]=>[7,1]=>5760
[3,5,7,2,6,4,1,8]=>[4,3,1]=>3360
[5,3,7,6,2,4,1,8]=>[5,2,1]=>4032
[5,3,7,6,1,2,8,4]=>[6,2]=>3360
[5,3,7,6,1,4,2,8]=>[3,2,2,1]=>1680
[5,3,7,6,4,1,2,8]=>[4,3,1]=>3360
[3,5,7,2,6,1,4,8]=>[7,1]=>5760
[3,5,2,7,6,1,4,8]=>[5,2,1]=>4032
[5,3,7,6,4,1,8,2]=>[4,4]=>1260
[3,7,5,4,1,8,2,6]=>[3,2,2,1]=>1680
[3,7,5,4,1,8,6,2]=>[4,3,1]=>3360
[3,7,5,1,4,8,6,2]=>[4,4]=>1260
[3,7,5,1,4,8,2,6]=>[4,2,2]=>1260
[3,5,7,1,2,6,8,4]=>[5,2,1]=>4032
[3,5,7,2,1,6,8,4]=>[7,1]=>5760
[3,5,2,7,1,6,4,8]=>[4,2,1,1]=>2520
[3,5,7,2,1,6,4,8]=>[6,1,1]=>3360
[5,3,7,1,6,2,4,8]=>[7,1]=>5760
[3,5,7,1,4,6,8,2]=>[7,1]=>5760
[3,5,7,1,4,6,2,8]=>[6,1,1]=>3360
[3,5,7,1,4,2,6,8]=>[7,1]=>5760
[3,5,7,2,1,4,6,8]=>[7,1]=>5760
[3,5,2,7,1,4,6,8]=>[4,3,1]=>3360
[3,2,5,7,4,1,6,8]=>[6,1,1]=>3360
[3,5,2,7,4,1,6,8]=>[7,1]=>5760
[3,5,7,4,2,1,6,8]=>[4,2,1,1]=>2520
[3,5,7,4,1,2,6,8]=>[6,1,1]=>3360
[3,5,4,7,1,6,8,2]=>[7,1]=>5760
[3,5,4,7,1,2,6,8]=>[7,1]=>5760
[3,5,4,7,2,1,6,8]=>[5,2,1]=>4032
[3,5,4,2,7,1,6,8]=>[7,1]=>5760
[3,2,5,4,7,1,6,8]=>[5,1,1,1]=>1344
[3,5,4,7,2,1,8,6]=>[6,2]=>3360
[3,5,4,7,1,2,8,6]=>[8]=>5040
[5,7,6,3,1,8,4,2]=>[6,2]=>3360
[5,7,6,3,1,8,2,4]=>[4,2,2]=>1260
[3,5,7,4,1,2,8,6]=>[7,1]=>5760
[3,5,7,4,2,1,8,6]=>[5,2,1]=>4032
[3,2,5,7,4,1,8,6]=>[7,1]=>5760
[3,2,5,7,1,4,8,6]=>[4,3,1]=>3360
[3,5,2,7,1,4,8,6]=>[4,4]=>1260
[3,5,7,2,1,4,8,6]=>[8]=>5040
[3,5,7,1,4,2,8,6]=>[8]=>5040
[3,7,5,2,1,8,6,4]=>[5,3]=>2688
[3,7,2,5,1,8,6,4]=>[8]=>5040
[3,2,7,5,1,8,6,4]=>[7,1]=>5760
[3,2,7,5,1,8,4,6]=>[5,2,1]=>4032
[3,7,2,5,1,8,4,6]=>[6,2]=>3360
[3,7,5,2,1,8,4,6]=>[3,3,2]=>1120
[2,1,7,5,8,4,6,3]=>[6,2]=>3360
[1,3,4,5,6,7,9,2,8]=>[8,1]=>45360
[2,3,4,5,6,7,1,9,8]=>[7,2]=>25920
[2,1,4,5,6,7,8,9,3]=>[7,2]=>25920
[3,1,4,5,6,7,8,2,9]=>[8,1]=>45360
[5,8,3,4,1,7,6,2]=>[2,2,2,1,1]=>420
[5,8,7,2,4,1,6,3]=>[8]=>5040
[3,8,6,4,1,7,5,2]=>[5,2,1]=>4032
[4,3,5,6,8,1,7,2]=>[4,3,1]=>3360
[3,7,6,4,1,8,5,2]=>[7,1]=>5760
[3,7,4,1,8,6,5,2]=>[4,3,1]=>3360
[3,8,4,1,7,6,5,2]=>[3,2,2,1]=>1680
[3,2,7,6,1,5,4,8]=>[6,1,1]=>3360
[3,2,8,7,6,1,5,4]=>[7,1]=>5760
[5,7,8,2,4,1,6,3]=>[6,2]=>3360
[4,2,5,8,1,6,7,3]=>[5,1,1,1]=>1344
[4,2,5,8,1,7,3,6]=>[7,1]=>5760
[5,8,2,4,1,6,3,7]=>[4,2,1,1]=>2520
[8,4,2,6,5,1,3,7]=>[7,1]=>5760
[3,2,6,8,1,5,4,7]=>[4,3,1]=>3360
[8,3,2,5,6,1,4,7]=>[6,2]=>3360
[3,2,8,6,7,1,5,4]=>[5,2,1]=>4032
[3,2,6,8,7,1,5,4]=>[3,2,2,1]=>1680
[3,2,6,7,1,5,4,8]=>[4,2,1,1]=>2520
[8,7,3,2,5,6,1,4]=>[5,1,1,1]=>1344
[7,2,8,1,5,3,6,4]=>[6,1,1]=>3360
[8,4,2,7,5,1,3,6]=>[4,3,1]=>3360
[7,4,2,8,5,1,3,6]=>[7,1]=>5760
[7,2,4,1,8,3,6,5]=>[5,2,1]=>4032
[3,2,8,5,7,1,4,6]=>[4,3,1]=>3360
[2,6,5,7,1,8,3,4]=>[8]=>5040
[2,5,1,8,7,4,3,6]=>[5,3]=>2688
[8,1,4,6,3,5,2,7]=>[4,4]=>1260
[8,3,5,4,1,6,2,7]=>[6,1,1]=>3360
[8,6,3,4,1,5,2,7]=>[6,1,1]=>3360
[5,4,7,6,8,2,3,1]=>[3,3,2]=>1120
[4,1,8,2,3,7,6,5]=>[3,3,2]=>1120
[2,1,8,5,3,4,7,6]=>[5,2,1]=>4032
[5,2,4,6,8,7,3,1]=>[4,3,1]=>3360
[1,6,8,3,4,5,7,2]=>[6,1,1]=>3360
[5,7,4,8,6,1,3,2]=>[5,3]=>2688
[5,4,2,6,7,8,1,3]=>[5,3]=>2688
[6,4,2,7,3,5,8,1]=>[8]=>5040
[7,4,1,8,3,5,6,2]=>[5,3]=>2688
[6,5,4,8,7,3,1,2]=>[8]=>5040
[8,7,4,2,1,3,6,5]=>[5,3]=>2688
[8,7,1,3,2,5,6,4]=>[4,4]=>1260
[6,8,2,3,1,7,5,4]=>[4,4]=>1260
[7,4,3,2,6,8,5,1]=>[5,2,1]=>4032
[2,7,4,3,8,5,6,1]=>[6,2]=>3360
[8,3,7,2,1,5,6,4]=>[8]=>5040
[5,7,8,2,4,3,1,6]=>[5,3]=>2688
[8,4,7,3,2,6,1,5]=>[7,1]=>5760
[8,3,1,6,7,4,2,5]=>[6,2]=>3360
[3,2,5,7,4,8,1,6]=>[5,2,1]=>4032
[8,2,7,3,4,1,5,6]=>[4,3,1]=>3360
[7,1,6,3,5,8,2,4]=>[4,3,1]=>3360
[2,8,5,6,7,1,4,3]=>[8]=>5040
[1,5,2,7,8,6,4,3]=>[4,2,1,1]=>2520
[2,6,8,5,1,4,7,3]=>[5,2,1]=>4032
[1,4,2,8,6,5,7,3]=>[4,2,1,1]=>2520
[3,5,1,6,8,7,2,4]=>[6,2]=>3360
[5,7,6,2,1,3,8,4]=>[4,2,2]=>1260
[2,5,8,7,4,1,6,3]=>[6,2]=>3360
[4,1,7,5,2,6,8,3]=>[4,3,1]=>3360
[7,6,2,4,5,1,8,3]=>[6,1,1]=>3360
[7,3,4,2,5,8,6,1]=>[4,3,1]=>3360
[8,7,4,2,5,1,6,3]=>[7,1]=>5760
[8,1,4,5,2,6,7,3]=>[6,1,1]=>3360
[5,2,4,8,6,7,1,3]=>[4,3,1]=>3360
[8,5,6,2,1,3,7,4]=>[5,2,1]=>4032
[4,2,1,5,6,7,8,3]=>[7,1]=>5760
[3,4,6,5,1,7,8,2]=>[8]=>5040
[7,3,5,2,4,6,1,8]=>[4,2,1,1]=>2520
[5,3,7,2,4,6,1,8]=>[6,1,1]=>3360
[3,7,5,2,4,6,1,8]=>[6,1,1]=>3360
[5,7,3,2,4,6,1,8]=>[5,1,1,1]=>1344
[1,5,3,2,4,7,6,8]=>[3,2,1,1,1]=>1120
[1,5,3,2,7,4,6,8]=>[5,1,1,1]=>1344
[5,7,3,2,1,4,6,8]=>[4,2,1,1]=>2520
[5,7,3,2,4,1,6,8]=>[6,1,1]=>3360
[3,7,2,5,4,1,6,8]=>[5,2,1]=>4032
[5,1,3,2,4,7,6,8]=>[4,2,1,1]=>2520
[5,1,3,2,7,4,6,8]=>[6,1,1]=>3360
[7,1,3,2,5,4,6,8]=>[5,1,1,1]=>1344
[1,7,3,2,5,4,6,8]=>[4,1,1,1,1]=>420
[7,1,3,5,2,4,6,8]=>[6,1,1]=>3360
[5,1,3,7,2,4,6,8]=>[3,3,1,1]=>1120
[3,2,7,5,1,4,6,8]=>[6,1,1]=>3360
[3,7,5,1,2,4,6,8]=>[7,1]=>5760
[5,7,3,1,2,4,6,8]=>[6,1,1]=>3360
[1,5,3,7,2,4,6,8]=>[3,2,1,1,1]=>1120
[5,3,2,7,4,1,6,8]=>[5,2,1]=>4032
[5,3,2,4,7,1,6,8]=>[4,2,1,1]=>2520
[5,3,2,1,4,7,6,8]=>[3,2,2,1]=>1680
[5,3,2,1,7,4,6,8]=>[5,2,1]=>4032
[1,3,2,7,5,4,6,8]=>[3,2,1,1,1]=>1120
[1,3,7,2,5,4,6,8]=>[5,1,1,1]=>1344
[7,3,1,2,5,4,6,8]=>[6,1,1]=>3360
[5,3,1,2,7,4,6,8]=>[7,1]=>5760
[5,3,1,2,4,7,6,8]=>[5,2,1]=>4032
[3,2,5,1,4,7,6,8]=>[4,2,1,1]=>2520
[7,3,1,5,2,4,6,8]=>[7,1]=>5760
[1,3,7,5,2,4,6,8]=>[6,1,1]=>3360
[7,5,1,3,2,4,6,8]=>[5,2,1]=>4032
[5,7,1,3,2,4,6,8]=>[7,1]=>5760
[3,7,1,5,2,4,6,8]=>[5,2,1]=>4032
[3,7,1,2,5,4,6,8]=>[4,2,1,1]=>2520
[3,7,2,1,5,4,6,8]=>[6,1,1]=>3360
[3,2,1,7,5,4,6,8]=>[3,2,1,1,1]=>1120
[3,1,2,7,5,4,6,8]=>[3,3,1,1]=>1120
[3,1,7,2,5,4,6,8]=>[6,1,1]=>3360
[3,1,7,5,2,4,6,8]=>[7,1]=>5760
[7,1,5,3,2,4,6,8]=>[7,1]=>5760
[1,7,5,3,2,4,6,8]=>[6,1,1]=>3360
[1,2,3,4,5,7,9,6,8]=>[4,1,1,1,1,1]=>756
[1,2,3,4,6,9,5,7,8]=>[5,1,1,1,1]=>3024
[1,2,3,5,9,4,6,7,8]=>[6,1,1,1]=>10080
[1,2,4,9,3,5,6,7,8]=>[7,1,1]=>25920
[1,3,9,2,4,5,6,7,8]=>[8,1]=>45360
[1,8,5,4,2,7,6,3]=>[4,2,1,1]=>2520
[7,5,3,4,2,8,1,6]=>[2,2,2,1,1]=>420
[8,5,6,2,7,4,3,1]=>[6,2]=>3360
[1,7,2,3,6,8,5,4]=>[7,1]=>5760
[3,5,6,4,8,2,7,1]=>[6,1,1]=>3360
[3,5,1,4,8,2,7,6]=>[4,2,1,1]=>2520
[1,7,5,4,8,2,6,3]=>[3,3,1,1]=>1120
[3,7,5,1,6,4,8,2]=>[5,3]=>2688
[2,7,5,4,8,1,3,6]=>[7,1]=>5760
[2,7,5,4,8,6,1,3]=>[3,3,1,1]=>1120
[1,7,5,4,8,6,3,2]=>[5,1,1,1]=>1344
[2,5,1,4,8,7,3,6]=>[7,1]=>5760
[3,6,4,2,8,7,1,5]=>[6,2]=>3360
[3,5,2,4,8,1,6,7]=>[7,1]=>5760
[3,5,6,4,8,1,2,7]=>[4,3,1]=>3360
[1,5,6,4,8,7,2,3]=>[6,1,1]=>3360
[3,6,4,1,8,7,2,5]=>[3,3,2]=>1120
[3,6,4,5,8,7,2,1]=>[5,3]=>2688
[1,6,4,3,8,5,2,7]=>[5,2,1]=>4032
[7,1,3,4,5,8,2,6]=>[3,2,1,1,1]=>1120
[7,6,1,4,5,3,8,2]=>[6,1,1]=>3360
[7,6,1,3,5,4,8,2]=>[7,1]=>5760
[7,1,3,2,5,8,4,6]=>[4,2,1,1]=>2520
[1,6,4,2,8,5,3,7]=>[7,1]=>5760
[7,6,5,8,2,4,3,1]=>[8]=>5040
[7,6,5,8,3,1,4,2]=>[6,2]=>3360
[2,6,4,3,8,1,7,5]=>[3,2,2,1]=>1680
[2,6,4,3,8,5,7,1]=>[5,2,1]=>4032
[7,2,3,1,5,8,6,4]=>[5,1,1,1]=>1344
[7,1,5,6,3,8,4,2]=>[6,2]=>3360
[7,3,6,5,1,4,8,2]=>[8]=>5040
[7,2,6,5,3,8,1,4]=>[5,2,1]=>4032
[7,2,3,1,4,8,6,5]=>[6,1,1]=>3360
[7,2,3,5,4,8,6,1]=>[4,2,1,1]=>2520
[2,6,4,5,8,1,7,3]=>[4,3,1]=>3360
[1,5,6,4,8,3,7,2]=>[3,2,1,1,1]=>1120
[2,5,6,4,8,3,1,7]=>[5,2,1]=>4032
[3,5,6,1,4,7,8,2]=>[8]=>5040
[7,6,1,3,4,5,8,2]=>[8]=>5040
[7,1,3,2,4,8,5,6]=>[5,2,1]=>4032
[7,6,1,5,3,4,8,2]=>[8]=>5040
[7,6,1,5,4,3,8,2]=>[6,2]=>3360
[1,6,4,5,8,3,2,7]=>[7,1]=>5760
[7,6,5,8,1,3,2,4]=>[6,2]=>3360
[3,4,6,8,7,2,1,5]=>[8]=>5040
[3,5,6,8,2,1,7,4]=>[3,2,2,1]=>1680
[4,2,1,5,3,7,8,6]=>[4,3,1]=>3360
[4,2,5,6,3,1,8,7]=>[3,2,2,1]=>1680
[3,5,6,8,1,7,2,4]=>[6,2]=>3360
[4,1,5,6,3,2,8,7]=>[4,2,2]=>1260
[4,5,3,1,7,2,8,6]=>[5,2,1]=>4032
[4,1,3,5,2,7,8,6]=>[4,3,1]=>3360
[2,5,4,7,3,8,6,1]=>[8]=>5040
[3,5,7,1,8,4,2,6]=>[8]=>5040
[4,1,5,3,2,7,8,6]=>[5,3]=>2688
[4,5,3,7,1,2,8,6]=>[7,1]=>5760
[4,3,6,1,2,7,5,8]=>[5,2,1]=>4032
[5,1,3,2,4,6,7,8]=>[4,1,1,1,1]=>420
[3,6,1,7,4,5,2,8]=>[5,2,1]=>4032
[5,1,3,4,2,6,7,8]=>[3,1,1,1,1,1]=>112
[5,3,1,4,2,6,7,8]=>[4,1,1,1,1]=>420
[4,5,2,3,7,1,8,6]=>[8]=>5040
[4,2,6,1,3,7,5,8]=>[4,2,1,1]=>2520
[4,6,2,1,3,7,5,8]=>[5,2,1]=>4032
[3,6,2,1,7,4,8,5]=>[5,3]=>2688
[3,1,4,7,6,5,2,8]=>[5,2,1]=>4032
[3,6,2,7,1,5,8,4]=>[5,3]=>2688
[4,6,2,7,1,3,5,8]=>[4,3,1]=>3360
[3,5,7,1,8,2,6,4]=>[8]=>5040
[5,1,4,2,3,6,7,8]=>[5,1,1,1]=>1344
[3,6,1,7,2,5,8,4]=>[3,3,2]=>1120
[2,6,5,3,4,7,8,1]=>[5,3]=>2688
[3,6,1,7,5,4,2,8]=>[4,2,1,1]=>2520
[5,1,4,3,2,6,7,8]=>[3,2,1,1,1]=>1120
[5,4,1,3,2,6,7,8]=>[5,1,1,1]=>1344
[6,2,4,5,1,8,3,7]=>[7,1]=>5760
[2,1,4,8,6,3,7,5]=>[5,2,1]=>4032
[6,4,8,2,5,3,7,1]=>[4,2,1,1]=>2520
[8,6,2,4,7,5,1,3]=>[7,1]=>5760
[4,6,8,2,3,5,7,1]=>[7,1]=>5760
[2,6,8,1,4,5,7,3]=>[5,2,1]=>4032
[8,4,2,6,7,3,1,5]=>[4,4]=>1260
[7,6,4,5,1,3,8,2]=>[8]=>5040
[1,6,7,5,3,4,8,2]=>[7,1]=>5760
[7,6,2,3,8,4,1,5]=>[4,2,2]=>1260
[1,6,7,5,8,2,3,4]=>[3,2,2,1]=>1680
[6,2,5,8,3,4,7,1]=>[4,2,1,1]=>2520
[6,2,3,8,7,4,1,5]=>[6,1,1]=>3360
[2,4,7,3,5,8,6,1]=>[7,1]=>5760
[2,5,3,7,1,8,4,6]=>[3,2,2,1]=>1680
[5,2,8,3,1,4,6,7]=>[5,2,1]=>4032
[4,8,2,3,6,5,7,1]=>[5,2,1]=>4032
[5,8,1,3,6,4,7,2]=>[5,2,1]=>4032
[5,8,1,4,3,6,2,7]=>[3,3,1,1]=>1120
[5,8,4,1,3,7,6,2]=>[4,2,2]=>1260
[6,4,5,3,8,1,7,2]=>[5,2,1]=>4032
[4,6,5,3,7,1,2,8]=>[7,1]=>5760
[4,5,1,3,6,2,8,7]=>[3,3,2]=>1120
[4,2,6,5,1,7,3,8]=>[3,3,1,1]=>1120
[4,3,5,7,2,1,6,8]=>[4,3,1]=>3360
[3,4,7,6,8,1,2,5]=>[6,2]=>3360
[3,4,6,2,5,8,7,1]=>[4,2,1,1]=>2520
[3,5,2,4,6,1,8,7]=>[5,2,1]=>4032
[4,2,5,1,6,8,3,7]=>[5,2,1]=>4032
[1,8,2,3,6,5,7,4]=>[4,2,1,1]=>2520
[4,2,8,3,5,7,1,6]=>[6,1,1]=>3360
[4,3,8,6,5,7,1,2]=>[4,3,1]=>3360
[1,3,7,2,6,5,8,4]=>[5,2,1]=>4032
[1,3,6,4,2,5,8,7]=>[4,2,1,1]=>2520
[1,5,4,7,3,6,8,2]=>[6,1,1]=>3360
[5,2,3,8,4,1,7,6]=>[5,1,1,1]=>1344
[7,5,3,4,8,2,1,6]=>[4,2,1,1]=>2520
[7,2,8,3,4,1,5,6]=>[7,1]=>5760
[7,4,3,8,5,2,6,1]=>[6,1,1]=>3360
[4,6,2,7,3,1,5,8]=>[7,1]=>5760
[7,6,3,8,2,4,5,1]=>[7,1]=>5760
[7,2,8,5,1,3,4,6]=>[4,3,1]=>3360
[1,5,3,7,6,8,4,2]=>[4,2,1,1]=>2520
[1,6,3,7,8,2,4,5]=>[2,2,2,1,1]=>420
[1,4,3,7,8,5,2,6]=>[3,3,1,1]=>1120
[4,2,6,5,7,8,3,1]=>[7,1]=>5760
[4,2,6,7,5,8,1,3]=>[3,3,1,1]=>1120
[3,2,4,7,8,5,1,6]=>[4,3,1]=>3360
[3,2,6,7,8,1,4,5]=>[3,2,2,1]=>1680
[5,1,8,3,6,4,7,2]=>[7,1]=>5760
[3,8,5,6,1,7,2,4]=>[5,3]=>2688
[3,4,8,1,7,6,2,5]=>[7,1]=>5760
[6,7,4,8,5,1,3,2]=>[5,2,1]=>4032
[6,4,8,3,1,7,5,2]=>[4,4]=>1260
[5,7,4,8,2,6,3,1]=>[7,1]=>5760
[5,6,4,8,2,7,3,1]=>[8]=>5040
[5,6,8,3,1,7,4,2]=>[6,2]=>3360
[5,3,8,1,7,2,6,4]=>[8]=>5040
[6,5,3,8,2,7,4,1]=>[5,2,1]=>4032
[6,4,8,1,3,7,5,2]=>[8]=>5040
[7,6,3,1,4,2,5,8]=>[4,2,1,1]=>2520
[1,5,4,3,7,8,2,6]=>[3,2,2,1]=>1680
[7,8,4,2,5,3,1,6]=>[5,2,1]=>4032
[4,2,7,8,5,3,1,6]=>[6,1,1]=>3360
[4,2,5,3,1,7,8,6]=>[4,3,1]=>3360
[4,2,8,7,6,3,1,5]=>[4,3,1]=>3360
[4,2,7,6,3,1,5,8]=>[3,3,1,1]=>1120
[6,3,1,7,5,2,4,8]=>[4,2,1,1]=>2520
[6,3,1,8,7,5,2,4]=>[6,2]=>3360
[8,6,3,1,7,5,2,4]=>[4,3,1]=>3360
[4,2,7,6,3,1,8,5]=>[4,3,1]=>3360
[7,6,3,1,8,4,2,5]=>[5,2,1]=>4032
[7,6,4,2,1,8,3,5]=>[8]=>5040
[1,8,2,7,6,4,3,5]=>[7,1]=>5760
[8,3,5,7,6,4,2,1]=>[6,2]=>3360
[8,4,2,5,7,6,3,1]=>[5,2,1]=>4032
[7,5,2,4,8,6,3,1]=>[6,1,1]=>3360
[8,7,5,2,4,6,3,1]=>[5,2,1]=>4032
[7,5,2,4,6,3,1,8]=>[4,2,1,1]=>2520
[5,2,8,6,3,7,4,1]=>[4,3,1]=>3360
[8,4,7,5,2,6,3,1]=>[3,2,2,1]=>1680
[8,3,6,4,7,5,2,1]=>[5,2,1]=>4032
[1,8,2,7,5,3,6,4]=>[6,1,1]=>3360
[7,5,2,1,8,3,6,4]=>[8]=>5040
[7,5,2,6,3,1,8,4]=>[5,3]=>2688
[5,2,7,4,1,8,6,3]=>[4,2,1,1]=>2520
[5,2,8,7,4,1,6,3]=>[5,2,1]=>4032
[8,7,4,1,5,2,6,3]=>[4,3,1]=>3360
[7,4,1,5,2,8,6,3]=>[5,3]=>2688
[7,6,3,1,4,2,8,5]=>[5,2,1]=>4032
[7,5,2,8,6,3,1,4]=>[4,2,2]=>1260
[8,7,5,2,6,3,1,4]=>[5,3]=>2688
[7,5,2,1,3,6,4,8]=>[3,3,1,1]=>1120
[8,7,5,2,1,3,6,4]=>[8]=>5040
[7,5,2,1,3,8,6,4]=>[5,3]=>2688
[1,3,7,6,5,8,2,4]=>[3,3,1,1]=>1120
[8,6,4,7,5,2,1,3]=>[5,2,1]=>4032
[6,4,8,7,5,2,1,3]=>[5,2,1]=>4032
[6,4,7,5,2,1,3,8]=>[3,2,2,1]=>1680
[6,3,1,4,7,5,2,8]=>[6,1,1]=>3360
[6,3,1,4,8,7,5,2]=>[7,1]=>5760
[8,6,3,1,4,7,5,2]=>[7,1]=>5760
[8,5,7,6,3,1,4,2]=>[8]=>5040
[1,8,2,5,7,6,4,3]=>[3,3,1,1]=>1120
[1,8,2,6,4,7,5,3]=>[4,3,1]=>3360
[7,5,2,1,6,4,8,3]=>[8]=>5040
[6,3,8,7,4,1,5,2]=>[3,3,2]=>1120
[6,3,7,4,1,5,2,8]=>[3,3,1,1]=>1120
[7,4,1,6,3,5,2,8]=>[7,1]=>5760
[7,4,1,8,6,3,5,2]=>[5,3]=>2688
[8,4,6,3,1,7,5,2]=>[8]=>5040
[6,4,7,5,2,1,8,3]=>[3,3,2]=>1120
[1,6,4,7,5,3,8,2]=>[6,1,1]=>3360
[8,6,3,5,2,7,4,1]=>[5,2,1]=>4032
[6,3,5,2,8,7,4,1]=>[8]=>5040
[6,3,5,2,7,4,1,8]=>[7,1]=>5760
[1,4,7,3,5,2,6,8]=>[5,1,1,1]=>1344
[4,2,6,3,5,7,1,8]=>[5,1,1,1]=>1344
[2,4,5,8,1,6,7,3]=>[6,1,1]=>3360
[6,1,3,7,4,2,5,8]=>[3,3,1,1]=>1120
[3,2,6,8,1,5,7,4]=>[4,2,1,1]=>2520
[8,6,2,7,1,5,4,3]=>[6,2]=>3360
[7,6,8,3,1,5,4,2]=>[8]=>5040
[6,3,7,2,8,1,5,4]=>[6,2]=>3360
[7,5,2,8,6,1,4,3]=>[8]=>5040
[2,7,3,8,1,5,6,4]=>[5,2,1]=>4032
[1,6,8,5,2,4,3,7]=>[4,3,1]=>3360
[4,5,7,2,8,1,6,3]=>[8]=>5040
[8,4,6,5,3,1,7,2]=>[7,1]=>5760
[4,5,3,1,7,2,6,8]=>[4,2,1,1]=>2520
[7,8,1,2,4,3,6,5]=>[4,4]=>1260
[8,4,1,6,2,3,7,5]=>[7,1]=>5760
[6,1,3,4,2,8,5,7]=>[6,1,1]=>3360
[8,1,4,3,5,7,6,2]=>[3,2,2,1]=>1680
[5,2,4,1,3,7,8,6]=>[4,3,1]=>3360
[8,7,1,3,6,5,4,2]=>[6,2]=>3360
[1,8,5,7,4,2,6,3]=>[7,1]=>5760
[4,7,5,3,8,2,1,6]=>[8]=>5040
[6,3,5,8,7,4,1,2]=>[8]=>5040
[4,7,2,8,5,6,3,1]=>[3,3,1,1]=>1120
[1,4,8,7,3,5,6,2]=>[7,1]=>5760
[8,1,7,6,3,5,4,2]=>[5,3]=>2688
[3,6,8,5,7,4,1,2]=>[8]=>5040
[4,7,6,8,5,3,1,2]=>[5,2,1]=>4032
[3,8,7,5,6,4,2,1]=>[5,3]=>2688
[2,8,7,6,4,5,3,1]=>[3,3,2]=>1120
[1,8,7,6,5,3,4,2]=>[4,2,1,1]=>2520
[4,6,7,2,5,3,1,8]=>[6,1,1]=>3360
[2,4,7,8,1,6,5,3]=>[7,1]=>5760
[4,2,6,8,7,1,5,3]=>[5,2,1]=>4032
[5,1,8,4,2,7,6,3]=>[3,2,2,1]=>1680
[2,7,3,8,1,6,5,4]=>[4,2,1,1]=>2520
[2,6,8,4,1,7,5,3]=>[5,2,1]=>4032
[4,6,7,1,2,8,5,3]=>[6,2]=>3360
[3,6,1,8,2,7,5,4]=>[4,2,2]=>1260
[5,7,4,1,2,8,6,3]=>[8]=>5040
[6,3,7,1,2,8,5,4]=>[4,4]=>1260
[1,7,8,5,4,3,2,6]=>[3,2,2,1]=>1680
[1,2,6,7,8,4,3,5]=>[4,2,1,1]=>2520
[8,1,4,6,7,3,5,2]=>[3,3,2]=>1120
[4,7,1,3,6,8,2,5]=>[3,3,2]=>1120
[3,7,5,4,2,1,8,6]=>[7,1]=>5760
[1,3,6,7,4,2,8,5]=>[4,3,1]=>3360
[3,6,4,8,2,7,5,1]=>[4,4]=>1260
[8,1,6,7,5,3,2,4]=>[5,2,1]=>4032
[8,7,2,4,6,5,3,1]=>[3,2,2,1]=>1680
[8,7,2,5,4,6,1,3]=>[5,2,1]=>4032
[8,7,3,2,1,5,6,4]=>[7,1]=>5760
[3,7,8,2,1,6,5,4]=>[7,1]=>5760
[8,7,6,1,4,5,3,2]=>[8]=>5040
[1,8,5,4,6,2,3,7]=>[6,1,1]=>3360
[1,8,5,4,6,3,2,7]=>[3,3,1,1]=>1120
[3,6,4,2,7,8,5,1]=>[6,2]=>3360
[3,5,8,4,7,1,6,2]=>[7,1]=>5760
[1,5,8,4,7,3,6,2]=>[6,1,1]=>3360
[1,6,4,3,7,8,5,2]=>[3,2,2,1]=>1680
[2,6,4,3,7,1,8,5]=>[3,3,2]=>1120
[2,6,4,1,7,8,3,5]=>[8]=>5040
[7,2,3,4,8,6,5,1]=>[4,1,1,1,1]=>420
[7,2,3,1,8,6,4,5]=>[3,2,1,1,1]=>1120
[7,2,3,8,1,6,5,4]=>[3,2,1,1,1]=>1120
[1,5,8,4,7,6,2,3]=>[3,2,1,1,1]=>1120
[7,1,3,2,5,6,8,4]=>[5,1,1,1]=>1344
[7,6,1,8,5,4,2,3]=>[7,1]=>5760
[3,2,6,5,8,4,7,1]=>[6,1,1]=>3360
[4,3,7,1,6,5,8,2]=>[4,2,2]=>1260
[5,2,6,4,8,3,7,1]=>[3,2,1,1,1]=>1120
[5,2,6,4,8,1,7,3]=>[5,1,1,1]=>1344
[4,3,7,5,8,2,6,1]=>[4,4]=>1260
[5,3,7,4,8,2,6,1]=>[4,3,1]=>3360
[5,3,7,4,8,1,6,2]=>[7,1]=>5760
[4,3,7,1,5,2,8,6]=>[5,2,1]=>4032
[4,3,7,1,6,2,8,5]=>[6,2]=>3360
[5,4,8,2,6,3,7,1]=>[5,2,1]=>4032
[5,4,8,1,6,3,7,2]=>[7,1]=>5760
[4,1,7,5,2,3,6,8]=>[4,3,1]=>3360
[4,1,7,8,6,3,2,5]=>[8]=>5040
[1,2,6,8,3,7,4,5]=>[6,1,1]=>3360
[6,8,3,2,1,4,7,5]=>[6,1,1]=>3360
[7,2,4,1,6,5,8,3]=>[5,2,1]=>4032
[7,5,8,4,3,1,6,2]=>[4,3,1]=>3360
[6,8,2,4,1,3,7,5]=>[6,1,1]=>3360
[2,8,4,7,6,3,5,1]=>[5,3]=>2688
[4,2,7,3,8,5,6,1]=>[7,1]=>5760
[4,5,2,6,8,3,7,1]=>[7,1]=>5760
[4,8,3,2,5,7,6,1]=>[4,2,1,1]=>2520
[6,8,5,3,4,7,2,1]=>[5,3]=>2688
[6,8,4,1,5,3,7,2]=>[4,2,1,1]=>2520
[6,8,3,5,1,4,7,2]=>[4,2,1,1]=>2520
[6,8,5,4,2,3,7,1]=>[6,1,1]=>3360
[5,8,2,4,3,7,6,1]=>[5,2,1]=>4032
[8,1,3,2,5,6,4,7]=>[5,1,1,1]=>1344
[8,1,2,4,5,3,7,6]=>[5,1,1,1]=>1344
[10,1,3,2,5,4,7,6,9,8]=>[6,1,1,1,1]=>25200
[10,1,2,3,4,6,7,8,9,5]=>[6,1,1,1,1]=>25200
[6,5,3,8,4,2,7,1]=>[6,1,1]=>3360
[7,4,5,1,6,2,8,3]=>[8]=>5040
[4,7,3,5,6,2,8,1]=>[7,1]=>5760
[6,7,8,4,1,3,5,2]=>[7,1]=>5760
[3,1,6,8,4,7,5,2]=>[8]=>5040
[8,3,6,1,5,7,4,2]=>[7,1]=>5760
[3,2,7,5,8,6,1,4]=>[3,3,1,1]=>1120
[2,5,4,7,8,1,6,3]=>[8]=>5040
[2,4,6,7,8,1,5,3]=>[8]=>5040
[2,4,6,8,1,7,5,3]=>[8]=>5040
[7,4,3,8,6,2,1,5]=>[5,2,1]=>4032
[2,4,7,8,3,5,6,1]=>[4,4]=>1260
[3,2,7,6,1,8,4,5]=>[7,1]=>5760
[3,2,6,8,1,7,4,5]=>[7,1]=>5760
[4,3,6,2,1,8,5,7]=>[8]=>5040
[4,6,2,3,7,5,8,1]=>[8]=>5040
[5,8,4,2,3,6,7,1]=>[6,1,1]=>3360
[8,4,5,3,2,1,7,6]=>[4,3,1]=>3360
[5,8,3,4,2,1,7,6]=>[5,1,1,1]=>1344
[6,8,4,2,3,7,5,1]=>[8]=>5040
[6,4,8,3,2,7,1,5]=>[5,3]=>2688
[5,8,3,7,2,1,6,4]=>[7,1]=>5760
[2,5,6,4,7,1,8,3]=>[7,1]=>5760
[6,4,7,3,8,2,1,5]=>[6,2]=>3360
[1,2,6,5,8,7,3,4]=>[3,3,1,1]=>1120
[1,5,2,8,4,6,7,3]=>[5,1,1,1]=>1344
[5,1,2,7,3,6,8,4]=>[4,3,1]=>3360
[5,1,2,8,3,6,7,4]=>[4,2,1,1]=>2520
[5,6,3,4,8,7,2,1]=>[3,3,1,1]=>1120
[6,5,3,4,8,7,2,1]=>[6,1,1]=>3360
[4,1,2,8,3,6,7,5]=>[6,1,1]=>3360
[4,1,2,7,3,6,8,5]=>[7,1]=>5760
[7,5,3,8,4,6,2,1]=>[6,1,1]=>3360
[8,5,3,7,4,6,2,1]=>[4,2,1,1]=>2520
[5,8,1,2,3,4,7,6]=>[4,3,1]=>3360
[7,1,2,8,3,6,4,5]=>[7,1]=>5760
[6,1,8,2,3,5,7,4]=>[7,1]=>5760
[6,1,7,2,3,5,8,4]=>[8]=>5040
[1,6,8,2,4,5,7,3]=>[4,2,1,1]=>2520
[4,3,8,7,5,6,2,1]=>[6,1,1]=>3360
[1,8,2,7,4,6,5,3]=>[3,3,1,1]=>1120
[7,1,6,2,3,5,8,4]=>[5,3]=>2688
[8,1,6,2,3,5,7,4]=>[4,3,1]=>3360
[8,1,7,2,3,5,6,4]=>[4,4]=>1260
[5,8,3,7,4,6,2,1]=>[6,1,1]=>3360
[6,8,7,3,4,5,2,1]=>[8]=>5040
[1,8,7,2,4,5,3,6]=>[5,2,1]=>4032
[8,7,1,2,3,4,6,5]=>[4,4]=>1260
[8,6,1,2,3,4,7,5]=>[4,3,1]=>3360
[8,1,6,2,3,5,4,7]=>[5,3]=>2688
[1,7,6,2,4,5,3,8]=>[6,1,1]=>3360
[1,8,7,4,6,3,5,2]=>[4,2,1,1]=>2520
[1,8,3,5,7,2,6,4]=>[6,1,1]=>3360
[2,3,4,6,8,5,7,1]=>[7,1]=>5760
[2,3,5,7,4,8,6,1]=>[8]=>5040
[2,4,6,3,7,8,5,1]=>[6,2]=>3360
[2,5,7,1,8,6,3,4]=>[5,2,1]=>4032
[8,2,4,5,1,3,7,6]=>[6,1,1]=>3360
[2,6,7,1,8,4,5,3]=>[4,4]=>1260
[5,8,3,1,4,2,6,7]=>[4,3,1]=>3360
[3,8,4,2,6,7,1,5]=>[8]=>5040
[2,4,1,8,5,6,3,7]=>[6,1,1]=>3360
[1,6,2,7,8,5,3,4]=>[7,1]=>5760
[3,5,2,6,7,8,4,1]=>[8]=>5040
[4,5,1,6,7,3,8,2]=>[4,4]=>1260
[2,8,4,1,7,5,3,6]=>[8]=>5040
[8,5,3,1,7,4,2,6]=>[4,3,1]=>3360
[4,2,8,7,1,5,3,6]=>[7,1]=>5760
[5,2,6,8,1,7,4,3]=>[5,2,1]=>4032
[5,7,3,2,6,8,1,4]=>[7,1]=>5760
[8,4,7,3,1,6,2,5]=>[4,3,1]=>3360
[6,7,1,2,3,5,8,4]=>[4,4]=>1260
[3,1,6,7,8,4,2,5]=>[6,2]=>3360
[3,1,4,8,5,6,2,7]=>[6,1,1]=>3360
[8,3,1,4,5,7,2,6]=>[6,1,1]=>3360
[1,6,7,8,9,2,3,4,5]=>[2,2,2,2,1]=>945
[6,7,8,9,1,2,3,4,5,10]=>[9,1]=>403200
[6,7,8,1,2,3,4,5,9]=>[8,1]=>45360
[1,7,8,9,2,3,4,5,6]=>[8,1]=>45360
[1,7,8,9,10,2,3,4,5,6]=>[9,1]=>403200
[6,7,8,9,10,1,2,3,4,5,11]=>[2,2,2,2,2,1]=>10395
[5,6,7,8,9,1,2,3,4,10]=>[9,1]=>403200
[5,6,7,1,8,2,3,4,9]=>[4,2,2,1]=>11340
[4,6,7,8,1,2,3,5,9]=>[4,2,2,1]=>11340
[1,6,7,8,2,9,3,4,5]=>[4,2,2,1]=>11340
[1,5,7,8,9,2,3,4,6]=>[4,2,2,1]=>11340
[1,6,7,8,9,10,2,3,4,5]=>[9,1]=>403200
[1,7,8,9,10,11,2,3,4,5,6]=>[2,2,2,2,2,1]=>10395
[8,6,2,3,5,1,4,7]=>[7,1]=>5760
[8,2,4,5,7,3,1,6]=>[7,1]=>5760
[2,6,3,8,7,5,4,1]=>[7,1]=>5760
[8,2,3,7,5,4,1,6]=>[5,1,1,1]=>1344
[8,2,6,3,5,4,1,7]=>[3,3,1,1]=>1120
[8,6,1,5,2,4,3,7]=>[4,4]=>1260
[8,6,2,4,1,5,3,7]=>[7,1]=>5760
[8,4,1,6,5,3,2,7]=>[7,1]=>5760
[8,3,6,1,5,4,2,7]=>[7,1]=>5760
[8,3,2,6,5,4,1,7]=>[3,2,2,1]=>1680
[8,3,2,5,7,4,1,6]=>[6,2]=>3360
[8,3,1,7,5,4,2,6]=>[7,1]=>5760
[8,2,7,4,1,5,3,6]=>[4,2,1,1]=>2520
[6,1,3,8,7,5,4,2]=>[7,1]=>5760
[3,6,1,8,7,5,4,2]=>[6,2]=>3360
[3,8,1,5,7,6,4,2]=>[3,2,2,1]=>1680
[3,5,2,8,7,6,4,1]=>[7,1]=>5760
[3,4,8,2,7,6,5,1]=>[3,2,2,1]=>1680
[3,4,8,7,1,6,5,2]=>[7,1]=>5760
[8,1,3,5,7,6,4,2]=>[3,3,1,1]=>1120
[4,1,8,5,7,6,3,2]=>[7,1]=>5760
[8,2,7,1,4,5,6,3]=>[7,1]=>5760
[8,1,7,3,4,6,2,5]=>[7,1]=>5760
[8,3,1,7,2,6,5,4]=>[7,1]=>5760
[3,8,2,4,7,6,5,1]=>[4,2,1,1]=>2520
[2,8,3,7,4,6,5,1]=>[3,3,1,1]=>1120
[8,2,3,7,1,6,5,4]=>[5,1,1,1]=>1344
[8,2,7,1,3,6,5,4]=>[3,3,1,1]=>1120
[8,1,7,2,6,4,3,5]=>[6,2]=>3360
[8,1,7,5,2,4,3,6]=>[6,2]=>3360
[8,2,3,7,4,6,1,5]=>[5,1,1,1]=>1344
[2,4,8,5,7,6,3,1]=>[7,1]=>5760
[8,2,4,3,7,6,1,5]=>[4,2,1,1]=>2520
[8,2,7,3,5,1,4,6]=>[3,3,1,1]=>1120
[8,2,7,4,3,1,5,6]=>[3,3,1,1]=>1120
[8,2,7,3,1,5,6,4]=>[7,1]=>5760
[8,2,1,5,7,6,4,3]=>[3,3,1,1]=>1120
[6,2,1,8,7,5,4,3]=>[7,1]=>5760
[6,1,8,2,7,5,4,3]=>[6,2]=>3360
[8,1,7,3,5,2,6,4]=>[7,1]=>5760
[8,1,5,2,7,6,4,3]=>[7,1]=>5760
[8,1,7,2,4,6,5,3]=>[7,1]=>5760
[8,2,4,1,7,6,5,3]=>[4,2,1,1]=>2520
[4,2,8,3,7,6,5,1]=>[4,2,1,1]=>2520
[4,8,2,1,7,6,5,3]=>[3,2,2,1]=>1680
[5,1,8,7,2,6,4,3]=>[3,2,2,1]=>1680
[5,8,1,3,7,6,2,4]=>[7,1]=>5760
[8,2,5,4,1,7,6,3]=>[4,2,1,1]=>2520
[5,1,4,8,7,6,3,2]=>[7,1]=>5760
[8,1,4,3,7,6,5,2]=>[3,2,2,1]=>1680
[4,8,1,3,7,6,5,2]=>[3,2,2,1]=>1680
[4,3,8,1,7,6,5,2]=>[3,2,2,1]=>1680
[5,8,6,3,2,1,7,4]=>[7,1]=>5760
[5,7,6,3,2,4,1,8]=>[4,3,1]=>3360
[6,5,7,2,4,3,1,8]=>[4,3,1]=>3360
[5,7,1,3,2,8,6,4]=>[8]=>5040
[5,8,1,3,2,7,4,6]=>[8]=>5040
[8,5,1,3,2,4,6,7]=>[6,2]=>3360
[7,5,8,2,1,4,3,6]=>[8]=>5040
[6,7,1,2,5,4,8,3]=>[7,1]=>5760
[6,8,1,2,5,7,4,3]=>[7,1]=>5760
[8,1,6,4,2,3,5,7]=>[5,2,1]=>4032
[1,5,4,8,2,3,7,6]=>[4,2,1,1]=>2520
[1,7,8,2,3,5,6,4]=>[7,1]=>5760
[7,5,8,2,3,1,4,6]=>[8]=>5040
[7,4,1,2,6,8,3,5]=>[3,3,2]=>1120
[6,2,8,1,5,7,3,4]=>[6,1,1]=>3360
[7,3,5,4,2,1,8,6]=>[4,3,1]=>3360
[7,3,2,8,5,6,1,4]=>[2,2,2,1,1]=>420
[1,7,4,3,6,8,5,2]=>[5,2,1]=>4032
[4,7,6,5,2,3,8,1]=>[6,2]=>3360
[4,7,6,5,1,3,8,2]=>[3,3,2]=>1120
[6,7,4,2,1,8,5,3]=>[8]=>5040
[5,4,2,1,7,3,6,8]=>[7,1]=>5760
[6,5,8,1,7,3,4,2]=>[8]=>5040
[6,5,8,2,3,7,4,1]=>[8]=>5040
[4,1,2,8,5,3,6,7]=>[7,1]=>5760
[3,5,8,2,6,1,7,4]=>[7,1]=>5760
[3,7,6,1,5,2,8,4]=>[7,1]=>5760
[1,7,6,2,5,8,4,3]=>[3,3,1,1]=>1120
[1,7,6,5,8,4,2,3]=>[5,2,1]=>4032
[3,7,6,5,8,1,2,4]=>[3,3,2]=>1120
[4,3,6,8,5,1,2,7]=>[7,1]=>5760
[2,7,6,1,8,4,3,5]=>[6,2]=>3360
[7,1,2,6,3,5,4,8]=>[7,1]=>5760
[7,2,6,3,4,5,1,8]=>[4,2,1,1]=>2520
[6,1,2,5,7,8,4,3]=>[5,3]=>2688
[4,1,2,7,8,5,3,6]=>[5,3]=>2688
[4,7,3,1,2,6,8,5]=>[4,2,1,1]=>2520
[3,7,6,1,5,8,2,4]=>[5,2,1]=>4032
[3,8,5,6,4,2,7,1]=>[7,1]=>5760
[4,2,7,5,8,3,1,6]=>[7,1]=>5760
[5,6,2,7,3,4,8,1]=>[8]=>5040
[6,1,3,8,5,4,7,2]=>[5,1,1,1]=>1344
[2,7,6,8,5,1,3,4]=>[5,2,1]=>4032
[1,5,8,6,4,2,3,7]=>[4,3,1]=>3360
[2,5,8,6,4,1,7,3]=>[5,2,1]=>4032
[1,6,2,3,5,8,7,4]=>[5,1,1,1]=>1344
[4,7,2,3,1,6,8,5]=>[7,1]=>5760
[6,7,3,1,5,4,8,2]=>[3,3,1,1]=>1120
[7,4,6,2,8,3,5,1]=>[4,2,2]=>1260
[7,3,5,1,4,8,2,6]=>[6,2]=>3360
[3,4,6,5,1,2,7,8]=>[6,1,1]=>3360
[7,5,4,3,8,6,2,1]=>[5,2,1]=>4032
[4,3,8,2,6,7,5,1]=>[5,3]=>2688
[4,3,8,2,5,7,1,6]=>[7,1]=>5760
[5,1,8,6,4,7,2,3]=>[6,2]=>3360
[4,2,6,1,5,3,8,7]=>[2,2,2,1,1]=>420
[7,5,2,3,8,1,6,4]=>[5,3]=>2688
[7,5,2,3,8,4,1,6]=>[6,2]=>3360
[4,5,1,7,6,3,8,2]=>[8]=>5040
[8,1,7,5,2,3,4,6]=>[8]=>5040
[8,6,3,1,4,2,5,7]=>[5,2,1]=>4032
[4,5,1,6,2,8,7,3]=>[5,2,1]=>4032
[6,2,7,8,3,4,5,1]=>[4,3,1]=>3360
[9,2,3,4,5,6,7,8,1]=>[2,1,1,1,1,1,1,1]=>36
[8,2,3,4,5,6,7,1,9]=>[2,1,1,1,1,1,1,1]=>36
[7,2,3,4,5,6,1,8,9]=>[2,1,1,1,1,1,1,1]=>36
[6,2,3,4,5,1,7,8,9]=>[2,1,1,1,1,1,1,1]=>36
[5,2,3,4,1,6,7,8,9]=>[2,1,1,1,1,1,1,1]=>36
[4,2,3,1,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]=>36
[1,2,4,3,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]=>36
[1,2,4,6,8,9,7,5,3]=>[4,2,1,1,1]=>7560
[1,2,4,5,3,6,7,8,9]=>[3,1,1,1,1,1,1]=>168
[1,2,4,3,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]=>45
[1,2,4,6,8,10,9,7,5,3]=>[4,4,1,1]=>56700
[1,2,4,6,8,5,7,3]=>[5,1,1,1]=>1344
[2,1,7,5,8,6,3,4]=>[3,2,2,1]=>1680
[7,3,8,4,6,5,1,2]=>[3,2,2,1]=>1680
[5,3,6,4,1,2,8,7]=>[3,2,2,1]=>1680
[3,2,4,5,1,8,6,7]=>[4,3,1]=>3360
[4,2,5,1,7,8,3,6]=>[3,2,2,1]=>1680
[2,5,4,1,3,8,6,7]=>[5,3]=>2688
[1,4,5,3,8,2,6,7]=>[7,1]=>5760
[5,1,8,2,4,3,6,7]=>[4,4]=>1260
[1,5,4,8,2,3,6,7]=>[5,2,1]=>4032
[4,8,3,1,6,7,2,5]=>[5,2,1]=>4032
[3,4,8,2,6,5,7,1]=>[3,2,2,1]=>1680
[3,6,2,4,8,7,1,5]=>[5,2,1]=>4032
[4,7,3,2,6,8,1,5]=>[4,3,1]=>3360
[7,3,4,6,8,1,2,5]=>[6,2]=>3360
[3,6,7,2,5,8,1,4]=>[4,3,1]=>3360
[1,5,6,8,3,7,2,4]=>[5,2,1]=>4032
[6,1,5,8,3,4,7,2]=>[5,2,1]=>4032
[5,6,8,1,3,4,7,2]=>[7,1]=>5760
[2,8,5,6,3,4,7,1]=>[3,2,2,1]=>1680
[6,8,1,3,5,4,7,2]=>[4,2,1,1]=>2520
[8,1,6,3,5,4,7,2]=>[3,3,1,1]=>1120
[7,1,2,5,8,4,6,3]=>[8]=>5040
[6,2,4,8,1,7,3,5]=>[7,1]=>5760
[3,1,7,8,5,4,6,2]=>[7,1]=>5760
[2,7,1,8,4,3,5,6]=>[8]=>5040
[6,7,1,8,3,2,4,5]=>[8]=>5040
[2,7,6,3,5,8,1,4]=>[4,3,1]=>3360
[2,7,5,6,8,1,3,4]=>[8]=>5040
[6,7,2,8,1,3,4,5]=>[8]=>5040
[5,1,6,8,7,2,3,4]=>[6,2]=>3360
[1,5,7,6,8,2,3,4]=>[5,2,1]=>4032
[3,8,6,7,5,1,2,4]=>[4,3,1]=>3360
[4,7,5,8,6,3,1,2]=>[5,3]=>2688
[1,6,8,3,2,5,4,7]=>[4,3,1]=>3360
[2,6,8,1,5,4,7,3]=>[4,2,1,1]=>2520
[1,5,4,7,6,2,8,3]=>[4,3,1]=>3360
[6,1,5,8,3,2,7,4]=>[3,2,2,1]=>1680
[3,1,2,4,8,5,7,6]=>[3,3,1,1]=>1120
[7,1,5,4,8,3,2,6]=>[4,3,1]=>3360
[2,7,6,4,8,1,5,3]=>[7,1]=>5760
[7,2,5,4,8,1,6,3]=>[3,3,1,1]=>1120
[1,7,2,5,3,8,6,4]=>[7,1]=>5760
[2,4,1,3,6,8,5,7,9]=>[4,4,1]=>11340
[7,2,3,8,6,1,5,4]=>[4,2,1,1]=>2520
[5,3,8,4,1,2,6,7]=>[5,2,1]=>4032
[2,4,8,3,7,1,5,6]=>[6,2]=>3360
[5,2,8,4,1,6,3,7]=>[3,2,1,1,1]=>1120
[7,6,5,2,1,8,4,3]=>[8]=>5040
[2,7,5,1,8,3,6,4]=>[8]=>5040
[5,1,8,7,4,3,6,2]=>[8]=>5040
[3,8,7,2,4,6,1,5]=>[4,3,1]=>3360
[5,7,1,3,2,4,8,6]=>[8]=>5040
[4,2,7,6,3,5,8,1]=>[7,1]=>5760
[8,4,7,6,3,5,1,2]=>[8]=>5040
[8,1,7,4,2,3,5,6]=>[7,1]=>5760
[6,5,1,3,8,7,4,2]=>[5,3]=>2688
[4,7,8,3,2,5,1,6]=>[8]=>5040
[6,1,8,5,3,7,2,4]=>[4,4]=>1260
[5,1,6,8,3,7,4,2]=>[8]=>5040
[8,6,5,1,7,4,3,2]=>[5,3]=>2688
[7,6,4,1,3,5,8,2]=>[8]=>5040
[8,2,3,7,1,4,5,6]=>[6,1,1]=>3360
[2,8,3,7,1,4,5,6]=>[7,1]=>5760
[5,6,2,7,4,3,1,8]=>[4,3,1]=>3360
[8,6,2,7,4,1,3,5]=>[8]=>5040
[3,7,8,5,2,1,4,6]=>[4,4]=>1260
[6,8,4,7,3,1,5,2]=>[4,2,2]=>1260
[4,8,6,5,1,2,7,3]=>[4,3,1]=>3360
[4,8,6,5,1,2,3,7]=>[5,3]=>2688
[3,4,5,1,7,6,8,2]=>[7,1]=>5760
[3,8,7,6,5,1,2,4]=>[7,1]=>5760
[8,4,6,7,1,2,5,3]=>[8]=>5040
[5,7,2,6,1,8,4,3]=>[6,2]=>3360
[5,7,2,6,1,3,8,4]=>[6,2]=>3360
[5,8,2,6,1,4,7,3]=>[3,2,2,1]=>1680
[3,8,7,5,6,1,4,2]=>[6,2]=>3360
[6,8,4,7,2,1,5,3]=>[6,2]=>3360
[7,4,6,5,1,3,8,2]=>[6,2]=>3360
[1,7,3,4,5,2,8,6]=>[4,1,1,1,1]=>420
[1,7,2,5,4,3,8,6]=>[5,2,1]=>4032
[2,1,5,7,4,3,8,6]=>[6,2]=>3360
[6,4,1,3,8,7,5,2]=>[8]=>5040
[2,1,7,4,6,8,3,5]=>[3,2,2,1]=>1680
[8,6,4,2,7,3,5,1]=>[4,2,2]=>1260
[2,1,8,3,5,7,6,4]=>[3,2,2,1]=>1680
[7,2,4,8,6,1,5,3]=>[4,3,1]=>3360
[2,4,1,5,6,7,8,9,10,3]=>[10]=>362880
[2,3,4,5,6,7,9,1,10,8]=>[10]=>362880
[2,3,5,1,6,7,8,9,10,4]=>[10]=>362880
[2,3,4,5,6,8,1,9,10,7]=>[10]=>362880
[2,3,4,6,1,7,8,9,10,5]=>[10]=>362880
[2,3,4,5,7,1,8,9,10,6]=>[10]=>362880
[4,1,2,5,6,7,8,9,10,3]=>[10]=>362880
[4,3,1,5,6,7,8,10,2,9]=>[10]=>362880
[2,4,1,5,6,7,8,9,10,11,3]=>[11]=>3628800
[2,6,1,5,3,7,8,9,10,4]=>[10]=>362880
[2,3,4,5,6,7,8,10,1,11,9]=>[11]=>3628800
[5,3,4,1,6,7,9,2,10,8]=>[10]=>362880
[2,3,5,1,6,7,8,9,10,11,4]=>[11]=>3628800
[2,3,8,1,6,7,4,9,10,5]=>[10]=>362880
[2,3,4,5,6,7,9,1,10,11,8]=>[11]=>3628800
[6,3,4,5,1,8,2,9,10,7]=>[10]=>362880
[2,3,4,6,1,7,8,9,10,11,5]=>[11]=>3628800
[2,3,4,10,1,7,8,9,5,6]=>[10]=>362880
[2,3,4,5,6,8,1,9,10,11,7]=>[11]=>3628800
[2,3,4,5,7,1,8,9,10,11,6]=>[11]=>3628800
[8,2,1,3,4,5,6,7,9]=>[7,1,1]=>25920
[3,2,4,5,6,7,8,1,9]=>[7,1,1]=>25920
[9,2,1,3,4,5,6,7,8,10]=>[8,1,1]=>226800
[8,3,1,2,4,5,6,7,9]=>[8,1]=>45360
[8,2,3,1,4,5,6,7,9]=>[6,1,1,1]=>10080
[4,2,3,5,6,7,8,1,9]=>[6,1,1,1]=>10080
[6,4,3,2,8,1,7,5]=>[2,2,2,1,1]=>420
[6,2,4,3,8,1,7,5]=>[2,2,2,1,1]=>420
[5,8,4,3,1,6,7,2]=>[2,2,2,1,1]=>420
[8,7,2,4,6,10,1,3,5,9]=>[5,4,1]=>181440
[2,10,7,9,4,6,8,1,3,5]=>[9,1]=>403200
[6,5,2,4,8,10,1,3,7,9]=>[5,4,1]=>181440
[2,8,5,7,4,6,10,1,3,9]=>[6,3,1]=>201600
[10,5,2,4,7,9,6,8,1,3]=>[8,1,1]=>226800
[10,9,2,8,5,7,4,6,1,3]=>[5,4,1]=>181440
[8,7,6,5,2,4,10,1,3,9]=>[8,2]=>226800
[10,7,2,6,5,9,4,8,1,3]=>[8,1,1]=>226800
[6,10,5,9,8,7,2,4,1,3]=>[10]=>362880
[4,10,3,9,2,6,8,1,5,7]=>[8,1,1]=>226800
[4,3,10,7,9,2,6,8,1,5]=>[9,1]=>403200
[3,6,2,5,4,8,10,1,7,9]=>[5,3,2]=>120960
[3,6,10,2,5,9,4,8,1,7]=>[8,1,1]=>226800
[3,5,8,2,4,7,6,10,1,9]=>[5,3,2]=>120960
[3,5,7,10,2,4,6,9,8,1]=>[6,2,2]=>75600
[10,9,3,5,8,2,4,7,6,1]=>[4,3,2,1]=>151200
[8,7,3,6,2,5,4,10,1,9]=>[5,4,1]=>181440
[7,6,3,5,10,2,4,9,8,1]=>[5,2,2,1]=>90720
[3,6,10,9,8,2,5,7,4,1]=>[3,3,2,2]=>25200
[10,9,8,7,3,6,2,5,4,1]=>[4,3,2,1]=>151200
[5,4,3,8,2,7,6,10,1,9]=>[7,2,1]=>259200
[5,4,3,7,10,2,6,9,8,1]=>[4,3,2,1]=>151200
[5,10,4,9,3,8,2,7,6,1]=>[10]=>362880
[4,8,3,7,6,5,2,10,1,9]=>[7,2,1]=>259200
[4,7,3,6,5,10,2,9,8,1]=>[4,2,2,1,1]=>56700
[4,6,10,3,5,9,8,7,2,1]=>[4,3,2,1]=>151200
[10,9,4,8,3,7,6,5,2,1]=>[4,2,2,2]=>18900
[7,6,5,4,3,10,2,9,8,1]=>[5,2,2,1]=>90720
[6,5,4,10,3,9,8,7,2,1]=>[8,2]=>226800
[5,10,4,9,8,7,6,3,2,1]=>[8,2]=>226800
[12,11,2,4,6,8,10,1,3,5,7,9]=>[11,1]=>43545600
[10,9,2,4,6,8,12,1,3,5,7,11]=>[5,3,3,1]=>5322240
[8,12,7,11,2,4,6,10,1,3,5,9]=>[12]=>39916800
[2,10,7,9,4,6,8,12,1,3,5,11]=>[11,1]=>43545600
[2,4,12,7,9,11,6,8,10,1,3,5]=>[11,1]=>43545600
[10,9,8,7,2,4,6,12,1,3,5,11]=>[9,3]=>17740800
[12,9,2,8,7,11,4,6,10,1,3,5]=>[12]=>39916800
[12,11,10,9,8,7,2,4,6,1,3,5]=>[12]=>39916800
[6,5,2,4,8,10,12,1,3,7,9,11]=>[11,1]=>43545600
[6,12,5,11,2,4,8,10,1,3,7,9]=>[12]=>39916800
[6,10,5,9,2,4,8,12,1,3,7,11]=>[4,4,4]=>1247400
[6,5,12,9,11,2,4,8,10,1,3,7]=>[11,1]=>43545600
[12,11,6,10,5,9,2,4,8,1,3,7]=>[11,1]=>43545600
[2,8,12,5,7,11,4,6,10,1,3,9]=>[9,3]=>17740800
[12,5,11,10,2,4,7,9,6,8,1,3]=>[5,4,2,1]=>11975040
[10,9,2,8,5,7,4,6,12,1,3,11]=>[5,4,2,1]=>11975040
[8,7,6,5,2,4,10,12,1,3,9,11]=>[7,5]=>13685760
[7,6,12,5,2,4,9,11,8,10,1,3]=>[5,4,2,1]=>11975040
[2,12,7,11,6,10,5,9,4,8,1,3]=>[12]=>39916800
[6,10,5,9,8,7,2,4,12,1,3,11]=>[7,5]=>13685760
[6,8,12,5,7,11,10,9,2,4,1,3]=>[4,3,3,2]=>3326400
[8,7,6,12,5,11,10,9,2,4,1,3]=>[11,1]=>43545600
[7,12,6,11,10,9,8,5,2,4,1,3]=>[7,5]=>13685760
[4,12,3,11,2,6,8,10,1,5,7,9]=>[10,1,1]=>23950080
[4,10,3,9,2,6,8,12,1,5,7,11]=>[4,3,3,1,1]=>3326400
[4,3,12,9,11,2,6,8,10,1,5,7]=>[5,4,2,1]=>11975040
[12,11,4,10,3,9,2,6,8,1,5,7]=>[9,3]=>17740800
[4,8,3,7,2,6,10,12,1,5,9,11]=>[10,1,1]=>23950080
[4,8,12,3,7,11,2,6,10,1,5,9]=>[6,6]=>6652800
[4,3,10,7,9,2,6,8,12,1,5,11]=>[7,4,1]=>17107200
[12,4,11,3,10,7,9,2,6,8,1,5]=>[9,3]=>17740800
[12,4,9,3,8,7,11,2,6,10,1,5]=>[11,1]=>43545600
[4,8,12,11,10,3,7,9,2,6,1,5]=>[5,3,3,1]=>5322240
[12,11,10,9,4,8,3,7,2,6,1,5]=>[7,5]=>13685760
[3,12,6,2,5,9,11,4,8,10,1,7]=>[10,1,1]=>23950080
[12,11,3,6,10,2,5,9,4,8,1,7]=>[11,1]=>43545600
[3,5,8,2,4,7,6,10,12,1,9,11]=>[4,3,3,2]=>3326400
[3,5,8,12,2,4,7,11,6,10,1,9]=>[4,4,2,1,1]=>3742200
[10,9,3,5,8,2,4,7,6,12,1,11]=>[4,4,3,1]=>4989600
[9,8,3,5,7,12,2,4,6,11,10,1]=>[5,4,2,1]=>11975040
[3,5,12,11,8,10,2,4,7,9,6,1]=>[9,3]=>17740800
[8,7,3,6,2,5,4,10,12,1,9,11]=>[5,3,3,1]=>5322240
[7,6,3,5,9,12,2,4,8,11,10,1]=>[5,4,2,1]=>11975040
[7,12,6,11,3,5,10,2,4,9,8,1]=>[9,3]=>17740800
[3,6,10,9,8,2,5,7,4,12,1,11]=>[5,3,2,2]=>3991680
[3,9,6,8,5,7,12,2,4,11,10,1]=>[5,4,2,1]=>11975040
[3,2,12,6,8,11,10,5,7,9,4,1]=>[3,3,3,2,1]=>1478400
[10,9,8,7,3,6,2,5,4,12,1,11]=>[4,4,3,1]=>4989600
[12,11,10,9,8,7,3,6,2,5,4,1]=>[6,4,2]=>9979200
[6,5,4,12,3,11,2,8,10,1,7,9]=>[11,1]=>43545600
[6,5,4,10,3,9,2,8,12,1,7,11]=>[11,1]=>43545600
[5,4,3,7,10,2,6,9,8,12,1,11]=>[5,4,2,1]=>11975040
[5,10,4,9,3,8,2,7,6,12,1,11]=>[12]=>39916800
[12,11,5,4,3,8,10,2,7,9,6,1]=>[4,3,2,2,1]=>4989600
[12,11,5,10,4,9,3,8,2,7,6,1]=>[5,4,2,1]=>11975040
[4,8,3,7,6,12,5,11,2,10,1,9]=>[10,1,1]=>23950080
[12,11,4,6,10,3,5,9,8,7,2,1]=>[3,3,2,2,2]=>554400
[10,9,4,8,3,7,6,5,2,12,1,11]=>[4,4,2,2]=>1871100
[9,8,4,7,3,6,5,12,2,11,10,1]=>[5,4,2,1]=>11975040
[8,7,6,5,4,3,2,10,12,1,9,11]=>[3,3,2,2,2]=>554400
[7,6,5,4,3,9,12,2,8,11,10,1]=>[4,3,2,2,1]=>4989600
[7,6,5,12,4,11,3,10,2,9,8,1]=>[6,6]=>6652800
[6,5,4,9,3,8,7,12,2,11,10,1]=>[5,4,2,1]=>11975040
[5,8,4,7,6,12,3,11,10,9,2,1]=>[4,3,3,2]=>3326400
[9,8,7,6,5,4,3,12,2,11,10,1]=>[5,2,2,2,1]=>1995840
[4,2,8,1,5,7,6,3]=>[2,2,2,1,1]=>420
[6,3,7,2,5,4,8,1]=>[7,1]=>5760
[5,4,7,3,2,6,8,1]=>[7,1]=>5760
[5,7,2,6,3,4,8,1]=>[6,2]=>3360
[3,7,5,4,6,2,8,1]=>[7,1]=>5760
[6,8,3,2,1,7,4,5]=>[7,1]=>5760
[5,4,3,7,2,8,6,1]=>[7,1]=>5760
[3,6,5,7,2,8,4,1]=>[6,2]=>3360
[4,6,5,3,8,2,1,7]=>[6,2]=>3360
[6,3,8,4,1,7,2,5]=>[7,1]=>5760
[7,2,8,1,6,4,3,5]=>[7,1]=>5760
[8,2,6,4,3,5,1,7]=>[3,3,1,1]=>1120
[5,4,2,8,6,3,7,1]=>[7,1]=>5760
[2,8,7,5,3,1,4,6]=>[4,4]=>1260
[2,5,6,3,1,4,8,7]=>[3,3,2]=>1120
[2,4,7,8,5,3,1,6]=>[7,1]=>5760
[6,5,3,2,4,1,8,7]=>[3,2,2,1]=>1680
[6,5,8,7,3,2,4,1]=>[6,2]=>3360
[2,1,4,7,8,5,3,6]=>[3,3,2]=>1120
[8,3,1,6,5,7,4,2]=>[4,3,1]=>3360
[8,5,6,7,3,1,4,2]=>[6,2]=>3360
[8,7,5,3,2,6,4,1]=>[5,2,1]=>4032
[8,5,3,1,4,6,7,2]=>[5,1,1,1]=>1344
[8,5,1,6,4,3,7,2]=>[7,1]=>5760
[6,1,4,3,7,8,2,5]=>[6,2]=>3360
[6,1,2,7,5,8,3,4]=>[7,1]=>5760
[2,7,3,1,4,6,8,5]=>[6,1,1]=>3360
[2,8,3,1,6,5,7,4]=>[4,2,1,1]=>2520
[3,8,5,6,7,1,2,4]=>[8]=>5040
[6,5,1,2,8,4,7,3]=>[7,1]=>5760
[2,5,8,1,4,6,7,3]=>[4,2,1,1]=>2520
[2,1,8,7,5,4,6,3]=>[3,2,2,1]=>1680
[7,8,3,4,1,6,5,2]=>[3,2,1,1,1]=>1120
[8,7,3,4,2,6,5,1]=>[3,2,1,1,1]=>1120
[8,4,5,2,3,7,1,6]=>[4,2,2]=>1260
[4,7,2,8,6,3,1,5]=>[8]=>5040
[4,7,5,2,3,8,1,6]=>[4,2,2]=>1260
[6,4,7,5,2,8,3,1]=>[3,3,2]=>1120
[7,5,1,3,6,4,8,2]=>[8]=>5040
[6,5,2,3,7,8,4,1]=>[5,3]=>2688
[7,2,6,3,1,5,8,4]=>[7,1]=>5760
[1,8,4,2,5,7,6,3]=>[4,2,1,1]=>2520
[1,8,5,2,4,7,6,3]=>[5,2,1]=>4032
[1,4,6,2,8,7,5,3]=>[5,2,1]=>4032
[2,1,6,8,7,5,3,4]=>[4,2,2]=>1260
[1,2,8,3,5,7,6,4]=>[3,2,1,1,1]=>1120
[2,3,8,1,5,7,6,4]=>[5,2,1]=>4032
[3,2,8,1,5,7,6,4]=>[4,2,1,1]=>2520
[2,8,1,4,5,7,6,3]=>[4,2,1,1]=>2520
[3,8,4,5,1,6,2,7]=>[4,3,1]=>3360
[5,3,8,6,2,7,1,4]=>[8]=>5040
[8,4,6,3,1,2,5,7]=>[4,4]=>1260
[6,8,1,4,5,2,3,7]=>[6,1,1]=>3360
[1,5,8,4,6,2,3,7]=>[3,3,1,1]=>1120
[2,1,6,5,3,8,4,7]=>[6,2]=>3360
[5,6,8,1,4,2,3,7]=>[3,3,2]=>1120
[5,7,4,8,1,2,3,6]=>[6,2]=>3360
[8,2,1,5,3,7,4,6]=>[7,1]=>5760
[4,7,8,1,2,6,3,5]=>[5,2,1]=>4032
[8,7,1,5,6,2,3,4]=>[8]=>5040
[1,6,5,8,7,2,3,4]=>[3,2,2,1]=>1680
[5,1,2,7,6,8,3,4]=>[8]=>5040
[6,1,7,2,5,8,3,4]=>[5,2,1]=>4032
[1,7,6,5,8,2,3,4]=>[4,3,1]=>3360
[1,6,8,5,7,2,3,4]=>[5,2,1]=>4032
[7,5,1,2,6,8,3,4]=>[5,3]=>2688
[6,1,5,2,7,8,3,4]=>[5,3]=>2688
[1,6,3,8,7,2,4,5]=>[4,2,1,1]=>2520
[1,7,3,2,4,6,8,5]=>[5,1,1,1]=>1344
[8,3,1,4,2,5,7,6]=>[6,1,1]=>3360
[3,1,2,7,8,4,6,5]=>[3,3,2]=>1120
[5,1,2,6,8,7,3,4]=>[8]=>5040
[1,8,6,2,5,7,3,4]=>[3,3,1,1]=>1120
[5,7,8,1,2,6,3,4]=>[7,1]=>5760
[8,1,5,7,6,2,3,4]=>[8]=>5040
[7,1,6,8,5,2,3,4]=>[5,2,1]=>4032
[3,7,1,2,8,4,6,5]=>[4,2,2]=>1260
[8,3,1,2,7,6,4,5]=>[7,1]=>5760
[1,5,8,7,6,2,3,4]=>[4,3,1]=>3360
[7,8,6,1,5,2,3,4]=>[7,1]=>5760
[1,9,3,4,5,6,7,8,2]=>[2,1,1,1,1,1,1,1]=>36
[9,2,3,4,5,6,7,8,1,10]=>[2,1,1,1,1,1,1,1,1]=>45
[1,9,8,4,5,6,7,3,2]=>[2,2,1,1,1,1,1]=>378
[1,10,3,4,5,6,7,8,9,2]=>[2,1,1,1,1,1,1,1,1]=>45
[1,10,9,4,5,6,7,8,3,2]=>[2,2,1,1,1,1,1,1]=>630
[7,8,6,3,1,5,2,4]=>[8]=>5040
[7,8,1,3,4,5,2,6]=>[8]=>5040
[1,7,4,8,2,5,3,6]=>[7,1]=>5760
[3,8,6,1,4,2,7,5]=>[7,1]=>5760
[7,1,8,2,4,6,3,5]=>[7,1]=>5760
[7,6,8,4,1,5,3,2]=>[7,1]=>5760
[7,3,2,8,1,5,4,6]=>[6,2]=>3360
[3,5,4,1,7,2,6,8]=>[4,3,1]=>3360
[6,4,7,3,2,5,1,8]=>[7,1]=>5760
[7,6,5,3,8,4,1,2]=>[6,2]=>3360
[6,4,5,7,8,1,3,2]=>[6,2]=>3360
[3,7,4,1,6,8,5,2]=>[5,3]=>2688
[3,1,2,7,6,8,5,4]=>[5,3]=>2688
[6,3,2,8,4,5,1,7]=>[6,2]=>3360
[6,1,8,3,5,4,2,7]=>[7,1]=>5760
[3,8,5,2,4,6,1,7]=>[7,1]=>5760
[1,6,4,8,3,5,2,7]=>[7,1]=>5760
[1,5,4,8,6,3,7,2]=>[6,1,1]=>3360
[4,8,2,5,3,7,1,6]=>[8]=>5040
[3,8,4,5,2,6,7,1]=>[6,1,1]=>3360
[4,1,8,6,5,3,7,2]=>[6,1,1]=>3360
[5,7,8,4,6,3,2,1]=>[5,2,1]=>4032
[5,3,2,8,6,4,7,1]=>[5,2,1]=>4032
[6,8,1,2,7,4,3,5]=>[8]=>5040
[5,8,7,3,6,2,4,1]=>[5,3]=>2688
[7,5,2,3,4,8,6,1]=>[4,4]=>1260
[7,3,5,4,2,8,6,1]=>[4,3,1]=>3360
[5,6,1,3,2,4,7,8]=>[6,1,1]=>3360
[2,5,1,3,7,8,6,4]=>[8]=>5040
[4,3,7,2,1,8,6,5]=>[8]=>5040
[4,6,7,2,1,3,5,8]=>[7,1]=>5760
[4,6,2,3,1,5,7,8]=>[6,1,1]=>3360
[3,6,4,2,5,1,7,8]=>[5,1,1,1]=>1344
[3,1,6,4,7,5,2,8]=>[6,1,1]=>3360
[3,6,2,7,5,4,1,8]=>[6,1,1]=>3360
[2,4,7,5,3,6,1,8]=>[6,1,1]=>3360
[2,5,7,3,4,1,6,8]=>[7,1]=>5760
[2,3,5,8,6,4,7,1]=>[7,1]=>5760
[2,4,7,3,8,6,5,1]=>[7,1]=>5760
[3,4,2,7,5,8,6,1]=>[7,1]=>5760
[3,1,5,4,7,8,6,2]=>[7,1]=>5760
[4,5,7,2,3,1,8,6]=>[8]=>5040
[3,7,8,1,4,6,5,2]=>[7,1]=>5760
[2,5,8,7,4,1,3,6]=>[8]=>5040
[2,6,4,7,5,3,8,1]=>[7,1]=>5760
[6,2,4,7,1,3,8,5]=>[7,1]=>5760
[7,3,5,1,4,2,8,6]=>[8]=>5040
[5,4,7,1,3,2,8,6]=>[8]=>5040
[6,1,4,7,5,3,8,2]=>[7,1]=>5760
[8,7,4,3,1,5,6,2]=>[6,2]=>3360
[8,7,1,4,3,5,6,2]=>[7,1]=>5760
[6,1,8,4,7,3,2,5]=>[7,1]=>5760
[4,7,3,6,1,2,8,5]=>[7,1]=>5760
[5,2,1,7,4,3,8,6]=>[7,1]=>5760
[4,7,6,2,3,1,8,5]=>[8]=>5040
[7,6,8,2,5,3,4,1]=>[7,1]=>5760
[2,3,6,1,8,7,5,4]=>[8]=>5040
[2,6,8,7,5,3,1,4]=>[7,1]=>5760
[6,4,1,7,5,2,8,3]=>[7,1]=>5760
[5,7,8,2,3,6,1,4]=>[7,1]=>5760
[4,8,7,1,2,5,6,3]=>[6,2]=>3360
[2,8,7,4,1,5,6,3]=>[7,1]=>5760
[8,6,2,1,5,7,4,3]=>[7,1]=>5760
[3,8,6,7,5,2,1,4]=>[7,1]=>5760
[6,1,3,7,5,8,2,4]=>[6,1,1]=>3360
[4,7,3,1,8,5,6,2]=>[5,2,1]=>4032
[2,6,7,5,3,4,8,1]=>[8]=>5040
[2,6,4,5,7,3,8,1]=>[8]=>5040
[6,1,4,5,8,3,7,2]=>[7,1]=>5760
[6,1,8,5,3,4,7,2]=>[7,1]=>5760
[4,1,5,6,8,3,7,2]=>[7,1]=>5760
[6,4,1,8,7,2,5,3]=>[6,2]=>3360
[8,1,2,3,4,5,6,7,10,9]=>[8,2]=>226800
[1,7,2,3,4,5,6,9,8]=>[6,2,1]=>30240
[6,9,1,2,3,4,5,7,8]=>[9]=>40320
[1,3,8,5,2,7,4,6]=>[7,1]=>5760
[1,3,8,6,7,2,4,5]=>[7,1]=>5760
[2,8,3,7,6,1,4,5]=>[5,2,1]=>4032
[4,2,7,8,6,1,3,5]=>[5,2,1]=>4032
[1,3,8,7,6,2,4,5]=>[5,2,1]=>4032
[7,4,6,8,5,2,3,1]=>[7,1]=>5760
[5,2,6,7,8,1,3,4]=>[7,1]=>5760
[3,5,8,6,1,2,7,4]=>[7,1]=>5760
[4,2,6,8,7,1,3,5]=>[7,1]=>5760
[1,4,6,8,7,2,3,5]=>[7,1]=>5760
[4,5,3,8,1,7,2,6]=>[7,1]=>5760
[3,5,8,4,1,7,2,6]=>[7,1]=>5760
[1,6,5,7,8,2,3,4]=>[5,2,1]=>4032
[6,5,4,8,1,3,7,2]=>[7,1]=>5760
[7,6,4,8,5,1,3,2]=>[7,1]=>5760
[6,3,7,5,2,4,8,1]=>[8]=>5040
[8,1,2,7,4,5,3,6]=>[8]=>5040
[2,5,7,4,6,1,3,8]=>[4,2,1,1]=>2520
[6,1,7,4,5,3,8,2]=>[6,1,1]=>3360
[8,2,7,3,1,5,4,6]=>[4,3,1]=>3360
[8,1,3,7,5,6,4,2]=>[3,2,1,1,1]=>1120
[1,2,5,3,8,6,7,4]=>[4,1,1,1,1]=>420
[4,1,6,5,7,8,2,3]=>[5,3]=>2688
[6,1,3,7,4,2,8,5]=>[4,3,1]=>3360
[6,7,2,4,1,3,8,5]=>[7,1]=>5760
[7,3,8,4,2,6,5,1]=>[6,1,1]=>3360
[8,5,3,4,2,7,1,6]=>[4,2,1,1]=>2520
[1,3,8,2,5,6,7,4]=>[4,1,1,1,1]=>420
[1,8,6,7,2,5,4,3]=>[5,2,1]=>4032
[8,7,2,4,6,1,5,3]=>[7,1]=>5760
[7,8,6,5,2,4,3,1]=>[8]=>5040
[3,6,7,5,2,8,4,1]=>[8]=>5040
[5,4,6,7,8,1,3,2]=>[8]=>5040
[5,3,6,7,8,1,4,2]=>[6,2]=>3360
[5,3,7,6,8,4,1,2]=>[6,2]=>3360
[5,4,8,6,7,2,3,1]=>[5,3]=>2688
[5,4,8,6,3,1,2,7]=>[8]=>5040
[4,5,7,3,6,2,8,1]=>[5,3]=>2688
[4,5,6,3,8,2,7,1]=>[7,1]=>5760
[5,4,8,7,2,1,3,6]=>[8]=>5040
[2,5,4,7,8,1,3,6]=>[5,3]=>2688
[5,3,6,4,8,2,7,1]=>[3,3,1,1]=>1120
[5,3,7,4,6,2,8,1]=>[7,1]=>5760
[8,2,4,7,3,5,6,1]=>[5,2,1]=>4032
[4,5,6,2,7,3,8,1]=>[6,2]=>3360
[5,4,6,2,8,3,7,1]=>[3,2,2,1]=>1680
[8,4,6,1,7,2,5,3]=>[6,2]=>3360
[5,2,1,6,3,8,7,4]=>[3,3,1,1]=>1120
[4,5,6,3,7,1,8,2]=>[4,4]=>1260
[6,3,2,8,5,4,1,7]=>[5,2,1]=>4032
[4,3,1,5,2,8,6,7]=>[5,3]=>2688
[8,5,4,1,3,2,6,7]=>[8]=>5040
[3,8,4,1,5,2,6,7]=>[4,3,1]=>3360
[2,5,4,3,8,1,6,7]=>[6,2]=>3360
[2,5,7,4,3,1,6,8]=>[6,1,1]=>3360
[5,3,4,2,7,1,6,8]=>[4,3,1]=>3360
[3,7,5,4,1,2,6,8]=>[3,3,1,1]=>1120
[4,2,5,1,3,8,7,6]=>[2,2,2,1,1]=>420
[4,3,5,1,2,7,6,8]=>[3,2,2,1]=>1680
[4,1,6,3,5,2,7,8]=>[5,1,1,1]=>1344
[4,2,1,8,6,3,7,5]=>[6,1,1]=>3360
[3,1,7,2,5,6,4,8]=>[5,1,1,1]=>1344
[3,7,5,4,2,1,6,8]=>[6,1,1]=>3360
[3,7,2,4,1,6,5,8]=>[5,1,1,1]=>1344
[7,3,2,1,6,4,5,8]=>[5,2,1]=>4032
[2,8,6,1,7,4,3,5]=>[8]=>5040
[2,5,4,6,1,3,7,8]=>[3,3,1,1]=>1120
[2,5,6,4,1,3,7,8]=>[3,2,1,1,1]=>1120
[8,5,2,6,1,3,7,4]=>[7,1]=>5760
[7,1,2,5,4,6,3,8]=>[4,2,1,1]=>2520
[2,4,1,6,5,3,7,8]=>[5,1,1,1]=>1344
[4,1,2,7,5,6,3,8]=>[5,1,1,1]=>1344
[7,1,2,6,5,4,3,8]=>[4,2,1,1]=>2520
[8,2,1,5,6,3,7,4]=>[6,1,1]=>3360
[6,1,4,5,3,2,7,8]=>[3,3,1,1]=>1120
[3,1,6,5,4,2,7,8]=>[4,2,1,1]=>2520
[3,1,4,6,5,2,7,8]=>[5,1,1,1]=>1344
[5,8,3,1,7,6,4,2]=>[4,2,1,1]=>2520
[7,6,3,2,8,5,1,4]=>[5,2,1]=>4032
[5,6,3,8,7,4,1,2]=>[4,3,1]=>3360
[5,2,6,8,7,4,1,3]=>[4,3,1]=>3360
[4,3,8,5,7,2,6,1]=>[8]=>5040
[6,3,8,5,4,1,2,7]=>[4,2,2]=>1260
[6,3,8,4,5,1,2,7]=>[4,2,1,1]=>2520
[5,2,3,1,4,8,6,7]=>[3,3,1,1]=>1120
[5,4,1,3,2,8,6,7]=>[5,3]=>2688
[5,1,3,4,2,8,6,7]=>[3,3,1,1]=>1120
[4,2,7,3,8,5,1,6]=>[4,3,1]=>3360
[4,3,7,2,8,5,6,1]=>[8]=>5040
[5,3,1,2,4,8,6,7]=>[5,3]=>2688
[5,4,3,1,2,8,6,7]=>[4,3,1]=>3360
[5,2,3,4,1,8,6,7]=>[3,2,1,1,1]=>1120
[5,1,7,3,4,6,8,2]=>[7,1]=>5760
[5,8,7,4,3,1,6,2]=>[5,2,1]=>4032
[6,8,1,3,4,5,7,2]=>[5,2,1]=>4032
[3,1,7,8,2,5,4,6]=>[8]=>5040
[6,2,3,7,4,1,8,5]=>[4,2,1,1]=>2520
[6,3,7,4,1,2,5,8]=>[6,1,1]=>3360
[3,7,2,8,6,5,1,4]=>[4,2,2]=>1260
[3,6,7,5,1,2,4,8]=>[5,2,1]=>4032
[7,4,5,1,8,2,3,6]=>[8]=>5040
[7,2,3,1,8,4,5,6]=>[6,1,1]=>3360
[2,1,4,8,3,7,5,6]=>[6,2]=>3360
[1,2,7,8,4,3,6,5]=>[3,3,1,1]=>1120
[4,8,1,3,5,6,2,7]=>[3,3,1,1]=>1120
[5,3,7,8,4,2,6,1]=>[4,4]=>1260
[6,3,7,8,2,4,5,1]=>[4,4]=>1260
[8,5,2,4,3,1,7,6]=>[3,3,1,1]=>1120
[7,5,4,2,3,1,8,6]=>[4,4]=>1260
[3,5,4,6,7,1,8,2]=>[4,4]=>1260
[1,3,2,6,4,8,7,5]=>[4,2,1,1]=>2520
[1,4,2,5,3,8,7,6]=>[4,2,1,1]=>2520
[1,6,2,5,3,8,7,4]=>[6,1,1]=>3360
[2,5,1,4,3,8,7,6]=>[4,2,1,1]=>2520
[1,7,3,5,4,8,6,2]=>[4,2,1,1]=>2520
[1,8,3,6,4,7,5,2]=>[4,2,1,1]=>2520
[1,7,2,6,4,8,5,3]=>[7,1]=>5760
[1,5,2,7,4,8,6,3]=>[7,1]=>5760
[1,4,2,8,5,7,6,3]=>[4,2,1,1]=>2520
[4,8,1,3,2,6,5,7]=>[4,3,1]=>3360
[1,5,3,8,4,7,6,2]=>[4,2,1,1]=>2520
[1,8,4,7,3,6,5,2]=>[4,2,1,1]=>2520
[2,6,3,8,1,5,4,7]=>[4,3,1]=>3360
[8,3,1,4,2,6,5,7]=>[6,1,1]=>3360
[4,8,7,3,5,2,1,6]=>[4,3,1]=>3360
[6,8,7,3,5,2,4,1]=>[4,3,1]=>3360
[8,3,5,1,2,6,4,7]=>[4,3,1]=>3360
[8,6,3,1,5,4,2,7]=>[6,1,1]=>3360
[8,6,4,1,5,3,2,7]=>[7,1]=>5760
[8,6,5,4,1,3,2,7]=>[7,1]=>5760
[5,3,8,7,4,6,2,1]=>[7,1]=>5760
[2,3,8,7,4,6,1,5]=>[7,1]=>5760
[8,3,5,7,4,1,2,6]=>[5,3]=>2688
[4,8,5,3,1,2,7,6]=>[4,3,1]=>3360
[6,8,7,3,1,5,4,2]=>[3,3,2]=>1120
[6,8,5,4,1,3,7,2]=>[4,2,1,1]=>2520
[2,5,8,7,4,6,3,1]=>[7,1]=>5760
[4,8,7,6,5,1,3,2]=>[3,2,2,1]=>1680
[3,8,7,5,1,6,2,4]=>[7,1]=>5760
[2,3,8,7,5,6,1,4]=>[6,1,1]=>3360
[2,8,7,1,3,6,4,5]=>[7,1]=>5760
[8,5,4,7,2,1,3,6]=>[3,3,2]=>1120
[6,8,7,3,5,2,1,4]=>[7,1]=>5760
[3,5,8,6,4,2,7,1]=>[4,3,1]=>3360
[6,8,4,1,5,2,7,3]=>[6,1,1]=>3360
[6,8,2,1,7,5,3,4]=>[8]=>5040
[5,8,4,6,1,2,7,3]=>[5,2,1]=>4032
[2,4,8,6,5,1,7,3]=>[4,2,1,1]=>2520
[4,8,7,6,5,2,1,3]=>[7,1]=>5760
[4,8,7,5,1,6,2,3]=>[4,3,1]=>3360
[4,5,2,1,8,6,7,3]=>[4,2,1,1]=>2520
[4,5,8,3,1,6,7,2]=>[6,1,1]=>3360
[7,2,8,6,4,5,1,3]=>[3,2,2,1]=>1680
[8,7,2,6,5,1,3,4]=>[4,3,1]=>3360
[5,1,6,3,4,8,2,7]=>[8]=>5040
[3,5,2,6,4,8,1,7]=>[8]=>5040
[6,3,8,2,4,1,7,5]=>[5,2,1]=>4032
[6,3,8,7,5,4,2,1]=>[7,1]=>5760
[6,8,4,2,1,7,5,3]=>[4,4]=>1260
[5,2,6,4,3,8,1,7]=>[6,1,1]=>3360
[6,5,3,1,4,8,2,7]=>[7,1]=>5760
[3,8,1,7,6,2,5,4]=>[6,2]=>3360
[8,1,7,6,4,2,5,3]=>[8]=>5040
[7,2,6,3,8,5,4,1]=>[7,1]=>5760
[7,3,8,6,4,1,5,2]=>[5,3]=>2688
[1,7,5,8,2,4,3,6]=>[4,3,1]=>3360
[6,1,5,2,4,8,3,7]=>[8]=>5040
[2,6,7,4,3,8,5,1]=>[4,3,1]=>3360
[5,2,4,7,3,8,6,1]=>[7,1]=>5760
[8,3,7,2,5,1,6,4]=>[7,1]=>5760
[3,7,2,8,1,5,4,6]=>[8]=>5040
[7,2,8,1,4,3,6,5]=>[7,1]=>5760
[6,1,5,4,3,8,2,7]=>[5,2,1]=>4032
[1,7,4,5,6,8,2,3]=>[5,2,1]=>4032
[1,3,4,5,6,7,9,8,2]=>[7,1,1]=>25920
[1,6,4,2,3,5,7,8]=>[5,1,1,1]=>1344
[1,8,7,2,3,4,5,6]=>[4,3,1]=>3360
[1,5,8,6,2,3,4,7]=>[5,2,1]=>4032
[1,6,5,7,2,3,4,8]=>[4,2,1,1]=>2520
[1,7,5,6,2,3,4,8]=>[6,1,1]=>3360
[1,3,2,7,6,4,5,8]=>[4,2,1,1]=>2520
[1,2,3,7,6,4,5,8]=>[4,1,1,1,1]=>420
[1,5,4,2,3,7,6,8]=>[4,2,1,1]=>2520
[1,5,4,2,3,8,6,7]=>[4,3,1]=>3360
[1,3,2,8,6,4,5,7]=>[5,2,1]=>4032
[1,7,5,8,2,3,4,6]=>[7,1]=>5760
[1,8,7,5,2,3,4,6]=>[7,1]=>5760
[2,1,5,8,6,3,7,4]=>[3,2,2,1]=>1680
[2,5,8,4,6,1,7,3]=>[4,2,1,1]=>2520
[5,8,4,6,1,3,7,2]=>[3,2,2,1]=>1680
[2,4,6,8,5,3,7,1]=>[4,2,1,1]=>2520
[2,4,8,1,7,6,5,3]=>[3,2,2,1]=>1680
[4,3,8,1,5,7,6,2]=>[3,2,2,1]=>1680
[4,3,6,8,5,2,7,1]=>[3,3,1,1]=>1120
[3,6,8,5,4,2,7,1]=>[3,2,2,1]=>1680
[3,6,4,1,8,2,7,5]=>[3,2,2,1]=>1680
[3,6,4,1,5,2,8,7]=>[3,2,2,1]=>1680
[4,8,6,5,1,3,7,2]=>[3,2,2,1]=>1680
[2,8,3,5,6,7,1,4]=>[7,1]=>5760
[5,6,2,4,7,1,8,3]=>[7,1]=>5760
[2,7,5,4,6,1,8,3]=>[7,1]=>5760
[2,3,7,4,6,1,8,5]=>[7,1]=>5760
[2,6,7,4,1,3,8,5]=>[7,1]=>5760
[6,5,7,4,1,3,8,2]=>[7,1]=>5760
[2,4,6,3,5,7,8,1]=>[7,1]=>5760
[4,1,6,3,5,7,8,2]=>[7,1]=>5760
[3,6,4,2,5,7,8,1]=>[7,1]=>5760
[2,3,6,1,5,7,8,4]=>[7,1]=>5760
[4,3,6,2,5,7,8,1]=>[7,1]=>5760
[4,6,1,2,5,7,8,3]=>[7,1]=>5760
[2,6,4,1,5,7,8,3]=>[7,1]=>5760
[2,4,1,6,5,7,8,3]=>[7,1]=>5760
[7,5,4,2,6,1,8,3]=>[8]=>5040
[4,7,3,1,8,6,5,2]=>[4,2,1,1]=>2520
[5,6,4,2,7,1,8,3]=>[8]=>5040
[4,2,7,5,3,1,8,6]=>[7,1]=>5760
[5,3,6,4,8,2,1,7]=>[4,3,1]=>3360
[7,3,2,5,4,1,8,6]=>[4,2,2]=>1260
[4,6,3,8,7,2,1,5]=>[5,2,1]=>4032
[4,7,6,3,8,2,1,5]=>[6,2]=>3360
[4,7,3,8,6,2,1,5]=>[7,1]=>5760
[5,7,3,2,6,1,8,4]=>[4,3,1]=>3360
[5,7,3,2,6,4,1,8]=>[6,1,1]=>3360
[2,7,5,3,1,8,6,4]=>[8]=>5040
[7,3,2,4,1,8,6,5]=>[5,2,1]=>4032
[4,3,7,5,8,2,1,6]=>[8]=>5040
[4,3,7,5,2,6,1,8]=>[6,1,1]=>3360
[8,4,5,3,7,2,1,6]=>[8]=>5040
[4,3,5,2,8,6,1,7]=>[7,1]=>5760
[1,2,3,4,5,9,7,8,6]=>[2,1,1,1,1,1,1,1]=>36
[1,2,3,4,9,6,7,8,5]=>[2,1,1,1,1,1,1,1]=>36
[1,2,3,9,5,6,7,8,4]=>[2,1,1,1,1,1,1,1]=>36
[1,2,9,4,5,6,7,8,3]=>[2,1,1,1,1,1,1,1]=>36
[1,2,3,4,5,6,10,8,9,7]=>[2,1,1,1,1,1,1,1,1]=>45
[1,2,3,4,9,7,6,8,5]=>[2,2,1,1,1,1,1]=>378
[1,2,3,4,5,10,7,8,9,6]=>[2,1,1,1,1,1,1,1,1]=>45
[1,2,8,6,4,5,7,3]=>[3,2,1,1,1]=>1120
[1,2,3,9,6,5,7,8,4]=>[2,2,1,1,1,1,1]=>378
[1,2,3,4,10,6,7,8,9,5]=>[2,1,1,1,1,1,1,1,1]=>45
[1,8,5,3,4,6,7,2]=>[3,2,1,1,1]=>1120
[1,2,9,5,4,6,7,8,3]=>[2,2,1,1,1,1,1]=>378
[1,2,3,10,5,6,7,8,9,4]=>[2,1,1,1,1,1,1,1,1]=>45
[1,9,4,3,5,6,7,8,2]=>[2,2,1,1,1,1,1]=>378
[1,2,10,4,5,6,7,8,9,3]=>[2,1,1,1,1,1,1,1,1]=>45
[9,3,2,4,5,6,7,8,1]=>[2,2,1,1,1,1,1]=>378
[10,2,3,4,5,6,7,8,9,1]=>[2,1,1,1,1,1,1,1,1]=>45
[3,5,6,7,8,9,4,2,1]=>[4,3,2]=>15120
[7,8,4,1,6,3,5,2]=>[6,2]=>3360
[8,7,5,6,1,3,4,2]=>[8]=>5040
[1,2,3,5,7,4,6,9,8]=>[4,2,1,1,1]=>7560
[1,2,3,6,4,7,5,9,8]=>[4,2,1,1,1]=>7560
[1,2,3,4,6,8,5,7,10,9]=>[4,2,1,1,1,1]=>18900
[1,2,3,4,6,8,5,7,9]=>[4,1,1,1,1,1]=>756
[1,2,3,4,7,5,8,6,9]=>[4,1,1,1,1,1]=>756
[1,2,3,4,7,5,8,6,10,9]=>[4,2,1,1,1,1]=>18900
[1,2,3,5,7,4,6,9,8,10]=>[4,2,1,1,1,1]=>18900
[1,2,5,7,3,4,6,9,8]=>[3,2,2,1,1]=>7560
[1,2,4,5,7,3,6,9,8]=>[5,2,1,1]=>18144
[1,2,6,3,4,7,5,9,8]=>[5,2,1,1]=>18144
[1,2,5,6,3,7,4,9,8]=>[3,2,2,1,1]=>7560
[1,2,3,6,4,7,5,9,8,10]=>[4,2,1,1,1,1]=>18900
[3,2,6,4,1,8,5,7]=>[6,1,1]=>3360
[2,8,6,5,3,1,4,7]=>[8]=>5040
[5,4,8,6,2,3,1,7]=>[8]=>5040
[4,8,7,5,2,3,1,6]=>[8]=>5040
[5,2,4,7,6,8,3,1]=>[4,3,1]=>3360
[3,4,2,8,7,5,1,6]=>[8]=>5040
[8,5,7,6,3,2,4,1]=>[6,2]=>3360
[6,4,1,8,7,3,2,5]=>[5,3]=>2688
[1,8,5,4,2,7,3,6]=>[6,1,1]=>3360
[3,7,6,1,5,8,4,2]=>[7,1]=>5760
[3,6,5,8,2,7,4,1]=>[8]=>5040
[8,3,2,7,4,6,5,1]=>[3,2,2,1]=>1680
[7,5,8,4,1,3,6,2]=>[7,1]=>5760
[7,1,6,2,3,8,4,5]=>[4,4]=>1260
[6,4,7,1,3,2,8,5]=>[4,4]=>1260
[5,1,3,8,7,2,6,4]=>[5,2,1]=>4032
[8,7,1,6,2,5,3,4]=>[8]=>5040
[3,8,5,2,4,7,6,1]=>[6,2]=>3360
[7,1,5,2,4,8,3,6]=>[6,2]=>3360
[3,8,5,1,4,7,2,6]=>[4,4]=>1260
[7,2,5,4,1,3,8,6]=>[6,1,1]=>3360
[7,5,8,1,6,3,2,4]=>[8]=>5040
[2,3,1,9,4,5,6,7,8]=>[6,3]=>20160
[4,9,1,2,3,5,6,7,8]=>[9]=>40320
[3,9,1,2,4,5,6,7,8]=>[7,2]=>25920
[6,8,1,9,2,3,4,5,7]=>[3,3,3]=>2240
[7,10,1,2,3,4,5,6,8,9]=>[6,4]=>151200
[6,10,1,2,3,4,5,7,8,9]=>[10]=>362880
[4,8,1,2,3,9,5,6,7]=>[9]=>40320
[3,8,1,2,4,5,9,6,7]=>[5,2,2]=>9072
[4,10,1,2,3,5,6,7,8,9]=>[10]=>362880
[3,10,1,2,4,5,6,7,8,9]=>[8,2]=>226800
[1,8,2,3,4,5,6,7,9]=>[7,1,1]=>25920
[7,4,6,1,3,2,5,8]=>[7,1]=>5760
[1,4,5,8,6,3,2,7]=>[4,3,1]=>3360
[8,4,5,7,2,6,1,3]=>[7,1]=>5760
[4,5,2,6,7,3,1,8]=>[7,1]=>5760
[8,1,7,5,3,6,2,4]=>[7,1]=>5760
[5,2,8,3,6,1,4,7]=>[4,3,1]=>3360
[5,2,6,3,1,7,8,4]=>[5,2,1]=>4032
[4,3,5,1,6,7,8,2]=>[6,2]=>3360
[5,7,6,1,2,3,8,4]=>[6,2]=>3360
[3,6,7,5,1,2,8,4]=>[6,2]=>3360
[1,7,6,8,5,2,4,3]=>[6,1,1]=>3360
[5,7,6,8,1,2,4,3]=>[6,2]=>3360
[5,6,3,7,1,4,8,2]=>[5,2,1]=>4032
[5,3,2,1,8,6,4,7]=>[5,2,1]=>4032
[9,8,7,5,6,4,3,2,1]=>[3,2,2,2]=>2520
[2,1,9,8,6,7,5,4,3]=>[3,2,2,2]=>2520
[11,10,9,8,7,6,5,4,3,2,1]=>[2,2,2,2,2,1]=>10395
[10,9,8,7,5,6,4,3,2,1]=>[2,2,2,2,1,1]=>4725
[9,8,7,5,4,6,3,2,1]=>[2,2,2,2,1]=>945
[9,8,7,4,6,5,3,2,1]=>[2,2,2,2,1]=>945
[2,1,9,8,6,5,7,4,3]=>[2,2,2,2,1]=>945
[2,1,9,8,5,7,6,4,3]=>[2,2,2,2,1]=>945
[2,1,10,9,8,6,7,5,4,3]=>[2,2,2,2,1,1]=>4725
[2,1,11,10,9,8,7,6,5,4,3]=>[2,2,2,2,2,1]=>10395
[1,8,7,6,5,4,3,2,9]=>[2,2,2,1,1,1]=>1260
[1,9,8,7,6,5,4,3,2,10]=>[2,2,2,2,1,1]=>4725
[2,1,8,7,6,5,4,3,9]=>[2,2,2,2,1]=>945
[2,8,9,7,6,5,4,3,1]=>[5,2,2]=>9072
[7,8,6,1,4,5,2,3]=>[8]=>5040
[6,5,8,3,7,2,1,4]=>[5,3]=>2688
[7,8,5,3,6,2,1,4]=>[6,2]=>3360
[7,8,5,3,6,2,4,1]=>[8]=>5040
[7,8,4,3,2,6,5,1]=>[5,2,1]=>4032
[1,8,4,3,2,6,7,5]=>[3,2,1,1,1]=>1120
[5,4,3,8,2,1,7,6]=>[6,1,1]=>3360
[6,4,8,3,2,1,7,5]=>[5,2,1]=>4032
[1,8,4,3,2,7,6,5]=>[3,2,2,1]=>1680
[1,8,6,7,3,2,4,5]=>[5,2,1]=>4032
[7,8,6,1,3,2,4,5]=>[5,3]=>2688
[5,4,3,8,2,1,6,7]=>[7,1]=>5760
[1,8,4,3,2,5,7,6]=>[4,2,1,1]=>2520
[5,4,3,8,2,6,7,1]=>[5,1,1,1]=>1344
[4,5,6,7,8,1,2,9,3]=>[9]=>40320
[4,5,6,7,1,2,8,9,3]=>[9]=>40320
[4,5,6,1,2,7,8,9,3]=>[5,2,2]=>9072
[4,5,1,2,6,7,8,9,3]=>[9]=>40320
[6,4,2,3,5,1,8,7]=>[3,2,2,1]=>1680
[5,2,3,6,1,4,8,7]=>[2,2,2,1,1]=>420
[5,2,3,8,6,4,7,1]=>[5,1,1,1]=>1344
[5,2,3,7,4,8,1,6]=>[4,2,1,1]=>2520
[8,6,3,2,5,4,7,1]=>[3,2,1,1,1]=>1120
[7,2,3,4,5,8,1,6]=>[2,2,1,1,1,1]=>210
[7,2,8,1,5,3,4,6]=>[3,3,1,1]=>1120
[3,8,6,4,7,2,5,1]=>[5,2,1]=>4032
[2,1,8,6,4,5,7,3]=>[3,2,2,1]=>1680
[4,8,2,5,7,3,1,6]=>[4,4]=>1260
[5,8,2,3,4,7,1,6]=>[8]=>5040
[6,3,4,7,8,2,1,5]=>[6,2]=>3360
[3,8,5,1,4,7,6,2]=>[4,2,2]=>1260
[4,8,5,1,3,6,7,2]=>[2,2,2,1,1]=>420
[4,6,8,5,2,7,3,1]=>[8]=>5040
[3,7,8,5,2,6,4,1]=>[4,3,1]=>3360
[3,8,6,2,7,4,5,1]=>[6,2]=>3360
[8,5,4,7,1,3,6,2]=>[4,4]=>1260
[7,3,6,2,8,1,5,4]=>[8]=>5040
[8,1,5,2,3,7,6,4]=>[4,2,2]=>1260
[6,4,2,3,7,8,5,1]=>[3,3,2]=>1120
[8,4,2,3,6,7,1,5]=>[5,3]=>2688
[4,5,8,3,7,2,1,6]=>[8]=>5040
[3,7,2,8,4,5,1,6]=>[4,4]=>1260
[3,5,1,8,4,6,2,7]=>[5,2,1]=>4032
[4,2,1,5,6,8,3,7]=>[7,1]=>5760
[4,1,2,6,5,8,3,7]=>[7,1]=>5760
[4,1,8,3,2,6,7,5]=>[6,1,1]=>3360
[4,2,7,5,8,1,3,6]=>[5,2,1]=>4032
[4,6,2,7,8,3,1,5]=>[3,3,2]=>1120
[4,6,1,3,8,2,5,7]=>[3,3,2]=>1120
[7,5,4,1,6,3,2,8]=>[7,1]=>5760
[1,8,7,5,3,6,4,2]=>[4,2,1,1]=>2520
[8,5,4,1,6,3,2,7]=>[8]=>5040
[7,1,4,8,6,3,2,5]=>[5,3]=>2688
[5,3,6,8,2,7,1,4]=>[6,2]=>3360
[6,3,7,4,8,2,1,5]=>[5,2,1]=>4032
[4,3,6,8,2,7,1,5]=>[8]=>5040
[5,3,7,4,8,2,1,6]=>[7,1]=>5760
[1,5,8,3,6,7,4,2]=>[7,1]=>5760
[8,3,1,2,5,7,4,6]=>[7,1]=>5760
[7,8,1,2,3,4,5,9,6]=>[5,4]=>18144
[2,8,9,1,3,4,5,6,7]=>[5,4]=>18144
[2,8,9,10,1,3,4,5,6,7]=>[4,3,3]=>50400
[7,1,8,2,9,3,4,5,6]=>[5,4]=>18144
[6,1,7,2,8,3,9,4,5]=>[9]=>40320
[5,1,6,2,7,3,8,4,9]=>[6,2,1]=>30240
[8,1,9,2,10,3,4,5,6,7]=>[7,3]=>172800
[7,1,8,2,3,9,4,5,6]=>[4,3,2]=>15120
[7,1,8,2,9,3,10,4,5,6]=>[8,2]=>226800
[6,1,7,2,8,3,4,9,5]=>[6,3]=>20160
[5,1,6,2,7,3,9,4,8]=>[7,2]=>25920
[5,1,6,2,7,3,8,4,10,9]=>[6,2,2]=>75600
[4,1,5,2,7,3,8,6,9]=>[5,3,1]=>24192
[4,1,5,2,6,3,8,7,10,9]=>[3,3,2,2]=>25200
[5,1,3,7,4,8,2,6]=>[5,2,1]=>4032
[5,1,3,4,7,8,2,6]=>[4,2,1,1]=>2520
[5,1,7,8,3,4,2,6]=>[5,3]=>2688
[2,5,4,8,3,7,6,1]=>[6,2]=>3360
[5,6,8,2,3,4,1,7]=>[5,3]=>2688
[4,5,2,3,8,6,1,7]=>[7,1]=>5760
[3,7,4,5,8,1,2,6]=>[6,2]=>3360
[3,7,8,1,4,5,2,6]=>[6,2]=>3360
[4,8,1,3,7,5,2,6]=>[5,3]=>2688
[2,4,7,8,5,3,6,1]=>[4,3,1]=>3360
[4,3,5,8,2,1,7,6]=>[4,3,1]=>3360
[4,8,5,3,7,1,2,6]=>[8]=>5040
[4,8,5,7,3,1,2,6]=>[6,2]=>3360
[4,8,7,5,1,3,2,6]=>[5,3]=>2688
[3,7,8,4,1,5,2,6]=>[5,2,1]=>4032
[1,8,5,7,2,4,3,6]=>[7,1]=>5760
[1,8,5,4,2,3,6,7]=>[6,1,1]=>3360
[1,3,6,8,5,4,2,7]=>[6,1,1]=>3360
[1,6,3,8,2,7,4,5]=>[6,1,1]=>3360
[1,4,2,7,5,8,3,6]=>[4,2,1,1]=>2520
[1,3,6,8,2,7,5,4]=>[5,2,1]=>4032
[1,6,5,4,3,8,2,7]=>[4,2,1,1]=>2520
[1,8,3,6,2,4,5,7]=>[4,2,1,1]=>2520
[1,4,5,8,3,6,2,7]=>[4,2,1,1]=>2520
[1,2,7,8,4,5,3,6]=>[4,2,1,1]=>2520
[7,2,8,5,6,3,4,1]=>[7,1]=>5760
[7,6,3,8,5,4,2,1]=>[6,1,1]=>3360
[6,2,8,7,5,4,1,3]=>[4,2,1,1]=>2520
[6,2,8,4,3,7,1,5]=>[3,3,1,1]=>1120
[5,2,8,4,3,1,7,6]=>[5,1,1,1]=>1344
[1,2,5,4,8,3,7,6]=>[4,1,1,1,1]=>420
[1,4,3,6,8,7,2,5]=>[4,2,1,1]=>2520
[3,2,5,7,6,8,1,4]=>[7,1]=>5760
[5,3,2,6,8,4,7,1]=>[3,2,2,1]=>1680
[3,1,8,6,4,7,2,5]=>[8]=>5040
[5,3,2,8,7,6,4,1]=>[5,2,1]=>4032
[5,3,8,2,7,6,1,4]=>[4,3,1]=>3360
[6,5,4,8,3,7,2,1]=>[8]=>5040
[4,8,5,1,3,7,2,6]=>[4,2,2]=>1260
[4,3,8,7,2,6,5,1]=>[7,1]=>5760
[2,7,5,1,8,4,6,3]=>[5,3]=>2688
[7,8,5,2,1,6,4,3]=>[7,1]=>5760
[7,5,4,8,3,2,6,1]=>[8]=>5040
[3,8,5,6,2,7,1,4]=>[8]=>5040
[2,4,5,8,7,3,1,6]=>[8]=>5040
[2,4,5,8,6,7,1,3]=>[8]=>5040
[4,3,1,5,6,2,8,7]=>[6,2]=>3360
[4,1,5,8,6,7,2,3]=>[8]=>5040
[4,3,7,6,1,2,8,5]=>[8]=>5040
[4,7,5,6,1,2,8,3]=>[8]=>5040
[4,3,7,5,6,2,8,1]=>[8]=>5040
[4,5,1,8,6,7,3,2]=>[8]=>5040
[3,4,5,8,6,7,2,1]=>[8]=>5040
[2,1,5,8,6,7,4,3]=>[6,2]=>3360
[3,4,5,8,7,1,2,6]=>[8]=>5040
[4,7,1,5,6,2,8,3]=>[8]=>5040
[2,6,4,7,1,3,8,5]=>[8]=>5040
[5,3,8,6,4,7,2,1]=>[8]=>5040
[6,4,1,5,7,8,3,2]=>[8]=>5040
[3,6,4,7,2,1,8,5]=>[8]=>5040
[3,8,4,6,1,7,2,5]=>[8]=>5040
[3,8,5,6,4,7,2,1]=>[8]=>5040
[3,8,4,5,6,7,2,1]=>[8]=>5040
[3,8,6,5,2,7,4,1]=>[8]=>5040
[3,8,7,5,2,1,4,6]=>[8]=>5040
[3,8,6,5,1,7,2,4]=>[8]=>5040
[6,4,1,7,3,2,8,5]=>[8]=>5040
[5,1,4,6,7,2,8,3]=>[8]=>5040
[6,5,4,7,1,3,8,2]=>[8]=>5040
[2,1,6,5,3,7,8,4]=>[6,2]=>3360
[6,1,4,7,2,3,8,5]=>[8]=>5040
[2,1,3,4,5,6,8,9,7]=>[3,2,1,1,1,1]=>2520
[2,1,3,4,5,6,7,9,8]=>[2,2,1,1,1,1,1]=>378
[2,1,3,4,5,6,7,9,10,8]=>[3,2,1,1,1,1,1]=>5040
[2,3,1,4,5,6,8,9,7]=>[3,3,1,1,1]=>3360
[1,3,2,4,5,6,8,9,7]=>[3,2,1,1,1,1]=>2520
[2,3,1,4,5,6,7,9,8]=>[3,2,1,1,1,1]=>2520
[1,3,2,4,5,6,7,9,8]=>[2,2,1,1,1,1,1]=>378
[2,1,3,4,5,6,7,8,10,9]=>[2,2,1,1,1,1,1,1]=>630
[1,6,2,5,4,8,3,7]=>[5,2,1]=>4032
[6,1,3,5,8,2,4,7]=>[4,3,1]=>3360
[6,7,3,2,1,8,4,5]=>[4,3,1]=>3360
[2,5,7,3,1,4,8,6]=>[5,3]=>2688
[1,2,6,7,4,3,8,5]=>[4,2,1,1]=>2520
[2,7,5,8,1,6,3,4]=>[5,2,1]=>4032
[8,2,5,7,1,4,6,3]=>[4,3,1]=>3360
[8,3,5,7,6,1,4,2]=>[6,2]=>3360
[8,7,3,6,2,1,5,4]=>[4,3,1]=>3360
[8,6,5,2,7,4,3,1]=>[3,3,2]=>1120
[8,4,3,7,6,5,1,2]=>[5,2,1]=>4032
[8,4,2,7,5,1,6,3]=>[7,1]=>5760
[8,3,4,2,7,5,6,1]=>[3,3,2]=>1120
[8,4,7,6,5,1,2,3]=>[7,1]=>5760
[8,3,5,2,7,4,6,1]=>[6,2]=>3360
[8,6,2,4,7,3,1,5]=>[4,3,1]=>3360
[8,5,2,3,7,4,1,6]=>[8]=>5040
[8,5,3,2,7,6,4,1]=>[4,2,1,1]=>2520
[8,6,1,5,4,3,2,7]=>[6,2]=>3360
[2,4,5,8,3,1,6,7]=>[6,2]=>3360
[2,7,4,6,1,5,8,3]=>[8]=>5040
[2,4,3,8,5,1,6,7]=>[6,1,1]=>3360
[7,8,3,2,5,4,6,1]=>[6,1,1]=>3360
[1,5,6,7,3,8,2,4]=>[7,1]=>5760
[1,6,5,4,8,3,2,7]=>[6,1,1]=>3360
[1,7,3,5,8,4,6,2]=>[6,1,1]=>3360
[7,2,1,6,4,8,5,3]=>[7,1]=>5760
[7,5,8,3,2,4,6,1]=>[6,2]=>3360
[3,8,7,2,4,6,5,1]=>[7,1]=>5760
[1,3,7,6,4,8,5,2]=>[7,1]=>5760
[5,4,1,8,6,3,2,7]=>[4,4]=>1260
[6,4,1,8,5,3,2,7]=>[4,3,1]=>3360
[8,5,7,1,4,3,2,6]=>[8]=>5040
[8,6,5,1,4,3,2,7]=>[8]=>5040
[8,6,1,7,2,5,3,4]=>[5,3]=>2688
[1,8,6,3,4,2,5,7]=>[7,1]=>5760
[3,1,6,4,5,8,7,2]=>[5,1,1,1]=>1344
[3,1,6,4,5,8,2,7]=>[6,1,1]=>3360
[4,6,8,7,2,5,1,3]=>[3,3,2]=>1120
[7,6,3,8,4,5,2,1]=>[7,1]=>5760
[8,2,7,6,1,4,3,5]=>[3,2,2,1]=>1680
[5,6,3,8,4,1,2,7]=>[7,1]=>5760
[8,2,7,6,1,4,5,3]=>[5,2,1]=>4032
[5,2,3,4,7,1,6,8]=>[4,1,1,1,1]=>420
[8,7,5,3,1,6,4,2]=>[7,1]=>5760
[1,4,7,8,5,2,3,6]=>[4,2,1,1]=>2520
[3,2,6,7,4,1,5,8]=>[3,3,1,1]=>1120
[5,8,3,7,6,4,1,2]=>[5,2,1]=>4032
[6,5,1,7,2,4,8,3]=>[6,2]=>3360
[3,6,7,1,4,2,5,8]=>[5,2,1]=>4032
[8,1,2,7,5,4,3,6]=>[7,1]=>5760
[6,5,1,8,3,7,2,4]=>[6,2]=>3360
[1,8,7,5,3,2,6,4]=>[7,1]=>5760
[7,8,1,5,4,2,3,6]=>[3,3,2]=>1120
[7,6,3,1,2,8,5,4]=>[7,1]=>5760
[6,3,5,7,1,4,2,8]=>[7,1]=>5760
[1,7,5,2,6,4,8,3]=>[7,1]=>5760
[7,1,3,6,8,2,4,5]=>[5,2,1]=>4032
[1,2,5,7,8,4,6,3]=>[3,3,1,1]=>1120
[3,1,2,7,5,4,8,6]=>[4,3,1]=>3360
[6,7,4,1,3,2,8,5]=>[8]=>5040
[1,7,2,8,4,3,5,6]=>[7,1]=>5760
[1,6,3,5,7,8,2,4]=>[6,1,1]=>3360
[8,6,1,7,5,2,4,3]=>[3,2,2,1]=>1680
[7,6,4,1,8,3,2,5]=>[6,2]=>3360
[8,4,1,6,5,2,7,3]=>[3,3,1,1]=>1120
[1,5,3,4,7,8,2,6]=>[3,2,1,1,1]=>1120
[4,2,1,5,7,8,3,6]=>[5,2,1]=>4032
[5,4,1,6,7,8,2,3]=>[8]=>5040
[5,1,4,6,7,8,2,3]=>[4,4]=>1260
[4,1,5,3,7,8,2,6]=>[6,2]=>3360
[8,1,4,6,5,2,7,3]=>[6,1,1]=>3360
[7,1,5,4,6,3,2,8]=>[3,3,1,1]=>1120
[8,2,1,6,7,5,4,3]=>[4,3,1]=>3360
[1,2,4,7,6,3,8,5]=>[6,1,1]=>3360
[6,7,4,1,8,5,2,3]=>[6,2]=>3360
[8,6,4,1,5,7,3,2]=>[7,1]=>5760
[5,2,4,3,7,1,6,8]=>[4,2,1,1]=>2520
[6,1,5,4,8,3,2,7]=>[7,1]=>5760
[1,2,8,7,4,3,6,5]=>[6,1,1]=>3360
[3,2,1,7,5,8,4,6]=>[2,2,2,1,1]=>420
[1,3,6,4,7,8,2,5]=>[6,1,1]=>3360
[4,5,1,3,7,8,2,6]=>[3,3,2]=>1120
[5,2,3,1,7,8,4,6]=>[4,2,1,1]=>2520
[1,6,4,3,7,8,2,5]=>[5,2,1]=>4032
[7,6,4,3,1,5,2,8]=>[5,2,1]=>4032
[7,5,4,6,1,3,2,8]=>[4,3,1]=>3360
[8,4,6,5,1,2,7,3]=>[7,1]=>5760
[1,5,6,3,7,8,2,4]=>[4,3,1]=>3360
[7,1,2,3,4,5,8,9,10,6]=>[10]=>362880
[6,7,1,2,3,4,8,9,5]=>[9]=>40320
[6,1,2,3,4,7,8,9,10,5]=>[10]=>362880
[5,1,2,3,6,7,8,9,10,4]=>[10]=>362880
[1,5,2,4,3,8,7,6]=>[3,2,1,1,1]=>1120
[8,6,5,7,2,1,4,3]=>[6,2]=>3360
[1,6,3,8,4,5,7,2]=>[5,1,1,1]=>1344
[7,5,4,2,6,3,8,1]=>[5,3]=>2688
[7,8,6,5,4,3,2,9,1]=>[5,2,2]=>9072
[9,7,6,5,4,3,1,2,8]=>[5,2,2]=>9072
[2,4,3,5,6,7,8,9,1]=>[8,1]=>45360
[2,3,8,4,7,5,6,1]=>[4,3,1]=>3360
[3,7,2,8,6,4,5,1]=>[8]=>5040
[6,3,7,5,8,2,4,1]=>[8]=>5040
[4,3,7,8,6,2,5,1]=>[5,3]=>2688
[3,8,1,7,5,2,4,6]=>[3,2,2,1]=>1680
[2,4,7,8,6,1,5,3]=>[8]=>5040
[2,4,8,5,1,7,3,6]=>[4,4]=>1260
[2,8,3,5,1,6,4,7]=>[6,1,1]=>3360
[8,2,4,6,3,7,5,1]=>[5,2,1]=>4032
[4,5,3,8,2,1,7,6]=>[4,2,1,1]=>2520
[4,5,6,7,8,9,2,1,3]=>[6,3]=>20160
[5,6,7,8,9,2,1,3,4]=>[7,2]=>25920
[6,7,8,9,2,1,3,4,5]=>[7,2]=>25920
[7,8,9,2,1,3,4,5,6]=>[6,3]=>20160
[8,9,2,1,3,4,5,6,7]=>[5,4]=>18144
[1,4,6,2,7,5,3,8]=>[4,2,1,1]=>2520
[8,2,1,4,5,6,7,3]=>[3,1,1,1,1,1]=>112
[7,3,1,2,5,6,4,8]=>[5,1,1,1]=>1344
[7,8,2,1,5,4,6,3]=>[4,3,1]=>3360
[1,4,8,5,2,6,3,7]=>[3,3,1,1]=>1120
[5,2,3,7,8,1,6,4]=>[6,1,1]=>3360
[1,2,8,4,3,6,7,5]=>[3,1,1,1,1,1]=>112
[1,2,7,5,3,4,6,8]=>[5,1,1,1]=>1344
[1,7,3,2,6,8,4,5]=>[3,3,1,1]=>1120
[3,5,8,6,1,4,2,7]=>[6,2]=>3360
[1,8,4,2,7,6,3,5]=>[6,1,1]=>3360
[7,3,8,1,6,5,4,2]=>[3,3,2]=>1120
[7,3,8,2,6,5,4,1]=>[6,2]=>3360
[7,1,3,8,6,5,4,2]=>[5,2,1]=>4032
[8,1,3,7,6,5,4,2]=>[3,2,2,1]=>1680
[2,4,1,8,7,3,6,5]=>[8]=>5040
[7,3,8,6,1,5,4,2]=>[5,3]=>2688
[3,5,1,7,8,2,6,4]=>[6,2]=>3360
[5,4,7,8,2,1,6,3]=>[8]=>5040
[6,3,8,7,1,5,4,2]=>[3,3,2]=>1120
[8,6,4,7,1,5,3,2]=>[5,3]=>2688
[6,4,7,1,5,3,2,8]=>[6,1,1]=>3360
[3,4,6,2,1,8,5,7]=>[6,2]=>3360
[5,6,4,8,3,2,1,7]=>[6,2]=>3360
[5,7,4,8,2,1,6,3]=>[5,3]=>2688
[4,7,5,8,2,1,6,3]=>[8]=>5040
[5,7,4,2,6,3,8,1]=>[8]=>5040
[5,7,4,1,6,2,8,3]=>[8]=>5040
[8,5,6,1,7,3,2,4]=>[3,3,2]=>1120
[4,5,1,6,7,8,3,2]=>[8]=>5040
[4,5,2,6,1,3,8,7]=>[6,2]=>3360
[8,4,6,7,2,5,1,3]=>[8]=>5040
[7,1,4,6,8,3,5,2]=>[5,3]=>2688
[6,7,1,2,4,8,5,3]=>[4,4]=>1260
[2,3,6,4,7,5,8,1]=>[7,1]=>5760
[7,8,1,3,4,5,6,2]=>[6,2]=>3360
[1,8,2,6,7,3,4,5]=>[7,1]=>5760
[4,7,3,2,8,1,5,6]=>[7,1]=>5760
[7,1,2,6,3,8,5,4]=>[5,3]=>2688
[8,1,2,6,3,7,5,4]=>[8]=>5040
[4,7,8,3,1,6,2,5]=>[5,2,1]=>4032
[7,4,3,1,6,2,8,5]=>[7,1]=>5760
[7,4,3,1,8,6,2,5]=>[4,2,1,1]=>2520
[3,7,6,2,4,8,1,5]=>[8]=>5040
[4,3,7,2,8,6,1,5]=>[5,2,1]=>4032
[6,1,2,7,4,3,8,5]=>[4,4]=>1260
[5,1,2,6,3,8,7,4]=>[4,3,1]=>3360
[5,1,2,7,3,8,6,4]=>[4,4]=>1260
[6,1,2,7,3,5,8,4]=>[5,3]=>2688
[7,5,3,2,1,8,6,4]=>[7,1]=>5760
[4,2,1,5,3,6,7,8]=>[4,1,1,1,1]=>420
[8,6,4,3,2,1,9,7,5]=>[7,2]=>25920
[7,5,4,3,2,1,8,6,9]=>[4,2,2,1]=>11340
[8,6,4,2,1,9,7,5,3]=>[5,3,1]=>24192
[7,5,3,2,1,8,6,4,9]=>[7,1,1]=>25920
[7,4,3,2,1,8,5,9,6]=>[3,3,2,1]=>10080
[6,4,3,2,1,7,5,8,9]=>[4,2,1,1,1]=>7560
[7,5,3,1,8,6,4,2,9]=>[3,3,1,1,1]=>3360
[7,4,2,1,8,5,3,9,6]=>[5,4]=>18144
[6,4,2,1,7,5,3,8,9]=>[7,1,1]=>25920
[6,3,2,1,7,4,8,5,9]=>[3,3,2,1]=>10080
[5,3,2,1,6,4,7,8,9]=>[4,2,1,1,1]=>7560
[7,4,1,8,5,2,9,6,3]=>[4,4,1]=>11340
[6,3,1,7,4,2,8,5,9]=>[4,4,1]=>11340
[5,3,1,6,4,2,7,8,9]=>[6,1,1,1]=>10080
[6,2,1,7,3,8,4,9,5]=>[6,2,1]=>30240
[5,2,1,6,3,7,4,8,9]=>[3,3,1,1,1]=>3360
[4,2,1,5,3,6,7,8,9]=>[4,1,1,1,1,1]=>756
[4,1,5,2,6,3,7,8,9]=>[3,3,1,1,1]=>3360
[3,1,4,2,5,6,7,8,9]=>[4,1,1,1,1,1]=>756
[9,7,5,4,3,2,1,10,8,6]=>[7,2,1]=>259200
[8,6,5,4,3,2,1,9,7,10]=>[4,2,2,1,1]=>56700
[9,7,5,3,2,1,10,8,6,4]=>[6,3,1]=>201600
[8,6,4,3,2,1,9,7,5,10]=>[7,2,1]=>259200
[8,5,4,3,2,1,9,6,10,7]=>[3,3,2,2]=>25200
[7,5,4,3,2,1,8,6,9,10]=>[4,2,2,1,1]=>56700
[8,6,4,2,1,9,7,5,3,10]=>[5,3,1,1]=>120960
[8,5,3,2,1,9,6,4,10,7]=>[5,4,1]=>181440
[7,5,3,2,1,8,6,4,9,10]=>[7,1,1,1]=>86400
[7,4,3,2,1,8,5,9,6,10]=>[3,3,2,1,1]=>50400
[6,4,3,2,1,7,5,8,9,10]=>[4,2,1,1,1,1]=>18900
[8,5,3,1,9,6,4,2,10,7]=>[8,1,1]=>226800
[7,5,3,1,8,6,4,2,9,10]=>[3,3,1,1,1,1]=>8400
[8,5,2,1,9,6,3,10,7,4]=>[5,4,1]=>181440
[7,4,2,1,8,5,3,9,6,10]=>[5,4,1]=>181440
[6,4,2,1,7,5,3,8,9,10]=>[7,1,1,1]=>86400
[7,3,2,1,8,4,9,5,10,6]=>[6,2,2]=>75600
[6,3,2,1,7,4,8,5,9,10]=>[3,3,2,1,1]=>50400
[5,3,2,1,6,4,7,8,9,10]=>[4,2,1,1,1,1]=>18900
[7,4,1,8,5,2,9,6,3,10]=>[4,4,1,1]=>56700
[7,3,1,8,4,2,9,5,10,6]=>[7,3]=>172800
[6,3,1,7,4,2,8,5,9,10]=>[4,4,1,1]=>56700
[5,3,1,6,4,2,7,8,9,10]=>[6,1,1,1,1]=>25200
[6,2,1,7,3,8,4,9,5,10]=>[6,2,1,1]=>151200
[5,2,1,6,3,7,4,8,9,10]=>[3,3,1,1,1,1]=>8400
[4,2,1,5,3,6,7,8,9,10]=>[4,1,1,1,1,1,1]=>1260
[5,1,6,2,7,3,8,4,9,10]=>[6,2,1,1]=>151200
[4,1,5,2,6,3,7,8,9,10]=>[3,3,1,1,1,1]=>8400
[3,1,4,2,5,6,7,8,9,10]=>[4,1,1,1,1,1,1]=>1260
[1,5,8,4,7,6,3,2]=>[5,1,1,1]=>1344
[3,2,7,4,8,6,1,5]=>[3,2,1,1,1]=>1120
[6,4,3,8,5,2,1,7]=>[6,1,1]=>3360
[8,2,5,4,7,6,1,3]=>[5,1,1,1]=>1344
[7,2,5,4,8,6,1,3]=>[3,2,1,1,1]=>1120
[3,2,5,4,8,6,1,7]=>[5,1,1,1]=>1344
[8,4,3,6,5,2,1,7]=>[3,3,1,1]=>1120
[5,8,1,3,7,2,6,4]=>[8]=>5040
[4,7,5,1,8,2,6,3]=>[3,3,2]=>1120
[6,3,2,1,8,7,4,5]=>[4,2,2]=>1260
[6,2,3,1,8,7,4,5]=>[4,2,1,1]=>2520
[3,4,8,1,7,5,6,2]=>[5,3]=>2688
[7,2,5,1,8,3,6,4]=>[7,1]=>5760
[4,2,8,1,7,5,6,3]=>[3,2,2,1]=>1680
[7,3,1,5,2,8,6,4]=>[8]=>5040
[7,1,6,4,2,8,5,3]=>[4,3,1]=>3360
[3,7,4,1,5,8,6,2]=>[4,3,1]=>3360
[5,8,6,1,2,7,4,3]=>[8]=>5040
[6,8,1,4,3,7,5,2]=>[5,2,1]=>4032
[6,7,1,4,3,8,5,2]=>[7,1]=>5760
[4,7,1,5,3,8,6,2]=>[4,4]=>1260
[6,8,1,2,4,7,5,3]=>[8]=>5040
[7,1,6,4,8,3,5,2]=>[5,2,1]=>4032
[8,6,4,1,3,7,5,2]=>[8]=>5040
[8,5,3,6,1,7,4,2]=>[4,3,1]=>3360
[8,5,6,1,2,7,4,3]=>[6,2]=>3360
[8,6,2,5,4,7,3,1]=>[4,2,2]=>1260
[8,5,7,3,2,4,6,1]=>[4,2,2]=>1260
[8,5,2,1,4,3,6,7]=>[8]=>5040
[8,1,2,4,5,6,7,3]=>[4,1,1,1,1]=>420
[6,1,4,3,2,7,8,5]=>[6,2]=>3360
[1,8,3,6,7,2,4,5]=>[6,1,1]=>3360
[1,2,8,3,7,4,6,5]=>[6,1,1]=>3360
[1,9,2,3,4,5,6,7,8,10]=>[8,1,1]=>226800
[1,7,2,3,4,5,6,8,9]=>[6,1,1,1]=>10080
[2,4,1,3,6,5,8,7,10,9,11]=>[4,2,2,2,1]=>207900
[8,2,6,5,4,3,1,7]=>[3,2,2,1]=>1680
[8,2,7,6,4,5,3,1]=>[3,2,2,1]=>1680
[8,7,3,5,4,2,6,1]=>[3,2,2,1]=>1680
[12,10,9,8,7,6,5,4,3,2,1,11]=>[3,2,2,2,2,1]=>415800
[4,6,7,2,1,8,3,5]=>[6,2]=>3360
[3,7,1,8,2,5,4,6]=>[6,2]=>3360
[4,5,8,6,1,3,7,2]=>[7,1]=>5760
[4,5,8,6,2,7,3,1]=>[6,2]=>3360
[4,6,7,1,5,3,8,2]=>[5,2,1]=>4032
[4,6,7,2,1,8,5,3]=>[8]=>5040
[4,2,5,6,7,8,3,1]=>[4,3,1]=>3360
[4,1,3,5,6,7,8,2]=>[7,1]=>5760
[3,7,8,4,5,1,6,2]=>[6,1,1]=>3360
[4,6,8,3,2,7,1,5]=>[8]=>5040
[4,6,8,2,3,7,1,5]=>[5,3]=>2688
[3,8,1,7,4,5,2,6]=>[6,2]=>3360
[4,5,8,3,7,1,2,6]=>[5,3]=>2688
[3,7,8,4,6,2,5,1]=>[4,3,1]=>3360
[3,6,1,5,7,8,2,4]=>[6,2]=>3360
[3,8,2,5,4,7,1,6]=>[6,2]=>3360
[3,8,6,2,5,1,7,4]=>[3,3,1,1]=>1120
[4,5,8,6,2,1,7,3]=>[3,2,2,1]=>1680
[4,5,8,6,1,2,7,3]=>[5,2,1]=>4032
[4,6,8,5,2,7,1,3]=>[6,2]=>3360
[3,7,8,5,2,6,1,4]=>[7,1]=>5760
[3,7,8,5,4,1,6,2]=>[6,2]=>3360
[4,6,8,5,3,1,7,2]=>[7,1]=>5760
[7,8,2,3,5,4,1,6]=>[5,2,1]=>4032
[4,6,5,2,7,8,1,3]=>[8]=>5040
[1,6,5,2,3,4,8,7]=>[3,2,2,1]=>1680
[4,6,5,1,7,3,8,2]=>[6,2]=>3360
[5,7,3,1,2,4,8,6]=>[7,1]=>5760
[6,3,2,5,1,7,4,8]=>[5,2,1]=>4032
[6,1,2,4,8,5,3,7]=>[7,1]=>5760
[3,6,5,8,1,7,2,4]=>[3,3,2]=>1120
[1,2,3,4,5,6,8,7,9]=>[2,1,1,1,1,1,1,1]=>36
[1,2,3,4,5,6,7,9,8,10]=>[2,1,1,1,1,1,1,1,1]=>45
[1,2,3,4,5,7,6,8,9]=>[2,1,1,1,1,1,1,1]=>36
[9,2,3,4,5,6,7,1,8]=>[3,1,1,1,1,1,1]=>168
[5,2,7,3,4,6,1,8]=>[5,1,1,1]=>1344
[1,3,5,8,6,4,7,2]=>[6,1,1]=>3360
[1,3,5,8,6,7,2,4]=>[5,2,1]=>4032
[6,1,7,4,8,5,3,2]=>[5,2,1]=>4032
[5,7,4,1,3,6,8,2]=>[4,3,1]=>3360
[7,4,3,1,6,5,8,2]=>[5,2,1]=>4032
[8,6,1,7,5,3,2,4]=>[7,1]=>5760
[7,8,1,4,6,5,3,2]=>[3,2,2,1]=>1680
[7,8,6,1,4,5,3,2]=>[6,2]=>3360
[6,2,7,3,8,5,4,1]=>[4,3,1]=>3360
[1,2,7,5,3,4,8,6]=>[6,1,1]=>3360
[7,2,8,3,6,4,5,1]=>[7,1]=>5760
[6,2,7,8,3,1,4,5]=>[5,2,1]=>4032
[1,7,8,2,5,3,4,6]=>[3,3,1,1]=>1120
[1,2,8,7,3,4,6,5]=>[3,3,1,1]=>1120
[8,2,7,4,5,1,6,3]=>[5,1,1,1]=>1344
[3,8,1,5,7,2,6,4]=>[6,2]=>3360
[7,5,4,8,6,1,2,3]=>[5,3]=>2688
[8,7,5,1,4,3,6,2]=>[8]=>5040
[8,4,1,3,7,5,6,2]=>[5,3]=>2688
[4,8,1,3,7,5,6,2]=>[3,3,2]=>1120
[4,5,1,3,8,6,7,2]=>[3,3,1,1]=>1120
[1,2,6,8,5,3,4,7]=>[3,2,1,1,1]=>1120
[5,6,8,7,3,1,2,4]=>[8]=>5040
[6,7,5,3,8,1,2,4]=>[4,2,2]=>1260
[6,8,5,7,3,1,2,4]=>[4,2,2]=>1260
[5,1,4,2,6,8,7,3]=>[7,1]=>5760
[6,3,2,4,7,1,8,5]=>[3,2,2,1]=>1680
[1,5,8,6,2,4,3,7]=>[3,2,2,1]=>1680
[5,1,8,6,2,4,3,7]=>[3,3,2]=>1120
[5,8,6,3,7,1,2,4]=>[8]=>5040
[5,7,6,3,8,1,2,4]=>[6,2]=>3360
[6,8,7,5,3,1,2,4]=>[6,2]=>3360
[1,2,5,3,6,8,7,4]=>[5,1,1,1]=>1344
[7,3,6,1,4,8,2,5]=>[8]=>5040
[7,8,1,6,5,3,4,2]=>[5,2,1]=>4032
[8,7,3,2,1,4,6,5]=>[4,3,1]=>3360
[8,3,5,1,7,4,2,6]=>[4,4]=>1260
[5,8,2,6,4,3,7,1]=>[7,1]=>5760
[2,8,6,3,4,1,7,5]=>[7,1]=>5760
[1,7,2,3,5,8,6,4]=>[6,1,1]=>3360
[2,8,3,7,5,1,6,4]=>[6,1,1]=>3360
[6,4,8,7,2,1,5,3]=>[4,2,2]=>1260
[2,8,4,3,6,7,1,5]=>[6,2]=>3360
[7,3,2,5,6,1,8,4]=>[6,2]=>3360
[1,6,7,8,2,4,3,5]=>[5,2,1]=>4032
[4,1,2,8,5,3,7,6]=>[6,1,1]=>3360
[3,8,4,2,5,1,7,6]=>[6,1,1]=>3360
[1,8,5,6,4,3,2,7]=>[4,3,1]=>3360
[2,8,3,5,6,4,1,7]=>[4,3,1]=>3360
[7,6,8,3,2,5,1,4]=>[3,3,2]=>1120
[2,7,1,4,5,3,8,6]=>[6,1,1]=>3360
[1,5,2,7,4,3,6,8]=>[6,1,1]=>3360
[5,1,3,8,4,6,2,7]=>[6,1,1]=>3360
[6,5,8,7,1,3,2,4]=>[8]=>5040
[2,7,3,5,1,6,8,4]=>[6,1,1]=>3360
[5,7,6,8,2,1,4,3]=>[8]=>5040
[1,3,6,5,2,7,4,8]=>[6,1,1]=>3360
[1,2,6,5,3,4,7,8]=>[4,1,1,1,1]=>420
[1,7,2,5,6,8,3,4]=>[4,3,1]=>3360
[1,7,2,4,8,3,5,6]=>[6,1,1]=>3360
[1,6,2,4,5,3,7,8]=>[3,1,1,1,1,1]=>112
[1,3,2,8,4,5,7,6]=>[4,2,1,1]=>2520
[1,6,8,2,4,3,5,7]=>[7,1]=>5760
[1,6,7,2,5,3,4,8]=>[5,1,1,1]=>1344
[1,2,8,3,6,7,4,5]=>[6,1,1]=>3360
[1,7,2,5,3,4,8,6]=>[7,1]=>5760
[10,3,4,5,6,7,8,9,1,2]=>[10]=>362880
[9,3,4,5,6,7,8,1,10,2]=>[10]=>362880
[8,3,4,5,6,7,1,9,10,2]=>[10]=>362880
[7,3,4,5,6,1,8,9,10,2]=>[10]=>362880
[6,3,4,5,1,7,8,9,10,2]=>[10]=>362880
[5,3,4,1,6,7,8,9,10,2]=>[10]=>362880
[4,3,1,5,6,7,8,9,10,2]=>[10]=>362880
[11,3,4,5,6,7,8,9,10,1,2]=>[11]=>3628800
[10,9,4,5,6,7,8,1,2,3]=>[8,2]=>226800
[10,3,4,5,6,7,8,9,1,11,2]=>[11]=>3628800
[10,3,8,5,6,7,1,9,2,4]=>[6,4]=>151200
[9,3,4,5,6,7,8,1,10,11,2]=>[11]=>3628800
[10,3,4,7,6,1,8,9,2,5]=>[6,4]=>151200
[8,3,4,5,6,7,1,9,10,11,2]=>[11]=>3628800
[10,3,4,5,1,7,8,9,2,6]=>[10]=>362880
[7,3,4,5,6,1,8,9,10,11,2]=>[11]=>3628800
[5,3,4,1,6,10,8,9,2,7]=>[10]=>362880
[6,3,4,5,1,7,8,9,10,11,2]=>[11]=>3628800
[4,3,1,5,6,7,10,9,2,8]=>[10]=>362880
[5,3,4,1,6,7,8,9,10,11,2]=>[11]=>3628800
[3,1,4,5,6,7,8,10,2,9]=>[10]=>362880
[4,3,1,5,6,7,8,9,10,11,2]=>[11]=>3628800
[7,1,5,6,2,3,8,4]=>[8]=>5040
[8,2,1,4,6,7,3,5]=>[6,1,1]=>3360
[7,2,6,1,3,4,8,5]=>[7,1]=>5760
[4,1,3,7,2,5,8,6]=>[7,1]=>5760
[6,2,7,5,1,3,8,4]=>[7,1]=>5760
[1,7,5,6,2,3,8,4]=>[7,1]=>5760
[3,7,6,1,2,4,8,5]=>[4,4]=>1260
[8,6,1,3,5,7,2,4]=>[4,3,1]=>3360
[1,7,4,3,8,2,5,6]=>[5,2,1]=>4032
[6,1,5,3,4,8,2,7]=>[5,3]=>2688
[3,6,7,5,2,8,1,4]=>[5,3]=>2688
[7,8,4,1,5,6,2,3]=>[6,1,1]=>3360
[5,8,1,3,6,7,2,4]=>[8]=>5040
[2,8,4,3,7,1,5,6]=>[4,2,2]=>1260
[3,8,4,6,7,1,2,5]=>[4,4]=>1260
[6,3,8,4,7,1,2,5]=>[5,2,1]=>4032
[1,2,5,4,8,3,6,7]=>[5,1,1,1]=>1344
[7,1,3,8,2,4,5,6]=>[4,3,1]=>3360
[8,1,3,7,2,4,5,6]=>[7,1]=>5760
[3,5,4,7,8,1,2,6]=>[8]=>5040
[8,3,1,4,7,2,5,6]=>[5,2,1]=>4032
[1,6,4,7,8,2,3,5]=>[3,2,2,1]=>1680
[5,2,3,6,7,8,1,4]=>[3,3,1,1]=>1120
[6,2,7,3,8,5,1,4]=>[7,1]=>5760
[1,3,7,8,5,6,2,4]=>[3,2,1,1,1]=>1120
[8,2,6,7,5,1,3,4]=>[6,1,1]=>3360
[8,1,7,4,6,2,3,5]=>[5,2,1]=>4032
[2,5,8,4,7,1,3,6]=>[7,1]=>5760
[4,5,8,7,1,2,3,6]=>[8]=>5040
[4,1,8,5,7,2,3,6]=>[8]=>5040
[1,8,7,4,6,2,3,5]=>[4,2,1,1]=>2520
[2,6,5,4,1,8,3,7]=>[7,1]=>5760
[6,2,5,1,4,8,3,7]=>[7,1]=>5760
[6,5,4,1,3,8,2,7]=>[8]=>5040
[6,3,5,4,2,8,1,7]=>[4,3,1]=>3360
[1,3,8,7,4,2,6,5]=>[7,1]=>5760
[8,7,4,3,1,5,2,6]=>[4,2,2]=>1260
[8,2,5,1,4,6,7,3]=>[5,1,1,1]=>1344
[3,8,4,5,1,6,7,2]=>[4,2,1,1]=>2520
[8,5,4,1,3,6,7,2]=>[6,1,1]=>3360
[8,3,1,7,5,6,4,2]=>[4,2,1,1]=>2520
[8,4,7,6,5,3,1,2]=>[7,1]=>5760
[8,1,4,5,7,6,3,2]=>[4,3,1]=>3360
[2,4,1,8,5,7,6,3]=>[5,2,1]=>4032
[8,2,1,4,7,6,3,5]=>[5,1,1,1]=>1344
[8,3,1,7,4,2,6,5]=>[8]=>5040
[8,2,7,3,1,6,5,4]=>[6,1,1]=>3360
[1,8,4,2,3,7,6,5]=>[5,2,1]=>4032
[3,1,2,8,7,4,6,5]=>[5,3]=>2688
[8,5,1,2,4,3,7,6]=>[4,3,1]=>3360
[2,8,3,7,4,1,6,5]=>[7,1]=>5760
[8,4,5,7,6,2,3,1]=>[6,2]=>3360
[2,3,1,8,7,6,4,5]=>[4,3,1]=>3360
[4,2,8,7,3,1,5,6]=>[7,1]=>5760
[1,3,4,8,7,2,5,6]=>[5,2,1]=>4032
[8,1,3,4,6,7,2,5]=>[6,1,1]=>3360
[3,4,8,2,6,7,1,5]=>[6,2]=>3360
[3,6,8,2,5,1,7,4]=>[6,1,1]=>3360
[3,8,2,5,7,4,6,1]=>[4,4]=>1260
[8,4,2,1,7,5,6,3]=>[5,3]=>2688
[8,2,7,5,6,4,1,3]=>[4,3,1]=>3360
[6,2,8,5,4,1,7,3]=>[2,2,2,1,1]=>420
[6,8,5,4,1,7,2,3]=>[7,1]=>5760
[2,8,1,5,7,6,3,4]=>[7,1]=>5760
[3,1,8,2,7,5,6,4]=>[5,3]=>2688
[8,5,7,1,6,4,2,3]=>[8]=>5040
[2,8,4,7,3,6,5,1]=>[4,3,1]=>3360
[8,4,7,2,1,6,5,3]=>[5,2,1]=>4032
[1,8,4,7,6,5,2,3]=>[5,2,1]=>4032
[3,5,8,1,7,4,6,2]=>[8]=>5040
[8,4,7,1,3,6,5,2]=>[4,3,1]=>3360
[8,2,3,9,5,6,7,1,4]=>[2,2,1,1,1,1,1]=>378
[8,2,9,4,5,6,7,1,3]=>[2,2,1,1,1,1,1]=>378
[8,9,3,4,5,6,7,1,2]=>[2,2,1,1,1,1,1]=>378
[4,2,3,1,9,8,7,6,5]=>[2,2,2,1,1,1]=>1260
[3,2,1,9,8,6,7,5,4]=>[2,2,2,1,1,1]=>1260
[9,2,10,4,5,6,7,8,1,3]=>[2,2,1,1,1,1,1,1]=>630
[2,3,4,7,6,8,1,5]=>[5,3]=>2688
[3,8,1,2,5,6,4,7]=>[4,2,1,1]=>2520
[3,7,1,2,5,6,4,8]=>[3,2,1,1,1]=>1120
[8,5,2,1,4,6,7,3]=>[6,1,1]=>3360
[4,8,1,6,5,2,7,3]=>[6,1,1]=>3360
[4,2,6,3,8,5,7,1]=>[6,1,1]=>3360
[4,5,2,6,7,1,8,3]=>[5,3]=>2688
[8,3,5,4,2,7,1,6]=>[4,3,1]=>3360
[2,8,6,4,7,3,1,5]=>[5,2,1]=>4032
[3,1,8,6,5,2,7,4]=>[6,1,1]=>3360
[8,3,1,5,2,6,7,4]=>[6,1,1]=>3360
[3,8,2,4,1,5,7,6]=>[6,1,1]=>3360
[5,8,3,2,4,1,7,6]=>[6,1,1]=>3360
[6,5,3,2,4,8,1,7]=>[4,3,1]=>3360
[5,2,4,6,1,3,8,7]=>[3,2,2,1]=>1680
[7,2,3,4,6,8,1,5]=>[3,2,1,1,1]=>1120
[8,3,4,6,7,5,1,2]=>[8]=>5040
[6,8,3,4,7,5,2,1]=>[6,1,1]=>3360
[5,8,6,1,3,4,7,2]=>[5,2,1]=>4032
[4,8,1,5,7,6,3,2]=>[5,2,1]=>4032
[3,7,4,6,8,2,5,1]=>[8]=>5040
[4,7,1,6,8,3,2,5]=>[4,2,2]=>1260
[4,5,2,8,1,7,3,6]=>[8]=>5040
[3,7,5,2,8,6,1,4]=>[7,1]=>5760
[4,8,5,2,6,7,1,3]=>[8]=>5040
[5,4,8,6,1,2,7,3]=>[3,2,2,1]=>1680
[8,4,6,5,2,7,3,1]=>[3,3,2]=>1120
[8,1,6,4,7,5,2,3]=>[7,1]=>5760
[5,2,7,6,4,8,1,3]=>[7,1]=>5760
[8,6,2,3,5,1,7,4]=>[6,1,1]=>3360
[8,2,5,7,4,1,3,6]=>[4,3,1]=>3360
[7,2,4,5,6,8,1,3]=>[5,2,1]=>4032
[7,1,3,5,6,2,8,4]=>[7,1]=>5760
[7,1,5,8,4,6,3,2]=>[7,1]=>5760
[6,3,8,4,7,1,5,2]=>[3,2,2,1]=>1680
[7,1,4,3,2,8,5,6]=>[4,2,2]=>1260
[5,3,6,1,4,2,8,7]=>[3,3,2]=>1120
[5,7,2,1,4,3,8,6]=>[5,3]=>2688
[7,1,8,3,5,2,4,6]=>[7,1]=>5760
[7,2,4,8,1,5,6,3]=>[4,3,1]=>3360
[7,1,8,4,2,5,6,3]=>[5,2,1]=>4032
[6,4,2,5,8,1,7,3]=>[5,2,1]=>4032
[2,1,7,5,8,3,6,4]=>[3,3,2]=>1120
[7,3,8,5,6,2,1,4]=>[6,2]=>3360
[2,7,4,8,1,5,6,3]=>[5,3]=>2688
[7,4,8,3,1,5,6,2]=>[4,4]=>1260
[6,1,5,8,3,7,4,2]=>[6,2]=>3360
[2,6,3,5,8,7,4,1]=>[7,1]=>5760
[8,6,5,3,7,2,1,4]=>[6,2]=>3360
[4,8,5,3,7,2,1,6]=>[5,3]=>2688
[7,4,8,6,5,3,2,1]=>[7,1]=>5760
[7,4,8,5,6,3,1,2]=>[6,2]=>3360
[7,8,4,1,3,5,6,2]=>[6,2]=>3360
[7,8,3,4,1,5,6,2]=>[4,2,1,1]=>2520
[7,3,1,8,2,5,6,4]=>[6,2]=>3360
[7,2,3,8,1,5,6,4]=>[4,2,1,1]=>2520
[6,4,8,7,3,2,1,5]=>[5,3]=>2688
[2,7,4,8,6,3,1,5]=>[5,3]=>2688
[6,4,8,2,3,1,7,5]=>[3,2,2,1]=>1680
[7,2,1,8,3,5,6,4]=>[5,2,1]=>4032
[5,1,6,3,8,2,4,7]=>[8]=>5040
[3,6,5,1,4,8,7,2]=>[4,3,1]=>3360
[7,5,4,8,1,6,2,3]=>[4,3,1]=>3360
[4,3,5,8,7,1,2,6]=>[4,4]=>1260
[3,5,6,8,1,4,2,7]=>[8]=>5040
[4,3,5,8,2,1,6,7]=>[5,3]=>2688
[6,4,7,2,3,1,5,8]=>[3,2,2,1]=>1680
[6,8,1,5,4,2,7,3]=>[5,2,1]=>4032
[7,8,6,3,5,1,2,4]=>[7,1]=>5760
[6,1,8,4,7,2,3,5]=>[4,3,1]=>3360
[5,6,4,3,7,1,8,2]=>[6,2]=>3360
[6,5,3,7,2,4,8,1]=>[5,2,1]=>4032
[5,6,2,8,4,3,7,1]=>[4,3,1]=>3360
[7,1,3,6,5,8,4,2]=>[6,1,1]=>3360
[5,7,4,3,6,8,2,1]=>[4,2,2]=>1260
[4,6,2,7,8,3,5,1]=>[5,3]=>2688
[5,1,2,4,6,7,8,3]=>[7,1]=>5760
[4,6,3,5,2,8,7,1]=>[6,1,1]=>3360
[5,6,3,4,8,2,7,1]=>[3,2,1,1,1]=>1120
[5,2,6,4,1,7,8,3]=>[4,2,1,1]=>2520
[5,8,4,6,3,2,7,1]=>[7,1]=>5760
[5,4,3,8,6,2,7,1]=>[6,1,1]=>3360
[5,7,8,2,4,3,6,1]=>[8]=>5040
[5,6,2,4,8,3,7,1]=>[3,3,1,1]=>1120
[6,4,7,8,2,3,5,1]=>[8]=>5040
[3,7,5,2,4,8,1,6]=>[6,2]=>3360
[4,7,5,2,3,8,6,1]=>[6,2]=>3360
[6,4,7,3,2,5,8,1]=>[8]=>5040
[5,7,3,2,8,4,6,1]=>[4,3,1]=>3360
[5,3,7,2,8,4,6,1]=>[5,3]=>2688
[4,3,7,2,5,8,6,1]=>[7,1]=>5760
[4,7,3,2,5,8,6,1]=>[6,1,1]=>3360
[4,7,3,2,6,8,5,1]=>[7,1]=>5760
[7,5,3,2,6,4,8,1]=>[4,3,1]=>3360
[8,5,2,6,7,3,4,1]=>[6,2]=>3360
[8,4,2,6,3,7,5,1]=>[6,2]=>3360
[7,4,6,2,3,8,5,1]=>[6,2]=>3360
[7,5,6,2,8,3,4,1]=>[6,2]=>3360
[5,7,6,2,8,3,4,1]=>[3,3,2]=>1120
[4,7,6,2,3,8,5,1]=>[8]=>5040
[7,6,3,2,5,8,1,4]=>[4,2,1,1]=>2520
[7,6,4,2,5,8,3,1]=>[7,1]=>5760
[2,10,4,5,6,7,8,9,1,3]=>[10]=>362880
[9,8,4,5,6,7,1,2,10,3]=>[8,2]=>226800
[2,10,9,5,6,7,8,1,3,4]=>[8,2]=>226800
[2,11,4,5,6,7,8,9,10,1,3]=>[11]=>3628800
[11,3,4,5,6,7,8,9,10,1,12,2]=>[12]=>39916800
[9,3,8,5,6,7,1,2,10,4]=>[7,3]=>172800
[9,7,4,5,6,1,8,2,10,3]=>[7,3]=>172800
[2,10,4,9,6,7,8,1,3,5]=>[7,3]=>172800
[2,10,8,5,6,7,1,9,3,4]=>[7,3]=>172800
[2,12,4,5,6,7,8,9,10,11,1,3]=>[12]=>39916800
[6,3,8,5,4,7,2,1]=>[6,2]=>3360
[1,3,2,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]=>36
[1,4,2,3,5,6,7,8,9]=>[3,1,1,1,1,1,1]=>168
[1,3,2,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]=>45
[2,4,6,3,8,7,5,1]=>[8]=>5040
[2,4,3,6,8,7,1,5]=>[5,2,1]=>4032
[2,4,6,3,8,7,1,5]=>[6,2]=>3360
[2,4,6,5,8,7,1,3]=>[8]=>5040
[2,4,6,8,5,7,3,1]=>[4,3,1]=>3360
[2,4,6,8,5,7,1,3]=>[7,1]=>5760
[2,4,6,8,3,7,1,5]=>[8]=>5040
[2,4,6,8,1,7,3,5]=>[5,3]=>2688
[2,4,6,5,8,3,7,1]=>[5,2,1]=>4032
[2,4,6,5,8,1,7,3]=>[7,1]=>5760
[2,4,6,8,5,1,7,3]=>[6,1,1]=>3360
[2,4,6,8,7,3,5,1]=>[4,2,2]=>1260
[2,4,6,8,7,1,5,3]=>[6,2]=>3360
[2,4,6,8,7,1,3,5]=>[8]=>5040
[2,4,6,8,5,1,3,7]=>[7,1]=>5760
[2,4,6,5,1,8,3,7]=>[4,4]=>1260
[2,4,6,5,3,8,1,7]=>[8]=>5040
[2,4,6,5,8,3,1,7]=>[6,2]=>3360
[2,4,6,8,5,3,1,7]=>[5,2,1]=>4032
[2,4,6,8,7,3,1,5]=>[6,2]=>3360
[2,4,6,8,7,5,1,3]=>[8]=>5040
[4,8,7,5,2,1,3,6]=>[6,2]=>3360
[6,1,4,7,5,8,2,3]=>[7,1]=>5760
[1,8,6,5,3,2,7,4]=>[6,1,1]=>3360
[1,6,3,5,8,2,4,7]=>[4,2,1,1]=>2520
[4,6,1,7,8,5,3,2]=>[4,4]=>1260
[6,1,2,7,8,4,5,3]=>[8]=>5040
[6,1,3,2,7,8,5,4]=>[5,2,1]=>4032
[5,6,3,1,7,4,8,2]=>[7,1]=>5760
[4,8,3,7,1,6,5,2]=>[4,2,1,1]=>2520
[8,7,2,6,5,1,4,3]=>[7,1]=>5760
[5,8,3,2,1,7,6,4]=>[3,2,2,1]=>1680
[5,4,3,8,1,7,6,2]=>[3,2,2,1]=>1680
[6,5,3,8,7,1,4,2]=>[5,2,1]=>4032
[4,3,8,2,7,6,5,1]=>[5,2,1]=>4032
[4,8,2,7,6,5,3,1]=>[6,2]=>3360
[7,8,2,6,5,4,1,3]=>[3,2,2,1]=>1680
[3,8,7,6,2,5,1,4]=>[5,3]=>2688
[4,8,3,7,2,1,6,5]=>[4,3,1]=>3360
[8,6,3,1,7,5,4,2]=>[7,1]=>5760
[8,6,3,7,1,5,4,2]=>[5,2,1]=>4032
[4,8,3,7,6,2,5,1]=>[7,1]=>5760
[5,8,2,7,6,4,1,3]=>[5,3]=>2688
[8,4,2,1,7,6,5,3]=>[5,2,1]=>4032
[1,6,4,2,5,3,7,8]=>[4,1,1,1,1]=>420
[1,8,6,2,7,3,4,5]=>[5,2,1]=>4032
[1,6,3,2,4,5,7,8]=>[4,1,1,1,1]=>420
[1,5,2,6,4,3,7,8]=>[5,1,1,1]=>1344
[1,5,2,4,6,3,7,8]=>[4,1,1,1,1]=>420
[1,8,6,2,3,7,4,5]=>[7,1]=>5760
[1,5,2,8,6,3,4,7]=>[4,3,1]=>3360
[1,3,6,8,2,7,4,5]=>[7,1]=>5760
[1,4,3,8,2,5,6,7]=>[6,1,1]=>3360
[1,7,2,3,8,5,4,6]=>[4,3,1]=>3360
[1,3,8,4,2,5,6,7]=>[6,1,1]=>3360
[1,6,2,8,5,4,3,7]=>[6,1,1]=>3360
[1,7,2,3,8,6,4,5]=>[4,2,1,1]=>2520
[1,5,3,8,2,7,4,6]=>[4,2,1,1]=>2520
[1,4,8,2,5,6,3,7]=>[3,2,1,1,1]=>1120
[1,5,7,3,2,8,4,6]=>[3,2,2,1]=>1680
[1,2,7,3,6,8,4,5]=>[3,3,1,1]=>1120
[1,7,2,3,6,8,4,5]=>[4,3,1]=>3360
[1,4,8,3,2,5,6,7]=>[7,1]=>5760
[1,7,2,5,8,3,4,6]=>[7,1]=>5760
[8,2,3,4,5,6,7,9,1]=>[3,1,1,1,1,1,1]=>168
[7,2,3,4,5,6,9,8,1]=>[3,1,1,1,1,1,1]=>168
[6,2,3,4,5,9,7,8,1]=>[3,1,1,1,1,1,1]=>168
[5,2,3,4,9,6,7,8,1]=>[3,1,1,1,1,1,1]=>168
[4,2,3,9,5,6,7,8,1]=>[3,1,1,1,1,1,1]=>168
[3,2,9,4,5,6,7,8,1]=>[3,1,1,1,1,1,1]=>168
[2,9,3,4,5,6,7,8,1]=>[3,1,1,1,1,1,1]=>168
[9,2,3,4,5,6,7,8,10,1]=>[3,1,1,1,1,1,1,1]=>240
[6,2,3,4,5,1,8,9,7]=>[3,2,1,1,1,1]=>2520
[8,2,3,4,5,6,7,10,9,1]=>[3,1,1,1,1,1,1,1]=>240
[5,2,3,4,1,7,9,8,6]=>[3,2,1,1,1,1]=>2520
[7,2,3,4,5,6,10,8,9,1]=>[3,1,1,1,1,1,1,1]=>240
[6,2,3,5,8,1,7,4]=>[3,2,1,1,1]=>1120
[4,2,3,1,6,9,7,8,5]=>[3,2,1,1,1,1]=>2520
[6,2,3,4,5,10,7,8,9,1]=>[3,1,1,1,1,1,1,1]=>240
[5,2,4,8,1,6,7,3]=>[3,2,1,1,1]=>1120
[3,2,1,5,9,6,7,8,4]=>[3,2,1,1,1,1]=>2520
[5,2,3,4,10,6,7,8,9,1]=>[3,1,1,1,1,1,1,1]=>240
[2,1,4,9,5,6,7,8,3]=>[3,2,1,1,1,1]=>2520
[4,2,3,10,5,6,7,8,9,1]=>[3,1,1,1,1,1,1,1]=>240
[1,3,9,4,5,6,7,8,2]=>[3,1,1,1,1,1,1]=>168
[3,2,10,4,5,6,7,8,9,1]=>[3,1,1,1,1,1,1,1]=>240
[2,10,3,4,5,6,7,8,9,1]=>[3,1,1,1,1,1,1,1]=>240
[2,6,4,5,7,3,1,8]=>[7,1]=>5760
[1,3,7,5,6,8,4,2]=>[7,1]=>5760
[1,3,6,7,4,5,8,2]=>[7,1]=>5760
[1,5,6,3,4,2,7,8]=>[5,1,1,1]=>1344
[1,5,3,6,4,2,7,8]=>[4,1,1,1,1]=>420
[1,5,3,7,4,6,2,8]=>[4,1,1,1,1]=>420
[1,5,7,3,6,4,8,2]=>[7,1]=>5760
[2,5,7,4,1,3,8,6]=>[4,3,1]=>3360
[6,7,3,1,8,5,2,4]=>[5,2,1]=>4032
[4,6,3,5,8,2,1,7]=>[5,2,1]=>4032
[7,2,4,8,6,3,1,5]=>[5,2,1]=>4032
[7,4,5,2,1,8,6,3]=>[6,2]=>3360
[4,7,5,2,1,8,6,3]=>[8]=>5040
[8,5,3,6,2,1,7,4]=>[4,2,1,1]=>2520
[4,5,7,3,1,2,8,6]=>[8]=>5040
[4,5,1,8,3,2,7,6]=>[7,1]=>5760
[5,7,4,6,3,2,1,8]=>[7,1]=>5760
[3,6,1,2,4,8,7,5]=>[5,2,1]=>4032
[2,5,3,8,4,1,7,6]=>[6,1,1]=>3360
[7,5,2,3,1,8,6,4]=>[8]=>5040
[6,3,1,2,4,8,7,5]=>[7,1]=>5760
[4,7,5,2,3,6,1,8]=>[4,2,1,1]=>2520
[3,6,8,4,5,1,2,7]=>[6,1,1]=>3360
[5,2,3,7,6,4,1,8]=>[5,1,1,1]=>1344
[6,2,7,3,5,4,1,8]=>[5,1,1,1]=>1344
[7,2,6,5,3,4,1,8]=>[4,2,1,1]=>2520
[8,2,6,5,4,1,3,7]=>[5,2,1]=>4032
[6,2,8,4,5,1,3,7]=>[3,2,1,1,1]=>1120
[2,3,1,7,8,5,6,4]=>[5,3]=>2688
[7,2,8,5,1,4,3,6]=>[7,1]=>5760
[8,6,7,1,4,2,3,5]=>[4,2,2]=>1260
[6,8,7,1,4,3,2,5]=>[8]=>5040
[6,8,2,5,3,1,4,7]=>[6,2]=>3360
[3,7,8,5,1,4,2,6]=>[6,2]=>3360
[4,8,7,3,1,2,5,6]=>[5,3]=>2688
[4,8,6,2,3,1,5,7]=>[8]=>5040
[3,8,5,4,2,1,6,7]=>[7,1]=>5760
[4,5,3,8,2,1,6,7]=>[5,2,1]=>4032
[3,7,4,1,8,2,6,5]=>[3,3,2]=>1120
[3,8,4,1,7,6,2,5]=>[4,3,1]=>3360
[3,7,2,1,8,4,6,5]=>[6,2]=>3360
[8,7,1,6,5,2,3,4]=>[7,1]=>5760
[8,5,1,2,7,6,3,4]=>[7,1]=>5760
[3,8,2,1,7,6,4,5]=>[7,1]=>5760
[3,5,7,8,2,4,6,1]=>[6,2]=>3360
[7,8,2,5,4,3,6,1]=>[6,2]=>3360
[4,5,3,7,8,2,6,1]=>[7,1]=>5760
[1,5,4,7,3,6,2,8]=>[5,1,1,1]=>1344
[1,7,3,6,8,4,5,2]=>[4,2,1,1]=>2520
[4,6,8,2,7,3,5,1]=>[6,2]=>3360
[4,7,6,3,5,1,8,2]=>[4,3,1]=>3360
[7,8,3,6,1,5,4,2]=>[5,2,1]=>4032
[2,5,7,8,4,6,1,3]=>[7,1]=>5760
[3,7,5,6,2,1,4,8]=>[7,1]=>5760
[6,2,1,7,4,5,3,8]=>[6,1,1]=>3360
[1,2,6,4,7,5,3,8]=>[4,1,1,1,1]=>420
[7,5,6,3,8,4,2,1]=>[5,3]=>2688
[8,5,4,2,1,6,7,3]=>[6,1,1]=>3360
[2,6,8,4,7,5,1,3]=>[5,2,1]=>4032
[6,7,5,1,4,8,3,2]=>[8]=>5040
[7,4,1,6,5,3,8,2]=>[7,1]=>5760
[5,8,2,7,3,6,4,1]=>[5,2,1]=>4032
[1,6,5,7,3,8,4,2]=>[3,2,2,1]=>1680
[1,5,6,8,4,2,7,3]=>[6,1,1]=>3360
[7,5,4,1,8,2,6,3]=>[8]=>5040
[6,4,1,8,2,7,5,3]=>[8]=>5040
[7,8,5,3,2,6,1,4]=>[5,2,1]=>4032
[8,2,5,1,7,6,4,3]=>[6,1,1]=>3360
[6,7,4,3,8,2,5,1]=>[6,2]=>3360
[3,4,2,7,8,6,1,5]=>[5,2,1]=>4032
[7,8,6,1,4,3,2,5]=>[6,2]=>3360
[2,4,7,8,6,1,3,5]=>[6,2]=>3360
[3,7,8,6,5,2,4,1]=>[4,3,1]=>3360
[4,5,2,7,8,6,3,1]=>[7,1]=>5760
[4,6,2,5,3,1,7,8]=>[6,1,1]=>3360
[4,1,5,6,3,2,7,8]=>[4,2,1,1]=>2520
[2,6,7,5,4,1,3,8]=>[3,2,2,1]=>1680
[4,1,6,7,5,3,2,8]=>[4,2,1,1]=>2520
[6,7,4,3,1,5,2,8]=>[3,2,2,1]=>1680
[1,7,5,6,4,3,2,8]=>[4,2,1,1]=>2520
[7,6,5,3,1,8,4,2]=>[5,3]=>2688
[7,8,6,4,3,1,5,2]=>[5,2,1]=>4032
[4,1,7,8,6,5,3,2]=>[4,2,2]=>1260
[4,5,7,3,8,6,1,2]=>[4,3,1]=>3360
[6,8,5,3,7,2,1,4]=>[8]=>5040
[4,7,1,5,8,2,6,3]=>[5,3]=>2688
[2,7,5,8,3,6,4,1]=>[5,2,1]=>4032
[7,4,8,2,6,5,3,1]=>[4,2,2]=>1260
[7,5,4,8,2,6,3,1]=>[5,2,1]=>4032
[4,3,8,1,6,5,2,7]=>[4,2,2]=>1260
[2,3,6,5,7,8,1,4]=>[8]=>5040
[8,3,4,1,2,6,7,5]=>[6,1,1]=>3360
[7,3,4,8,5,2,1,6]=>[5,2,1]=>4032
[7,3,8,4,1,5,6,2]=>[4,3,1]=>3360
[7,2,4,5,1,8,3,6]=>[5,2,1]=>4032
[7,3,1,2,8,5,6,4]=>[8]=>5040
[4,8,2,3,5,7,6,1]=>[5,2,1]=>4032
[4,5,2,3,8,6,7,1]=>[6,1,1]=>3360
[6,7,4,8,5,3,2,1]=>[5,2,1]=>4032
[4,3,5,6,1,7,8,2]=>[8]=>5040
[3,5,2,6,4,7,8,1]=>[8]=>5040
[4,1,2,8,5,7,6,3]=>[5,2,1]=>4032
[3,1,5,6,4,7,8,2]=>[8]=>5040
[3,1,4,6,7,5,8,2]=>[8]=>5040
[2,6,4,5,8,1,3,7]=>[5,3]=>2688
[6,4,1,3,5,8,2,7]=>[7,1]=>5760
[3,4,1,7,2,6,8,5]=>[5,2,1]=>4032
[2,4,7,5,8,1,3,6]=>[6,2]=>3360
[3,1,6,4,8,7,5,2]=>[7,1]=>5760
[3,7,6,2,1,5,8,4]=>[4,4]=>1260
[4,2,6,1,3,7,8,5]=>[5,2,1]=>4032
[8,5,4,2,7,6,3,1]=>[5,2,1]=>4032
[2,8,4,6,7,1,3,5]=>[8]=>5040
[5,8,2,1,4,6,7,3]=>[3,3,1,1]=>1120
[8,4,6,1,2,5,7,3]=>[7,1]=>5760
[3,7,8,4,2,6,5,1]=>[3,3,1,1]=>1120
[5,6,2,8,7,1,3,4]=>[6,2]=>3360
[7,1,3,8,4,5,6,2]=>[7,1]=>5760
[7,8,1,4,3,5,6,2]=>[5,2,1]=>4032
[3,6,7,2,8,1,5,4]=>[8]=>5040
[2,6,7,1,3,5,8,4]=>[8]=>5040
[3,6,7,1,8,2,5,4]=>[6,2]=>3360
[3,4,1,8,7,2,6,5]=>[6,2]=>3360
[3,1,5,7,2,8,6,4]=>[4,4]=>1260
[3,8,1,4,7,2,6,5]=>[5,2,1]=>4032
[4,8,1,3,2,7,6,5]=>[3,3,2]=>1120
[4,1,8,3,2,7,6,5]=>[6,2]=>3360
[4,3,8,1,2,7,6,5]=>[4,2,2]=>1260
[3,8,4,2,7,1,6,5]=>[8]=>5040
[2,8,4,3,7,6,1,5]=>[5,2,1]=>4032
[3,2,4,8,7,1,6,5]=>[7,1]=>5760
[3,2,5,7,1,8,6,4]=>[4,3,1]=>3360
[4,2,8,3,1,7,6,5]=>[5,2,1]=>4032
[4,8,2,1,3,7,6,5]=>[4,2,2]=>1260
[4,2,8,1,3,7,6,5]=>[3,2,2,1]=>1680
[2,3,4,6,8,7,1,5]=>[6,2]=>3360
[5,6,4,7,1,2,8,3]=>[4,2,2]=>1260
[4,5,7,1,6,8,3,2]=>[4,2,2]=>1260
[3,2,7,6,8,1,4,5]=>[5,2,1]=>4032
[4,5,1,7,6,8,2,3]=>[8]=>5040
[6,7,2,8,3,1,4,5]=>[6,2]=>3360
[7,6,3,1,2,8,4,5]=>[4,3,1]=>3360
[6,2,7,8,4,1,3,5]=>[3,2,2,1]=>1680
[6,3,7,8,4,1,2,5]=>[3,3,2]=>1120
[7,8,5,2,4,1,3,6]=>[8]=>5040
[7,6,2,3,1,8,4,5]=>[8]=>5040
[4,2,5,1,3,7,8,6]=>[3,2,2,1]=>1680
[3,4,1,7,8,5,2,6]=>[3,3,2]=>1120
[4,1,3,7,8,5,2,6]=>[4,3,1]=>3360
[4,3,1,8,5,2,7,6]=>[6,1,1]=>3360
[7,6,3,5,8,4,2,1]=>[7,1]=>5760
[4,5,1,3,2,7,8,6]=>[3,3,2]=>1120
[5,1,3,2,4,7,8,6]=>[4,3,1]=>3360
[2,3,7,8,5,4,1,6]=>[4,3,1]=>3360
[8,3,5,6,1,7,2,4]=>[8]=>5040
[4,5,8,1,2,6,7,3]=>[2,2,2,1,1]=>420
[5,3,6,7,8,2,1,4]=>[5,3]=>2688
[1,3,4,8,6,2,7,5]=>[6,1,1]=>3360
[7,2,4,1,3,8,5,6]=>[5,2,1]=>4032
[8,4,5,2,6,1,7,3]=>[5,2,1]=>4032
[4,6,8,2,3,7,5,1]=>[8]=>5040
[4,5,7,2,3,6,1,8]=>[6,1,1]=>3360
[2,7,3,4,1,5,6,8]=>[5,1,1,1]=>1344
[6,7,2,3,4,8,1,5]=>[8]=>5040
[3,5,2,4,6,7,8,1]=>[7,1]=>5760
[4,2,6,3,5,7,8,1]=>[6,1,1]=>3360
[2,3,4,5,6,1,8,7,9]=>[6,2,1]=>30240
[2,3,4,5,1,7,6,8,9]=>[5,2,1,1]=>18144
[2,3,4,1,6,5,7,8,9]=>[4,2,1,1,1]=>7560
[2,3,1,5,4,6,7,8,9]=>[3,2,1,1,1,1]=>2520
[1,4,8,5,6,2,7,3]=>[4,2,1,1]=>2520
[2,8,7,4,5,1,6,3]=>[6,1,1]=>3360
[1,3,8,5,2,6,7,4]=>[5,1,1,1]=>1344
[7,2,8,4,5,1,6,3]=>[3,2,1,1,1]=>1120
[8,6,2,4,1,5,7,3]=>[6,1,1]=>3360
[1,6,4,3,2,7,8,5]=>[5,2,1]=>4032
[8,5,3,2,1,6,7,4]=>[5,1,1,1]=>1344
[1,7,5,2,3,6,8,4]=>[4,2,1,1]=>2520
[7,1,5,2,3,6,8,4]=>[5,2,1]=>4032
[8,1,2,5,3,6,7,4]=>[6,1,1]=>3360
[8,4,1,6,3,7,2,5]=>[4,4]=>1260
[6,7,5,3,8,2,1,4]=>[4,4]=>1260
[5,2,6,8,3,7,1,4]=>[5,2,1]=>4032
[4,2,5,8,6,7,1,3]=>[7,1]=>5760
[5,8,6,3,4,1,7,2]=>[5,2,1]=>4032
[3,7,2,4,1,8,6,5]=>[7,1]=>5760
[2,4,7,8,5,1,3,6]=>[5,2,1]=>4032
[2,5,3,8,4,1,6,7]=>[7,1]=>5760
[3,1,7,4,5,6,2,8]=>[4,1,1,1,1]=>420
[2,4,8,3,5,7,1,6]=>[7,1]=>5760
[8,1,7,2,4,3,5,6]=>[8]=>5040
[1,3,8,2,4,7,5,6]=>[7,1]=>5760
[1,3,7,2,4,6,5,8]=>[5,1,1,1]=>1344
[1,7,3,2,4,6,5,8]=>[4,1,1,1,1]=>420
[1,8,3,7,4,2,5,6]=>[3,3,1,1]=>1120
[8,7,3,1,4,2,5,6]=>[7,1]=>5760
[2,8,4,3,5,7,1,6]=>[5,2,1]=>4032
[3,2,8,7,4,1,5,6]=>[4,3,1]=>3360
[3,2,1,7,4,6,5,8]=>[3,2,1,1,1]=>1120
[3,2,6,5,1,7,8,4]=>[7,1]=>5760
[5,3,2,6,7,1,8,4]=>[6,2]=>3360
[3,2,8,6,7,4,1,5]=>[5,2,1]=>4032
[8,4,6,2,7,3,1,5]=>[4,2,2]=>1260
[4,3,8,6,7,2,1,5]=>[8]=>5040
[4,3,6,2,8,7,1,5]=>[6,2]=>3360
[3,8,4,7,6,5,1,2]=>[4,2,2]=>1260
[7,8,4,2,6,3,5,1]=>[8]=>5040
[3,2,7,8,6,4,5,1]=>[7,1]=>5760
[3,2,7,5,6,8,4,1]=>[7,1]=>5760
[5,7,8,6,3,2,4,1]=>[4,4]=>1260
[6,5,4,2,1,7,8,3]=>[8]=>5040
[5,4,2,1,7,6,3,8]=>[6,1,1]=>3360
[4,1,6,5,2,7,8,3]=>[4,4]=>1260
[5,4,1,6,7,2,8,3]=>[5,3]=>2688
[6,8,5,3,1,7,2,4]=>[8]=>5040
[5,2,6,3,8,7,1,4]=>[7,1]=>5760
[8,6,1,7,3,4,2,5]=>[4,4]=>1260
[1,8,3,6,7,4,2,5]=>[4,2,1,1]=>2520
[1,6,3,5,2,7,8,4]=>[6,1,1]=>3360
[1,5,7,3,2,6,4,8]=>[3,2,1,1,1]=>1120
[5,1,3,7,2,6,4,8]=>[3,2,1,1,1]=>1120
[8,1,6,7,2,4,3,5]=>[4,4]=>1260
[6,1,4,8,2,7,3,5]=>[8]=>5040
[6,2,4,8,3,7,1,5]=>[4,3,1]=>3360
[8,7,2,6,3,5,1,4]=>[8]=>5040
[8,1,7,6,5,2,3,4]=>[5,2,1]=>4032
[7,1,5,6,8,2,4,3]=>[5,3]=>2688
[6,7,1,5,2,4,8,3]=>[8]=>5040
[7,6,1,5,2,4,3,8]=>[4,3,1]=>3360
[7,1,6,3,5,4,2,8]=>[3,3,1,1]=>1120
[1,6,7,3,5,4,8,2]=>[6,1,1]=>3360
[1,7,3,5,6,8,4,2]=>[6,1,1]=>3360
[1,7,8,3,6,4,5,2]=>[7,1]=>5760
[1,8,7,6,4,5,2,3]=>[4,3,1]=>3360
[8,2,7,4,6,5,1,3]=>[4,2,1,1]=>2520
[2,8,5,7,6,4,1,3]=>[8]=>5040
[7,4,5,1,6,8,3,2]=>[8]=>5040
[4,1,7,5,6,8,3,2]=>[6,2]=>3360
[5,6,7,4,3,1,8,2]=>[7,1]=>5760
[6,7,8,5,3,1,4,2]=>[6,2]=>3360
[1,4,6,2,5,3,7,8]=>[2,2,1,1,1,1]=>210
[1,6,3,2,5,4,7,8]=>[3,1,1,1,1,1]=>112
[1,6,8,2,5,4,7,3]=>[3,2,1,1,1]=>1120
[1,5,4,2,6,3,7,8]=>[5,1,1,1]=>1344
[1,2,6,4,3,5,7,8]=>[3,1,1,1,1,1]=>112
[1,6,8,2,7,5,4,3]=>[5,2,1]=>4032
[1,7,4,3,2,6,8,5]=>[4,2,1,1]=>2520
[1,5,4,7,2,6,8,3]=>[4,2,1,1]=>2520
[1,3,7,6,2,8,5,4]=>[4,3,1]=>3360
[1,7,6,2,8,4,3,5]=>[5,2,1]=>4032
[1,5,2,8,4,3,7,6]=>[6,1,1]=>3360
[1,2,8,4,3,6,5,7]=>[4,1,1,1,1]=>420
[1,2,8,5,6,3,4,7]=>[6,1,1]=>3360
[1,7,3,5,2,8,6,4]=>[6,1,1]=>3360
[1,6,7,2,5,8,4,3]=>[6,1,1]=>3360
[1,5,8,3,2,7,4,6]=>[5,2,1]=>4032
[1,4,5,8,2,6,3,7]=>[6,1,1]=>3360
[1,7,6,4,8,2,5,3]=>[6,1,1]=>3360
[1,4,8,6,5,2,7,3]=>[3,2,1,1,1]=>1120
[1,3,8,2,6,5,4,7]=>[5,2,1]=>4032
[1,7,6,3,8,2,4,5]=>[5,2,1]=>4032
[1,5,2,7,6,4,8,3]=>[7,1]=>5760
[1,2,4,3,8,7,5,6]=>[4,2,1,1]=>2520
[1,4,3,8,7,2,5,6]=>[4,2,1,1]=>2520
[1,3,8,6,2,4,5,7]=>[5,2,1]=>4032
[1,3,8,5,4,2,6,7]=>[5,2,1]=>4032
[1,7,2,4,8,6,5,3]=>[5,1,1,1]=>1344
[1,6,5,3,2,8,7,4]=>[6,1,1]=>3360
[1,3,2,8,7,5,4,6]=>[5,2,1]=>4032
[1,2,8,6,5,4,3,7]=>[3,2,1,1,1]=>1120
[8,1,3,4,6,5,2,7]=>[4,2,1,1]=>2520
[8,3,1,4,6,5,2,7]=>[5,2,1]=>4032
[5,8,3,1,2,6,4,7]=>[6,1,1]=>3360
[4,8,1,7,5,2,3,6]=>[4,3,1]=>3360
[4,8,1,7,5,2,6,3]=>[7,1]=>5760
[8,5,1,4,2,6,3,7]=>[4,2,1,1]=>2520
[8,4,1,3,5,6,2,7]=>[6,1,1]=>3360
[8,5,3,2,1,6,4,7]=>[6,1,1]=>3360
[8,1,5,4,2,6,3,7]=>[6,1,1]=>3360
[8,5,2,4,1,6,3,7]=>[6,1,1]=>3360
[4,8,7,1,5,2,6,3]=>[5,2,1]=>4032
[4,8,7,1,5,2,3,6]=>[3,2,2,1]=>1680
[7,6,8,4,1,3,2,5]=>[7,1]=>5760
[7,6,8,4,1,3,5,2]=>[4,3,1]=>3360
[3,8,7,5,4,1,2,6]=>[6,2]=>3360
[4,8,2,7,5,1,3,6]=>[7,1]=>5760
[7,6,8,4,1,5,2,3]=>[5,2,1]=>4032
[8,7,6,1,5,2,3,4]=>[4,3,1]=>3360
[7,1,4,8,6,3,5,2]=>[8]=>5040
[8,1,6,5,3,4,7,2]=>[4,3,1]=>3360
[8,6,2,5,3,4,7,1]=>[5,2,1]=>4032
[8,6,5,1,3,4,7,2]=>[5,2,1]=>4032
[8,7,5,1,3,6,2,4]=>[3,2,2,1]=>1680
[8,7,1,5,3,6,2,4]=>[5,2,1]=>4032
[8,6,1,3,5,4,7,2]=>[6,1,1]=>3360
[7,1,4,8,3,6,5,2]=>[7,1]=>5760
[7,8,5,2,4,3,6,1]=>[8]=>5040
[7,3,8,2,5,4,6,1]=>[7,1]=>5760
[8,4,2,5,3,7,6,1]=>[4,2,2]=>1260
[4,8,1,5,3,7,6,2]=>[4,2,2]=>1260
[7,4,8,2,6,3,5,1]=>[6,2]=>3360
[7,4,8,2,6,3,1,5]=>[4,2,2]=>1260
[8,7,3,1,6,4,2,5]=>[5,2,1]=>4032
[8,7,3,1,6,4,5,2]=>[7,1]=>5760
[8,7,3,1,4,6,5,2]=>[6,1,1]=>3360
[8,4,3,2,7,5,6,1]=>[3,2,2,1]=>1680
[6,4,1,7,8,5,3,2]=>[8]=>5040
[7,6,3,4,1,8,5,2]=>[3,3,1,1]=>1120
[8,7,3,1,6,2,5,4]=>[4,3,1]=>3360
[7,8,6,4,2,5,1,3]=>[5,2,1]=>4032
[7,8,2,4,6,5,1,3]=>[3,2,2,1]=>1680
[8,1,7,3,5,6,2,4]=>[6,1,1]=>3360
[8,7,5,2,4,6,1,3]=>[7,1]=>5760
[8,1,7,5,4,6,2,3]=>[5,2,1]=>4032
[8,7,3,2,6,1,5,4]=>[7,1]=>5760
[5,3,1,7,6,4,2,8]=>[7,1]=>5760
[1,8,6,4,2,9,7,5,3]=>[3,3,1,1,1]=>3360
[9,7,5,3,1,8,6,4,2,10]=>[9,1]=>403200
[8,6,4,2,1,7,5,3,9]=>[8,1]=>45360
[8,7,5,3,1,6,4,2,9]=>[7,1,1]=>25920
[7,5,3,2,1,6,4,8]=>[5,1,1,1]=>1344
[7,6,5,3,1,4,2,8]=>[7,1]=>5760
[1,8,6,4,3,2,7,5]=>[5,1,1,1]=>1344
[1,9,7,5,3,2,8,6,4]=>[8,1]=>45360
[1,8,7,6,4,2,5,3]=>[7,1]=>5760
[1,9,8,6,4,2,7,5,3]=>[7,1,1]=>25920
[1,10,8,6,4,2,9,7,5,3]=>[9,1]=>403200
[1,4,8,6,7,5,3,2]=>[7,1]=>5760
[7,6,2,5,8,4,3,1]=>[8]=>5040
[1,7,3,6,8,5,4,2]=>[6,1,1]=>3360
[8,6,2,5,7,4,3,1]=>[6,2]=>3360
[7,1,3,6,8,5,4,2]=>[7,1]=>5760
[1,8,3,6,7,5,4,2]=>[4,2,1,1]=>2520
[8,1,7,6,4,5,3,2]=>[3,3,2]=>1120
[7,1,8,6,4,5,3,2]=>[5,3]=>2688
[1,8,2,6,4,3,5,7]=>[7,1]=>5760
[1,7,2,6,4,3,5,8]=>[6,1,1]=>3360
[1,7,2,5,4,6,3,8]=>[3,2,1,1,1]=>1120
[6,5,7,2,8,3,4,1]=>[8]=>5040
[6,2,7,5,8,1,4,3]=>[5,2,1]=>4032
[6,7,2,5,8,1,4,3]=>[6,2]=>3360
[6,5,7,3,8,1,4,2]=>[3,3,2]=>1120
[6,3,7,4,8,2,5,1]=>[7,1]=>5760
[6,2,7,4,8,1,5,3]=>[4,2,1,1]=>2520
[6,7,5,1,4,3,8,2]=>[5,3]=>2688
[7,8,5,1,4,3,6,2]=>[6,2]=>3360
[5,8,2,7,6,1,3,4]=>[5,3]=>2688
[5,1,8,7,3,4,2,6]=>[8]=>5040
[8,2,3,6,7,1,4,5]=>[6,1,1]=>3360
[4,2,3,1,5,8,6,7]=>[3,2,1,1,1]=>1120
[8,6,5,4,3,2,1,7,9]=>[3,2,2,1,1]=>7560
[3,1,2,4,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]=>240
[9,7,6,5,4,3,2,1,8,10]=>[3,2,2,2,1]=>25200
[2,4,8,7,5,3,1,6]=>[4,3,1]=>3360
[2,6,8,7,5,3,4,1]=>[5,2,1]=>4032
[2,6,5,1,4,3,8,7]=>[6,2]=>3360
[6,5,1,2,4,3,8,7]=>[3,3,2]=>1120
[4,6,5,3,1,2,8,7]=>[4,2,2]=>1260
[4,8,7,5,3,1,2,6]=>[8]=>5040
[4,6,8,7,5,3,1,2]=>[4,3,1]=>3360
[6,8,7,5,3,1,4,2]=>[4,2,2]=>1260
[8,7,5,6,3,1,4,2]=>[6,2]=>3360
[8,7,3,4,6,5,1,2]=>[4,2,1,1]=>2520
[2,1,4,8,7,3,6,5]=>[6,2]=>3360
[4,8,7,3,1,2,6,5]=>[8]=>5040
[8,7,3,4,1,2,6,5]=>[3,3,1,1]=>1120
[8,7,3,1,6,5,2,4]=>[3,2,2,1]=>1680
[8,7,3,2,6,5,1,4]=>[5,2,1]=>4032
[2,8,7,3,4,6,5,1]=>[4,3,1]=>3360
[2,8,7,3,6,5,1,4]=>[6,2]=>3360
[2,8,7,1,6,5,3,4]=>[4,2,2]=>1260
[8,7,1,2,6,5,3,4]=>[6,2]=>3360
[8,7,1,2,4,3,6,5]=>[8]=>5040
[2,1,8,7,3,4,6,5]=>[3,3,2]=>1120
[8,7,5,1,2,4,3,6]=>[4,4]=>1260
[2,8,7,1,4,3,6,5]=>[5,3]=>2688
[2,8,7,3,4,1,6,5]=>[8]=>5040
[2,8,7,5,6,3,4,1]=>[5,3]=>2688
[2,4,8,7,3,1,6,5]=>[5,3]=>2688
[2,8,7,3,1,4,6,5]=>[4,4]=>1260
[2,4,3,1,8,7,5,6]=>[4,3,1]=>3360
[4,3,1,2,6,8,7,5]=>[4,3,1]=>3360
[2,8,7,5,6,3,1,4]=>[8]=>5040
[2,8,7,5,3,1,6,4]=>[8]=>5040
[2,8,7,5,3,6,4,1]=>[4,3,1]=>3360
[2,8,7,5,6,1,4,3]=>[8]=>5040
[2,6,8,7,5,1,4,3]=>[3,2,2,1]=>1680
[6,8,7,5,1,2,4,3]=>[8]=>5040
[8,7,5,6,1,2,4,3]=>[4,4]=>1260
[8,7,1,2,4,6,5,3]=>[4,3,1]=>3360
[2,4,8,7,3,6,5,1]=>[7,1]=>5760
[8,7,2,4,3,6,5,1]=>[4,2,1,1]=>2520
[4,8,7,1,2,6,5,3]=>[5,2,1]=>4032
[8,7,5,3,1,2,6,4]=>[5,3]=>2688
[8,7,5,3,6,4,1,2]=>[4,4]=>1260
[8,7,1,4,3,6,5,2]=>[6,1,1]=>3360
[8,7,3,4,1,6,5,2]=>[5,1,1,1]=>1344
[11,2,3,4,5,6,7,8,9,10,1]=>[2,1,1,1,1,1,1,1,1,1]=>55
[10,3,2,4,5,6,7,8,9,1]=>[2,2,1,1,1,1,1,1]=>630
[9,4,3,2,5,6,7,8,1]=>[2,2,1,1,1,1,1]=>378
[1,9,2,3,4,5,6,8,7]=>[7,1,1]=>25920
[7,1,2,6,4,5,3,8]=>[4,3,1]=>3360
[1,10,2,3,4,5,6,7,9,8]=>[8,1,1]=>226800
[7,5,4,2,8,3,1,6]=>[6,2]=>3360
[8,3,6,1,5,2,4,7]=>[4,3,1]=>3360
[5,7,2,1,8,4,6,3]=>[8]=>5040
[7,2,8,6,4,3,1,5]=>[5,2,1]=>4032
[6,3,8,7,4,2,1,5]=>[8]=>5040
[7,6,3,2,8,4,1,5]=>[3,2,2,1]=>1680
[8,6,1,3,2,4,5,7]=>[8]=>5040
[5,8,3,7,4,2,1,6]=>[4,3,1]=>3360
[8,4,7,3,5,2,1,6]=>[7,1]=>5760
[5,4,8,1,3,2,6,7]=>[8]=>5040
[4,5,8,2,1,3,6,7]=>[4,4]=>1260
[8,1,3,5,2,4,6,7]=>[7,1]=>5760
[1,8,3,5,7,2,4,6]=>[3,3,1,1]=>1120
[8,1,4,2,7,6,3,5]=>[7,1]=>5760
[1,3,4,5,6,7,8,2,9]=>[7,1,1]=>25920
[1,3,4,5,6,7,8,10,2,9]=>[9,1]=>403200
[2,1,4,5,6,7,9,3,8]=>[7,2]=>25920
[2,1,4,5,6,7,8,3,9]=>[6,2,1]=>30240
[1,3,4,5,6,7,8,9,2,10]=>[8,1,1]=>226800
[1,5,7,3,6,8,2,4]=>[7,1]=>5760
[1,3,4,7,6,8,2,5]=>[4,3,1]=>3360
[1,2,4,7,8,5,3,6]=>[3,3,1,1]=>1120
[5,1,7,3,6,8,2,4]=>[8]=>5040
[5,8,6,1,7,3,2,4]=>[6,2]=>3360
[2,1,3,8,6,5,4,7]=>[3,2,2,1]=>1680
[1,3,2,8,6,5,4,7]=>[3,2,2,1]=>1680
[2,5,7,1,8,4,3,6]=>[6,2]=>3360
[3,5,7,1,6,8,2,4]=>[8]=>5040
[5,4,7,6,8,3,1,2]=>[8]=>5040
[8,4,6,7,5,2,1,3]=>[7,1]=>5760
[8,1,7,6,4,3,2,5]=>[8]=>5040
[1,3,9,8,7,6,5,4,2]=>[3,2,2,1,1]=>7560
[1,5,8,4,3,7,6,2]=>[4,2,1,1]=>2520
[8,1,3,5,2,7,6,4]=>[5,2,1]=>4032
[8,1,4,5,6,3,7,2]=>[4,3,1]=>3360
[7,3,4,1,6,8,2,5]=>[5,3]=>2688
[7,2,1,6,3,4,8,5]=>[5,2,1]=>4032
[2,3,5,1,4,8,7,6]=>[5,2,1]=>4032
[2,7,1,3,8,4,6,5]=>[6,2]=>3360
[3,8,7,1,6,2,5,4]=>[8]=>5040
[8,3,7,2,4,1,5,6]=>[5,3]=>2688
[8,6,7,2,1,4,3,5]=>[3,3,2]=>1120
[8,3,7,5,1,2,6,4]=>[4,4]=>1260
[3,4,7,6,1,2,8,5]=>[5,3]=>2688
[4,5,8,7,6,1,3,2]=>[8]=>5040
[8,7,3,5,6,1,4,2]=>[7,1]=>5760
[8,5,2,7,6,1,3,4]=>[8]=>5040
[6,4,7,2,1,5,8,3]=>[3,3,2]=>1120
[8,4,2,5,1,6,7,3]=>[6,1,1]=>3360
[8,5,3,1,6,4,7,2]=>[6,1,1]=>3360
[8,7,3,1,4,5,6,2]=>[7,1]=>5760
[8,6,4,1,7,5,2,3]=>[4,4]=>1260
[8,5,3,7,1,6,4,2]=>[4,2,1,1]=>2520
[7,4,8,2,6,1,5,3]=>[4,2,2]=>1260
[6,4,7,3,1,5,2,8]=>[4,3,1]=>3360
[8,5,3,1,6,4,2,7]=>[7,1]=>5760
[8,7,5,1,2,6,3,4]=>[4,3,1]=>3360
[8,6,4,1,2,7,5,3]=>[4,4]=>1260
[8,7,4,1,2,5,3,6]=>[8]=>5040
[6,5,3,7,4,2,1,8]=>[6,1,1]=>3360
[1,6,3,8,4,2,5,7]=>[4,2,1,1]=>2520
[4,7,2,5,3,6,1,8]=>[6,1,1]=>3360
[1,8,3,4,5,2,6,7]=>[4,1,1,1,1]=>420
[1,8,6,4,2,5,3,7]=>[6,1,1]=>3360
[8,2,6,4,1,5,7,3]=>[5,1,1,1]=>1344
[7,8,3,4,6,1,5,2]=>[4,2,1,1]=>2520
[4,8,7,5,3,1,6,2]=>[6,2]=>3360
[6,1,4,8,3,2,5,7]=>[5,3]=>2688
[4,1,8,5,3,2,6,7]=>[8]=>5040
[8,1,6,4,2,7,3,5]=>[4,3,1]=>3360
[3,1,7,4,2,5,8,6]=>[7,1]=>5760
[1,2,7,4,3,5,6,8]=>[4,1,1,1,1]=>420
[6,1,8,5,2,4,3,7]=>[5,3]=>2688
[6,8,2,5,1,4,7,3]=>[4,3,1]=>3360
[4,5,2,1,6,8,7,3]=>[5,2,1]=>4032
[7,2,8,6,5,1,4,3]=>[4,2,1,1]=>2520
[7,4,8,6,1,5,3,2]=>[8]=>5040
[8,7,2,6,1,4,5,3]=>[6,2]=>3360
[1,7,8,6,2,4,3,5]=>[5,2,1]=>4032
[7,6,3,1,2,5,4,8]=>[3,3,1,1]=>1120
[8,5,3,1,2,4,7,6]=>[4,2,1,1]=>2520
[8,2,1,6,5,3,4,7]=>[6,1,1]=>3360
[3,8,1,5,6,2,4,7]=>[6,2]=>3360
[6,8,4,1,5,2,3,7]=>[7,1]=>5760
[3,2,8,1,6,4,5,7]=>[7,1]=>5760
[5,2,1,3,7,6,4,8]=>[5,1,1,1]=>1344
[5,4,1,2,8,3,7,6]=>[5,2,1]=>4032
[5,8,4,1,2,3,7,6]=>[7,1]=>5760
[7,1,2,5,3,4,6,8]=>[7,1]=>5760
[1,6,7,3,2,8,4,5]=>[4,3,1]=>3360
[1,8,6,3,2,7,4,5]=>[4,3,1]=>3360
[1,5,3,7,2,8,4,6]=>[2,2,2,1,1]=>420
[1,4,6,2,8,5,3,7]=>[5,2,1]=>4032
[1,5,6,2,8,4,3,7]=>[7,1]=>5760
[3,4,8,6,5,7,2,1]=>[4,3,1]=>3360
[1,2,5,7,4,6,8,3]=>[5,1,1,1]=>1344
[1,2,4,7,6,8,3,5]=>[3,3,1,1]=>1120
[3,5,8,6,1,7,2,4]=>[8]=>5040
[2,3,7,1,8,6,4,5]=>[5,2,1]=>4032
[2,6,1,7,8,5,3,4]=>[8]=>5040
[3,2,1,6,8,4,7,5]=>[2,2,2,1,1]=>420
[4,8,3,1,6,5,7,2]=>[2,2,2,1,1]=>420
[1,6,8,5,4,2,7,3]=>[2,2,2,1,1]=>420
[6,5,8,4,2,1,7,3]=>[2,2,2,1,1]=>420
[1,7,8,6,5,4,2,3]=>[2,2,2,1,1]=>420
[6,8,7,4,5,1,3,2]=>[2,2,2,1,1]=>420
[3,6,4,2,5,1,8,7]=>[5,2,1]=>4032
[2,1,5,8,6,4,7,3]=>[5,2,1]=>4032
[4,2,8,5,6,3,7,1]=>[6,1,1]=>3360
[5,7,2,3,4,6,8,1]=>[7,1]=>5760
[1,8,7,3,2,5,6,4]=>[7,1]=>5760
[5,7,1,2,3,8,6,4]=>[5,3]=>2688
[7,8,6,2,4,1,5,3]=>[8]=>5040
[7,2,8,4,6,1,5,3]=>[4,2,1,1]=>2520
[7,1,5,8,2,3,6,4]=>[6,2]=>3360
[6,1,8,4,2,3,5,7]=>[7,1]=>5760
[7,3,6,2,1,8,5,4]=>[5,3]=>2688
[1,8,6,4,2,5,7,3]=>[5,1,1,1]=>1344
[5,6,2,1,8,4,7,3]=>[7,1]=>5760
[2,8,1,6,5,7,3,4]=>[7,1]=>5760
[5,1,6,4,3,8,7,2]=>[6,1,1]=>3360
[3,7,1,6,4,5,8,2]=>[3,3,2]=>1120
[3,5,2,1,4,6,7,8]=>[5,1,1,1]=>1344
[1,3,8,7,5,4,6,2]=>[3,3,1,1]=>1120
[9,3,4,2,5,6,7,8,1]=>[3,2,1,1,1,1]=>2520
[1,2,3,4,5,7,9,8,6]=>[3,1,1,1,1,1,1]=>168
[1,2,3,4,6,7,9,8,5]=>[4,1,1,1,1,1]=>756
[1,2,3,4,6,8,9,7,5]=>[5,1,1,1,1]=>3024
[1,2,3,4,6,9,8,7,5]=>[3,2,1,1,1,1]=>2520
[1,2,3,5,6,7,9,8,4]=>[5,1,1,1,1]=>3024
[1,2,3,5,6,8,9,7,4]=>[6,1,1,1]=>10080
[1,2,3,5,6,9,8,7,4]=>[4,2,1,1,1]=>7560
[1,2,3,5,7,9,8,6,4]=>[6,1,1,1]=>10080
[1,2,3,5,9,8,7,6,4]=>[3,2,1,1,1,1]=>2520
[1,2,4,5,7,8,9,6,3]=>[5,2,1,1]=>18144
[1,2,4,5,7,9,8,6,3]=>[7,1,1]=>25920
[1,2,4,5,9,8,7,6,3]=>[4,2,1,1,1]=>7560
[1,2,4,6,9,8,7,5,3]=>[6,1,1,1]=>10080
[1,2,4,9,8,7,6,5,3]=>[3,2,2,1,1]=>7560
[1,3,5,7,9,8,6,4,2]=>[4,4,1]=>11340
[1,3,5,9,8,7,6,4,2]=>[6,2,1]=>30240
[1,2,3,4,5,6,8,10,9,7]=>[3,1,1,1,1,1,1,1]=>240
[1,2,3,4,5,7,8,10,9,6]=>[4,1,1,1,1,1,1]=>1260
[1,2,3,4,5,7,9,10,8,6]=>[5,1,1,1,1,1]=>6048
[1,2,3,4,5,7,10,9,8,6]=>[3,2,1,1,1,1,1]=>5040
[1,2,3,4,6,7,8,10,9,5]=>[5,1,1,1,1,1]=>6048
[1,2,3,4,6,7,9,10,8,5]=>[6,1,1,1,1]=>25200
[1,2,3,4,6,7,10,9,8,5]=>[4,2,1,1,1,1]=>18900
[1,2,3,4,6,8,10,9,7,5]=>[6,1,1,1,1]=>25200
[1,2,3,4,6,10,9,8,7,5]=>[3,2,1,1,1,1,1]=>5040
[1,2,3,5,6,7,9,10,8,4]=>[7,1,1,1]=>86400
[1,2,3,5,6,7,10,9,8,4]=>[5,2,1,1,1]=>60480
[1,2,3,5,6,8,9,10,7,4]=>[5,2,1,1,1]=>60480
[1,2,3,5,6,8,10,9,7,4]=>[7,1,1,1]=>86400
[1,2,3,5,6,10,9,8,7,4]=>[4,2,1,1,1,1]=>18900
[1,2,3,5,7,9,10,8,6,4]=>[4,2,1,1,1,1]=>18900
[1,2,3,5,7,10,9,8,6,4]=>[6,1,1,1,1]=>25200
[1,2,3,5,10,9,8,7,6,4]=>[3,2,2,1,1,1]=>25200
[1,2,4,5,7,8,10,9,6,3]=>[5,3,1,1]=>120960
[1,2,4,5,7,9,10,8,6,3]=>[5,2,1,1,1]=>60480
[1,2,4,5,7,10,9,8,6,3]=>[7,1,1,1]=>86400
[1,2,4,5,10,9,8,7,6,3]=>[4,2,2,1,1]=>56700
[1,2,4,6,10,9,8,7,5,3]=>[6,2,1,1]=>151200
[1,2,4,10,9,8,7,6,5,3]=>[3,2,2,1,1,1]=>25200
[1,3,5,7,9,10,8,6,4,2]=>[9,1]=>403200
[1,3,5,7,10,9,8,6,4,2]=>[5,4,1]=>181440
[1,3,5,10,9,8,7,6,4,2]=>[6,2,1,1]=>151200
[1,3,10,9,8,7,6,5,4,2]=>[3,2,2,2,1]=>25200
[7,4,1,8,2,5,6,3]=>[8]=>5040
[3,1,7,2,5,6,8,4]=>[6,1,1]=>3360
[4,1,5,7,3,2,8,6]=>[6,2]=>3360
[6,4,1,7,2,8,5,3]=>[4,4]=>1260
[7,3,1,6,2,8,5,4]=>[5,3]=>2688
[4,8,2,5,3,1,6,7]=>[8]=>5040
[5,1,3,4,8,2,6,7]=>[6,1,1]=>3360
[6,1,4,5,7,8,2,3]=>[8]=>5040
[6,3,4,7,1,8,5,2]=>[8]=>5040
[7,8,5,1,3,4,6,2]=>[4,2,2]=>1260
[7,1,3,4,5,6,8,2]=>[4,1,1,1,1]=>420
[8,5,2,7,6,3,1,4]=>[4,4]=>1260
[1,8,3,5,6,2,7,4]=>[5,1,1,1]=>1344
[8,3,2,5,6,1,7,4]=>[5,2,1]=>4032
[4,2,5,1,6,8,7,3]=>[4,2,1,1]=>2520
[5,4,2,7,8,6,1,3]=>[7,1]=>5760
[3,7,6,8,5,2,4,1]=>[7,1]=>5760
[1,7,8,5,2,6,3,4]=>[6,1,1]=>3360
[7,6,1,2,5,3,8,4]=>[7,1]=>5760
[7,6,2,4,8,1,5,3]=>[7,1]=>5760
[6,7,5,1,8,2,3,4]=>[8]=>5040
[7,6,1,2,4,3,8,5]=>[8]=>5040
[6,7,2,1,5,3,8,4]=>[7,1]=>5760
[4,3,2,8,7,1,6,5]=>[6,2]=>3360
[4,8,3,1,7,6,5,2]=>[2,2,2,1,1]=>420
[5,3,8,7,1,6,4,2]=>[3,2,2,1]=>1680
[5,8,7,3,1,6,4,2]=>[3,2,2,1]=>1680
[5,3,8,2,1,7,6,4]=>[4,2,2]=>1260
[3,8,7,2,6,5,1,4]=>[3,3,2]=>1120
[7,4,1,8,6,5,3,2]=>[3,3,2]=>1120
[5,4,2,8,1,7,6,3]=>[4,2,2]=>1260
[5,8,4,2,1,7,6,3]=>[4,2,2]=>1260
[5,8,4,7,1,6,3,2]=>[3,2,2,1]=>1680
[5,4,8,3,1,7,6,2]=>[4,2,2]=>1260
[8,5,6,1,4,7,2,3]=>[8]=>5040
[6,7,4,1,2,5,8,3]=>[8]=>5040
[1,6,7,4,2,5,8,3]=>[3,3,1,1]=>1120
[3,6,7,5,8,1,2,4]=>[5,3]=>2688
[1,6,7,5,8,3,2,4]=>[4,3,1]=>3360
[3,8,6,5,7,4,1,2]=>[6,2]=>3360
[5,2,1,6,8,4,7,3]=>[4,2,1,1]=>2520
[6,5,8,7,4,2,3,1]=>[8]=>5040
[6,8,5,7,4,2,1,3]=>[8]=>5040
[2,7,5,3,6,4,8,1]=>[4,4]=>1260
[4,7,5,3,8,1,6,2]=>[8]=>5040
[2,7,5,8,6,3,4,1]=>[5,3]=>2688
[2,7,5,6,8,3,4,1]=>[8]=>5040
[2,7,5,6,8,3,1,4]=>[5,3]=>2688
[4,7,5,3,6,8,1,2]=>[8]=>5040
[2,7,5,6,3,8,4,1]=>[6,2]=>3360
[8,7,5,3,1,4,6,2]=>[8]=>5040
[2,7,5,3,1,4,8,6]=>[8]=>5040
[5,7,6,2,8,3,1,4]=>[6,2]=>3360
[5,1,6,3,2,4,8,7]=>[3,3,2]=>1120
[5,7,6,1,8,3,2,4]=>[4,2,2]=>1260
[3,8,7,2,1,5,4,6]=>[8]=>5040
[6,1,7,2,8,4,3,5]=>[4,2,2]=>1260
[3,7,6,2,8,5,1,4]=>[8]=>5040
[6,1,7,3,8,5,2,4]=>[8]=>5040
[7,1,8,3,2,5,4,6]=>[8]=>5040
[5,8,6,2,7,4,1,3]=>[5,3]=>2688
[2,4,6,7,8,5,1,3]=>[4,4]=>1260
[2,4,6,7,8,3,1,5]=>[4,2,2]=>1260
[4,7,6,2,8,5,1,3]=>[4,4]=>1260
[5,8,7,3,2,4,1,6]=>[8]=>5040
[4,6,5,8,7,3,1,2]=>[8]=>5040
[8,3,1,7,2,6,4,5]=>[5,2,1]=>4032
[4,5,1,2,8,7,3,6]=>[8]=>5040
[5,6,1,2,8,3,7,4]=>[7,1]=>5760
[5,8,7,1,6,2,4,3]=>[8]=>5040
[8,4,5,1,7,6,2,3]=>[7,1]=>5760
[6,3,1,4,8,2,7,5]=>[4,2,1,1]=>2520
[8,5,6,1,7,2,4,3]=>[8]=>5040
[7,5,6,1,3,8,4,2]=>[5,3]=>2688
[5,7,6,1,3,8,4,2]=>[8]=>5040
[6,7,1,4,2,8,5,3]=>[4,3,1]=>3360
[2,1,6,4,8,3,7,5]=>[2,2,2,1,1]=>420
[7,4,5,1,3,8,6,2]=>[6,2]=>3360
[1,5,7,8,4,2,3,6]=>[5,2,1]=>4032
[1,3,6,4,2,5,7,8]=>[4,1,1,1,1]=>420
[1,4,5,7,8,3,6,2]=>[7,1]=>5760
[1,5,7,8,3,6,2,4]=>[4,2,1,1]=>2520
[1,5,7,8,2,4,3,6]=>[3,2,2,1]=>1680
[6,8,4,7,3,2,1,5]=>[8]=>5040
[6,8,5,4,2,7,1,3]=>[4,3,1]=>3360
[1,8,4,6,3,2,7,5]=>[6,1,1]=>3360
[3,5,6,1,4,2,7,8]=>[6,1,1]=>3360
[7,1,3,2,4,6,8,5]=>[6,1,1]=>3360
[2,6,5,7,8,3,1,4]=>[8]=>5040
[4,1,8,2,6,7,5,3]=>[3,3,2]=>1120
[3,6,7,8,2,1,4,5]=>[8]=>5040
[2,5,7,1,6,3,4,8]=>[7,1]=>5760
[4,2,8,3,6,5,1,7]=>[5,2,1]=>4032
[6,3,8,7,2,4,5,1]=>[8]=>5040
[7,6,1,8,2,4,5,3]=>[8]=>5040
[2,5,6,3,4,8,1,7]=>[8]=>5040
[5,2,4,7,8,6,1,3]=>[6,1,1]=>3360
[7,2,1,3,4,8,5,6]=>[5,2,1]=>4032
[2,4,5,7,1,8,6,3]=>[8]=>5040
[8,1,6,2,3,4,7,5]=>[7,1]=>5760
[6,1,4,2,5,7,8,3]=>[7,1]=>5760
[6,5,1,2,3,7,8,9,4]=>[9]=>40320
[1,8,3,6,4,7,2,5]=>[6,1,1]=>3360
[1,4,7,2,5,6,3,8]=>[2,2,1,1,1,1]=>210
[3,4,8,6,7,2,1,5]=>[5,3]=>2688
[3,4,8,2,5,1,7,6]=>[4,2,1,1]=>2520
[1,4,6,7,8,3,5,2]=>[5,2,1]=>4032
[4,1,5,3,6,8,7,2]=>[7,1]=>5760
[5,8,7,4,6,2,3,1]=>[5,2,1]=>4032
[6,4,8,1,5,7,3,2]=>[7,1]=>5760
[2,4,7,8,5,6,1,3]=>[6,1,1]=>3360
[2,6,3,8,5,1,7,4]=>[3,2,1,1,1]=>1120
[2,8,5,4,1,3,7,6]=>[6,1,1]=>3360
[5,4,6,3,1,7,2,8]=>[5,2,1]=>4032
[4,3,6,5,1,8,2,7]=>[5,3]=>2688
[1,5,6,8,7,3,2,4]=>[3,2,2,1]=>1680
[1,4,8,3,6,5,2,7]=>[5,2,1]=>4032
[1,3,8,6,4,7,2,5]=>[7,1]=>5760
[1,2,8,6,4,3,7,5]=>[5,1,1,1]=>1344
[4,1,7,6,8,3,2,5]=>[6,2]=>3360
[7,2,3,8,4,5,6,1]=>[6,1,1]=>3360
[6,5,1,8,7,2,4,3]=>[8]=>5040
[5,8,4,3,7,2,1,6]=>[3,3,2]=>1120
[6,1,2,8,7,3,4,5]=>[4,4]=>1260
[4,5,1,7,6,2,8,3]=>[5,3]=>2688
[6,5,1,8,7,4,3,2]=>[8]=>5040
[7,5,1,8,6,4,3,2]=>[5,3]=>2688
[8,5,1,7,6,4,3,2]=>[8]=>5040
[8,5,3,7,6,1,4,2]=>[5,2,1]=>4032
[3,8,7,6,1,5,4,2]=>[6,2]=>3360
[10,9,1,2,3,4,5,6,7,11,8]=>[11]=>3628800
[9,1,8,2,3,4,5,6,10,7]=>[10]=>362880
[9,7,1,2,3,4,5,6,10,8]=>[10]=>362880
[2,10,1,9,3,4,5,6,7,8]=>[10]=>362880
[2,10,8,1,3,4,5,6,7,9]=>[10]=>362880
[2,11,10,1,3,4,5,6,7,8,9]=>[11]=>3628800
[8,3,7,5,4,1,6,2]=>[6,2]=>3360
[4,5,3,1,8,7,2,6]=>[5,2,1]=>4032
[3,4,8,1,5,2,6,7]=>[7,1]=>5760
[8,6,5,7,1,3,2,4]=>[8]=>5040
[1,5,8,6,2,7,4,3]=>[3,2,2,1]=>1680
[3,1,8,5,7,2,6,4]=>[8]=>5040
[6,8,5,3,4,2,1,7]=>[5,3]=>2688
[8,5,2,6,4,3,1,7]=>[5,3]=>2688
[8,5,2,6,1,4,7,3]=>[5,2,1]=>4032
[2,7,5,8,1,4,6,3]=>[8]=>5040
[3,2,6,7,1,8,5,4]=>[7,1]=>5760
[3,4,6,7,8,2,1,5]=>[6,2]=>3360
[3,2,6,7,8,4,1,5]=>[5,2,1]=>4032
[6,2,7,4,8,5,1,3]=>[6,1,1]=>3360
[6,7,1,3,8,5,4,2]=>[8]=>5040
[6,7,1,8,5,2,4,3]=>[7,1]=>5760
[1,2,6,7,8,5,3,4]=>[6,1,1]=>3360
[1,6,7,4,8,3,2,5]=>[4,2,1,1]=>2520
[1,4,6,7,8,3,2,5]=>[3,2,2,1]=>1680
[10,3,4,5,6,7,9,1,2,8]=>[7,3]=>172800
[8,7,2,1,5,4,6,3]=>[7,1]=>5760
[2,7,4,8,6,5,3,1]=>[6,2]=>3360
[7,6,5,2,4,1,8,3]=>[8]=>5040
[7,6,4,3,1,5,8,2]=>[6,2]=>3360
[6,1,8,7,2,3,5,4]=>[8]=>5040
[8,6,1,2,7,3,4,5]=>[8]=>5040
[3,6,8,2,7,1,5,4]=>[6,2]=>3360
[2,8,6,1,4,5,7,3]=>[7,1]=>5760
[6,8,7,2,5,4,1,3]=>[7,1]=>5760
[3,5,7,9,1,2,4,6,8,10]=>[9,1]=>403200
[4,1,2,3,5,6,7,8,9,10]=>[4,1,1,1,1,1,1]=>1260
[5,1,2,3,4,6,7,8,9,10]=>[5,1,1,1,1,1]=>6048
[8,1,2,3,4,5,6,7,9,10]=>[8,1,1]=>226800
[7,1,2,3,4,5,6,8,9,10]=>[7,1,1,1]=>86400
[6,1,2,3,4,5,7,8,9,10]=>[6,1,1,1,1]=>25200
[3,2,6,4,8,7,5,1]=>[6,1,1]=>3360
[4,7,2,8,6,5,1,3]=>[6,2]=>3360
[4,7,1,8,6,5,3,2]=>[6,2]=>3360
[2,7,4,8,3,6,1,5]=>[4,3,1]=>3360
[4,7,3,8,6,1,5,2]=>[7,1]=>5760
[4,3,6,8,7,2,5,1]=>[3,3,2]=>1120
[4,3,8,2,5,7,6,1]=>[5,2,1]=>4032
[4,1,2,6,8,7,5,3]=>[8]=>5040
[3,1,6,4,8,7,2,5]=>[5,2,1]=>4032
[4,1,6,8,7,5,2,3]=>[8]=>5040
[3,8,1,4,5,7,2,6]=>[4,2,1,1]=>2520
[3,8,1,4,2,5,7,6]=>[4,2,1,1]=>2520
[4,1,8,3,5,2,7,6]=>[6,1,1]=>3360
[3,8,1,2,5,4,7,6]=>[4,2,1,1]=>2520
[4,2,3,6,8,7,1,5]=>[4,2,1,1]=>2520
[4,2,8,3,5,1,7,6]=>[5,1,1,1]=>1344
[4,2,8,3,5,7,6,1]=>[4,2,1,1]=>2520
[3,8,2,4,5,7,6,1]=>[4,2,1,1]=>2520
[3,8,2,5,1,4,7,6]=>[7,1]=>5760
[4,2,8,5,7,1,3,6]=>[7,1]=>5760
[3,8,1,5,2,4,7,6]=>[5,2,1]=>4032
[7,5,6,4,1,3,2,8]=>[4,2,1,1]=>2520
[7,8,6,4,1,3,2,5]=>[5,2,1]=>4032
[7,1,4,2,5,6,3,8]=>[5,1,1,1]=>1344
[7,3,2,1,4,6,5,8]=>[4,2,1,1]=>2520
[7,6,1,4,3,2,5,8]=>[4,2,1,1]=>2520
[7,4,1,3,5,6,2,8]=>[5,1,1,1]=>1344
[2,7,1,3,5,6,8,4]=>[6,1,1]=>3360
[3,6,2,1,5,8,7,4]=>[6,1,1]=>3360
[2,3,6,1,5,8,7,4]=>[6,1,1]=>3360
[3,4,7,1,5,6,8,2]=>[6,1,1]=>3360
[3,6,7,4,1,2,8,5]=>[5,2,1]=>4032
[4,3,2,7,1,6,8,5]=>[5,2,1]=>4032
[7,3,2,8,1,6,4,5]=>[5,2,1]=>4032
[7,4,8,1,5,6,3,2]=>[6,1,1]=>3360
[2,6,8,1,5,3,7,4]=>[6,1,1]=>3360
[6,8,2,1,5,3,7,4]=>[6,1,1]=>3360
[4,8,2,5,3,6,7,1]=>[6,1,1]=>3360
[4,5,8,2,3,6,7,1]=>[6,1,1]=>3360
[2,4,8,5,3,6,7,1]=>[6,1,1]=>3360
[5,3,2,6,4,8,7,1]=>[5,2,1]=>4032
[2,4,5,3,8,6,7,1]=>[6,1,1]=>3360
[4,3,5,2,8,6,7,1]=>[6,1,1]=>3360
[4,8,5,3,2,6,7,1]=>[6,1,1]=>3360
[3,5,4,2,8,6,7,1]=>[6,1,1]=>3360
[4,1,2,7,5,6,8,3]=>[6,1,1]=>3360
[5,6,7,4,2,8,3,1]=>[5,2,1]=>4032
[2,5,7,4,6,8,3,1]=>[5,2,1]=>4032
[7,5,2,4,3,8,6,1]=>[4,3,1]=>3360
[6,8,1,2,5,4,7,3]=>[6,1,1]=>3360
[6,4,1,8,5,2,7,3]=>[6,1,1]=>3360
[2,6,1,8,5,4,7,3]=>[6,1,1]=>3360
[7,1,2,8,5,6,4,3]=>[6,1,1]=>3360
[4,3,2,6,8,5,7,1]=>[5,2,1]=>4032
[3,7,6,4,8,5,2,1]=>[5,2,1]=>4032
[3,1,6,8,5,4,7,2]=>[6,1,1]=>3360
[2,3,5,8,4,6,7,1]=>[6,1,1]=>3360
[3,5,2,8,4,6,7,1]=>[6,1,1]=>3360
[3,4,5,8,2,6,7,1]=>[6,1,1]=>3360
[5,4,2,8,3,6,7,1]=>[6,1,1]=>3360
[5,3,4,8,2,6,7,1]=>[6,1,1]=>3360
[2,5,4,8,3,6,7,1]=>[6,1,1]=>3360
[6,3,2,5,8,4,7,1]=>[5,2,1]=>4032
[6,1,8,3,5,4,7,2]=>[6,1,1]=>3360
[5,4,8,3,2,6,7,1]=>[6,1,1]=>3360
[5,8,2,3,4,6,7,1]=>[6,1,1]=>3360
[6,2,1,7,8,5,4,3]=>[5,2,1]=>4032
[7,4,6,8,3,2,5,1]=>[8]=>5040
[3,4,5,2,7,1,6,8]=>[5,2,1]=>4032
[7,5,6,1,2,3,8,4]=>[4,2,2]=>1260
[1,5,7,6,3,2,8,4]=>[7,1]=>5760
[8,4,6,7,3,2,5,1]=>[6,2]=>3360
[8,4,6,2,3,1,5,7]=>[6,2]=>3360
[7,5,2,1,4,3,8,6]=>[8]=>5040
[3,1,7,8,5,4,2,6]=>[4,3,1]=>3360
[7,6,4,8,3,1,2,5]=>[4,4]=>1260
[7,4,8,5,6,1,2,3]=>[6,2]=>3360
[6,2,8,5,1,3,4,7]=>[7,1]=>5760
[3,2,7,8,6,1,4,5]=>[7,1]=>5760
[6,8,2,5,1,3,7,4]=>[7,1]=>5760
[6,7,4,2,1,5,3,8]=>[4,3,1]=>3360
[5,7,4,1,3,6,2,8]=>[4,2,1,1]=>2520
[4,2,7,5,1,8,3,6]=>[3,2,2,1]=>1680
[4,1,6,5,3,8,2,7]=>[8]=>5040
[1,5,4,6,3,8,2,7]=>[7,1]=>5760
[1,8,6,4,7,3,2,5]=>[4,2,1,1]=>2520
[4,7,1,8,6,3,5,2]=>[8]=>5040
[5,4,8,1,7,3,6,2]=>[8]=>5040
[4,3,8,6,2,1,7,5]=>[4,3,1]=>3360
[8,3,6,2,4,1,7,5]=>[7,1]=>5760
[7,8,3,2,4,6,5,1]=>[6,1,1]=>3360
[7,2,8,5,3,1,6,4]=>[4,3,1]=>3360
[2,5,4,8,7,3,6,1]=>[8]=>5040
[6,4,2,8,7,3,1,5]=>[8]=>5040
[3,6,8,1,7,4,2,5]=>[8]=>5040
[7,8,6,3,1,4,5,2]=>[3,3,2]=>1120
[3,8,6,1,7,5,2,4]=>[8]=>5040
[2,7,5,4,8,3,1,6]=>[4,3,1]=>3360
[6,8,7,5,2,1,3,4]=>[4,2,2]=>1260
[7,6,2,8,5,1,3,4]=>[5,2,1]=>4032
[1,5,7,6,2,8,4,3]=>[5,2,1]=>4032
[1,6,5,2,7,8,4,3]=>[7,1]=>5760
[2,7,8,5,6,1,4,3]=>[6,2]=>3360
[4,7,8,1,2,5,6,3]=>[4,2,2]=>1260
[8,6,4,1,2,5,7,3]=>[4,3,1]=>3360
[6,1,4,7,2,5,8,3]=>[4,4]=>1260
[6,7,8,2,1,5,3,4]=>[5,3]=>2688
[5,6,3,2,7,4,1,8]=>[3,3,1,1]=>1120
[2,6,4,3,7,5,8,1]=>[6,2]=>3360
[7,2,3,6,1,8,4,5]=>[6,1,1]=>3360
[3,4,6,5,7,1,2,8]=>[4,3,1]=>3360
[7,6,2,3,5,4,8,1]=>[4,3,1]=>3360
[8,5,2,4,3,6,1,7]=>[3,3,1,1]=>1120
[8,5,7,2,4,1,6,3]=>[5,3]=>2688
[7,4,8,2,1,5,6,3]=>[4,2,2]=>1260
[2,3,6,7,8,5,1,4]=>[8]=>5040
[8,2,1,7,6,5,3,4]=>[5,2,1]=>4032
[5,7,4,1,6,8,2,3]=>[6,2]=>3360
[6,5,1,2,8,3,4,7]=>[5,3]=>2688
[5,6,8,1,3,7,2,4]=>[5,3]=>2688
[3,7,4,8,6,1,2,5]=>[6,2]=>3360
[1,6,8,5,3,2,4,7]=>[5,2,1]=>4032
[5,8,1,6,7,4,2,3]=>[6,2]=>3360
[7,2,8,4,6,1,3,5]=>[6,1,1]=>3360
[6,2,7,4,3,8,1,5]=>[6,1,1]=>3360
[1,7,8,4,6,2,3,5]=>[6,1,1]=>3360
[7,1,8,4,6,2,3,5]=>[7,1]=>5760
[8,1,6,5,4,7,2,3]=>[6,2]=>3360
[4,1,6,8,7,3,2,5]=>[6,2]=>3360
[5,1,4,6,7,3,8,2]=>[5,3]=>2688
[7,1,3,4,6,2,8,5]=>[6,1,1]=>3360
[3,4,1,6,2,5,8,7,9]=>[4,2,2,1]=>11340
[3,4,1,2,6,5,8,7,9]=>[2,2,2,2,1]=>945
[3,4,1,6,2,5,8,7,10,9]=>[4,2,2,2]=>18900
[3,5,1,6,2,4,8,7,9]=>[2,2,2,2,1]=>945
[2,5,1,6,3,4,8,7,9]=>[4,2,2,1]=>11340
[3,5,1,2,6,4,8,7,9]=>[4,2,2,1]=>11340
[2,5,1,3,6,4,8,7,9]=>[6,2,1]=>30240
[8,7,1,4,6,3,2,5]=>[5,2,1]=>4032
[1,4,7,5,8,6,3,2]=>[4,2,1,1]=>2520
[6,1,8,3,4,7,2,5]=>[4,4]=>1260
[1,8,6,3,5,2,7,4]=>[5,1,1,1]=>1344
[4,7,1,6,8,3,5,2]=>[4,4]=>1260
[7,1,8,4,2,5,3,6]=>[7,1]=>5760
[1,4,8,7,5,2,6,3]=>[4,2,1,1]=>2520
[1,5,6,4,2,3,7,8]=>[2,2,1,1,1,1]=>210
[5,7,3,6,8,4,2,1]=>[3,2,2,1]=>1680
[5,8,7,4,2,1,3,6]=>[5,2,1]=>4032
[1,8,7,3,2,5,4,6]=>[4,3,1]=>3360
[1,2,5,4,8,7,3,6]=>[5,1,1,1]=>1344
[1,2,4,8,6,3,5,7]=>[6,1,1]=>3360
[1,5,2,4,7,3,8,6]=>[6,1,1]=>3360
[8,6,3,5,7,4,1,2]=>[7,1]=>5760
[8,5,3,2,1,4,7,6]=>[6,1,1]=>3360
[1,2,7,6,8,4,3,5]=>[2,2,2,1,1]=>420
[1,6,3,2,5,7,8,4]=>[5,1,1,1]=>1344
[1,7,3,4,2,6,8,5]=>[4,1,1,1,1]=>420
[1,6,3,5,8,4,2,7]=>[6,1,1]=>3360
[1,5,6,3,2,8,4,7]=>[5,2,1]=>4032
[1,2,5,8,4,6,3,7]=>[5,1,1,1]=>1344
[1,5,3,2,7,8,4,6]=>[4,2,1,1]=>2520
[4,1,8,6,2,3,7,5]=>[7,1]=>5760
[7,5,8,6,2,3,4,1]=>[6,2]=>3360
[1,7,6,4,3,8,5,2]=>[6,1,1]=>3360
[1,8,5,7,6,3,2,4]=>[4,3,1]=>3360
[1,4,7,3,6,8,5,2]=>[7,1]=>5760
[1,6,3,5,7,8,4,2]=>[3,3,1,1]=>1120
[1,5,6,3,2,7,8,4]=>[5,2,1]=>4032
[1,2,7,6,8,4,5,3]=>[4,2,1,1]=>2520
[1,8,4,7,5,3,2,6]=>[6,1,1]=>3360
[6,8,5,2,1,7,4,3]=>[8]=>5040
[1,2,6,8,4,3,7,5]=>[3,2,1,1,1]=>1120
[7,6,2,5,3,4,1,8]=>[5,2,1]=>4032
[7,6,2,4,5,3,1,8]=>[3,2,1,1,1]=>1120
[7,6,2,4,3,5,1,8]=>[4,2,1,1]=>2520
[7,6,2,3,5,4,1,8]=>[4,2,1,1]=>2520
[8,4,2,7,1,6,3,5]=>[4,3,1]=>3360
[8,7,6,1,5,3,2,4]=>[3,2,2,1]=>1680
[8,7,6,1,4,3,5,2]=>[6,2]=>3360
[8,7,6,1,3,5,4,2]=>[5,3]=>2688
[8,7,6,1,5,4,2,3]=>[5,2,1]=>4032
[5,3,7,2,8,1,6,4]=>[8]=>5040
[8,3,5,4,2,1,6,7]=>[4,3,1]=>3360
[7,8,4,3,1,5,2,6]=>[6,2]=>3360
[8,7,6,1,2,5,3,4]=>[5,3]=>2688
[8,7,6,1,2,5,4,3]=>[8]=>5040
[8,7,6,1,4,2,5,3]=>[8]=>5040
[4,7,5,8,6,1,3,2]=>[8]=>5040
[6,5,7,3,8,4,1,2]=>[5,3]=>2688
[8,7,5,4,1,2,6,3]=>[4,3,1]=>3360
[8,6,7,1,5,3,2,4]=>[4,3,1]=>3360
[5,7,1,3,4,2,8,6]=>[4,4]=>1260
[7,3,5,6,4,8,1,2]=>[6,2]=>3360
[1,5,3,7,8,4,6,2]=>[3,3,1,1]=>1120
[1,5,7,3,8,2,6,4]=>[7,1]=>5760
[1,3,7,5,8,6,2,4]=>[3,3,1,1]=>1120
[3,7,5,8,4,1,2,6]=>[6,2]=>3360
[5,3,7,6,8,1,2,4]=>[5,3]=>2688
[3,1,2,7,5,8,4,6]=>[3,2,2,1]=>1680
[3,1,2,5,7,8,6,4]=>[5,3]=>2688
[3,7,1,2,8,5,6,4]=>[6,2]=>3360
[5,3,1,7,4,6,8,2]=>[7,1]=>5760
[2,4,7,3,5,6,1,8]=>[5,1,1,1]=>1344
[5,7,6,4,2,3,1,8]=>[4,2,1,1]=>2520
[7,4,8,2,5,6,1,3]=>[2,2,2,1,1]=>420
[5,8,2,4,6,1,3,7]=>[4,3,1]=>3360
[6,1,4,8,5,2,7,3]=>[3,3,1,1]=>1120
[3,4,5,8,1,6,7,2]=>[3,3,1,1]=>1120
[5,6,8,4,7,3,1,2]=>[4,3,1]=>3360
[3,1,6,8,5,2,7,4]=>[4,2,1,1]=>2520
[2,3,8,1,5,6,4,7]=>[6,1,1]=>3360
[5,4,8,1,2,6,7,3]=>[4,2,1,1]=>2520
[4,1,8,2,3,6,7,5]=>[3,3,1,1]=>1120
[5,2,3,8,1,7,4,6]=>[4,2,1,1]=>2520
[1,5,3,8,2,4,6,7]=>[4,2,1,1]=>2520
[8,6,2,7,5,1,4,3]=>[5,2,1]=>4032
[5,7,6,1,3,2,8,4]=>[8]=>5040
[3,5,4,6,1,7,8,2]=>[8]=>5040
[8,1,5,4,6,3,7,2]=>[3,3,1,1]=>1120
[8,4,6,3,1,7,2,5]=>[5,3]=>2688
[8,4,2,5,6,3,7,1]=>[5,2,1]=>4032
[5,4,7,2,8,6,1,3]=>[5,2,1]=>4032
[2,7,1,8,6,5,4,3]=>[6,2]=>3360
[3,7,6,1,8,5,4,2]=>[8]=>5040
[8,6,4,2,1,3,5,7,9]=>[4,4,1]=>11340
[8,6,2,1,4,3,5,7,9]=>[5,3,1]=>24192
[8,4,2,1,6,3,5,7,9]=>[8,1]=>45360
[6,4,2,1,8,3,5,7,9]=>[5,3,1]=>24192
[8,6,4,2,9,1,3,5,7]=>[9]=>40320
[9,6,4,2,7,1,3,5,8]=>[9]=>40320
[9,7,4,2,5,1,3,6,8]=>[4,4,1]=>11340
[9,7,5,2,3,1,4,6,8]=>[4,3,2]=>15120
[9,7,5,3,1,2,4,6,8]=>[9]=>40320
[10,8,6,4,2,1,3,5,7,9]=>[6,3,1]=>201600
[10,8,6,2,1,4,3,5,7,9]=>[10]=>362880
[8,2,1,4,3,6,5,7,9]=>[5,1,1,1,1]=>3024
[10,8,4,2,1,6,3,5,7,9]=>[9,1]=>403200
[4,2,1,6,3,5,8,7,9]=>[5,2,1,1]=>18144
[10,6,4,2,1,8,3,5,7,9]=>[10]=>362880
[6,4,2,1,8,3,5,9,7]=>[5,4]=>18144
[8,6,4,2,1,10,3,5,7,9]=>[7,3]=>172800
[6,4,2,7,1,3,5,8,9]=>[7,1,1]=>25920
[8,6,4,2,9,1,3,5,7,10]=>[9,1]=>403200
[6,2,8,3,1,4,5,7]=>[7,1]=>5760
[8,9,4,2,5,1,3,6,7]=>[5,3,1]=>24192
[9,6,4,2,7,1,3,5,8,10]=>[9,1]=>403200
[2,7,8,3,1,4,5,6]=>[4,4]=>1260
[9,6,7,2,3,1,4,5,8]=>[9]=>40320
[9,7,4,2,5,1,3,6,8,10]=>[4,4,1,1]=>56700
[9,7,4,5,1,2,3,6,8]=>[9]=>40320
[9,7,5,2,3,1,4,6,8,10]=>[4,3,2,1]=>151200
[9,7,5,3,1,2,4,6,8,10]=>[9,1]=>403200
[1,5,3,2,8,6,7,4]=>[4,1,1,1,1]=>420
[1,8,5,3,2,6,7,4]=>[5,1,1,1]=>1344
[1,5,6,7,3,2,8,4]=>[4,3,1]=>3360
[1,7,5,2,3,4,8,6]=>[5,2,1]=>4032
[1,7,5,2,4,8,6,3]=>[7,1]=>5760
[1,6,7,8,3,2,4,5]=>[5,2,1]=>4032
[1,4,8,6,2,3,5,7]=>[7,1]=>5760
[1,2,8,6,3,5,7,4]=>[5,1,1,1]=>1344
[1,2,7,8,4,3,5,6]=>[6,1,1]=>3360
[1,8,6,7,4,2,3,5]=>[7,1]=>5760
[1,6,7,8,4,2,3,5]=>[3,2,2,1]=>1680
[1,6,7,8,3,4,2,5]=>[7,1]=>5760
[1,7,4,2,3,8,5,6]=>[5,2,1]=>4032
[1,7,8,4,2,3,5,6]=>[3,3,1,1]=>1120
[1,7,3,5,6,2,8,4]=>[6,1,1]=>3360
[1,7,8,3,4,2,5,6]=>[7,1]=>5760
[1,2,3,7,8,5,4,6]=>[3,2,1,1,1]=>1120
[1,2,7,4,6,3,8,5]=>[5,1,1,1]=>1344
[1,7,8,4,5,2,3,6]=>[5,1,1,1]=>1344
[1,7,8,3,4,5,2,6]=>[5,2,1]=>4032
[6,8,7,2,3,4,1,5]=>[8]=>5040
[3,8,7,5,2,6,1,4]=>[4,3,1]=>3360
[4,8,7,3,2,5,1,6]=>[4,4]=>1260
[5,3,8,1,6,7,4,2]=>[5,3]=>2688
[5,8,2,1,3,7,6,4]=>[6,2]=>3360
[5,1,8,3,6,7,4,2]=>[8]=>5040
[3,1,8,4,6,2,7,5]=>[6,1,1]=>3360
[8,4,1,6,5,2,3,7]=>[4,3,1]=>3360
[1,8,7,6,4,3,5,2]=>[5,2,1]=>4032
[6,1,8,7,5,3,4,2]=>[5,2,1]=>4032
[6,8,7,3,2,4,1,5]=>[5,3]=>2688
[2,3,7,5,6,8,4,1]=>[8]=>5040
[2,8,7,6,4,5,1,3]=>[5,3]=>2688
[4,8,7,6,3,1,5,2]=>[3,3,2]=>1120
[5,3,2,7,6,4,8,1]=>[6,2]=>3360
[7,3,5,2,8,4,6,1]=>[8]=>5040
[3,5,2,7,4,6,8,1]=>[7,1]=>5760
[3,7,5,2,4,8,6,1]=>[8]=>5040
[3,4,7,6,8,2,5,1]=>[5,3]=>2688
[8,1,6,7,3,4,2,5]=>[8]=>5040
[1,2,9,3,4,5,6,8,7]=>[6,1,1,1]=>10080
[1,2,3,8,4,5,9,6,7]=>[4,2,1,1,1]=>7560
[1,2,3,4,9,5,6,8,7]=>[4,1,1,1,1,1]=>756
[2,1,3,4,8,5,7,6]=>[3,2,1,1,1]=>1120
[1,2,3,4,5,9,6,8,7]=>[3,1,1,1,1,1,1]=>168
[7,1,2,3,4,8,5,9,6]=>[6,3]=>20160
[6,9,1,2,3,4,8,5,7]=>[9]=>40320
[1,2,10,3,4,5,6,7,9,8]=>[7,1,1,1]=>86400
[5,1,9,2,3,4,8,6,7]=>[9]=>40320
[1,2,3,9,4,5,6,10,7,8]=>[5,2,1,1,1]=>60480
[4,1,2,3,5,8,6,9,7]=>[4,4,1]=>11340
[1,2,3,4,10,5,6,7,9,8]=>[5,1,1,1,1,1]=>6048
[3,1,2,4,9,5,8,6,7]=>[5,3,1]=>24192
[1,2,3,4,5,10,6,7,9,8]=>[4,1,1,1,1,1,1]=>1260
[2,1,3,4,5,9,6,8,7]=>[3,2,1,1,1,1]=>2520
[1,2,3,4,5,6,9,10,7,8]=>[2,2,1,1,1,1,1,1]=>630
[8,1,2,3,4,5,9,6,10,7]=>[7,3]=>172800
[1,11,2,3,4,5,6,7,8,10,9]=>[9,1,1]=>2217600
[1,7,2,3,4,5,9,8,6]=>[7,1,1]=>25920
[7,10,1,2,3,4,5,9,6,8]=>[6,4]=>151200
[1,6,2,3,4,5,9,8,7]=>[5,2,1,1]=>18144
[6,1,2,3,7,4,8,9,5]=>[5,4]=>18144
[6,1,10,2,3,4,5,9,7,8]=>[6,4]=>151200
[5,7,1,2,6,8,3,4]=>[8]=>5040
[1,2,3,8,5,4,6,9,7]=>[5,1,1,1,1]=>3024
[5,9,1,2,6,3,4,8,7]=>[4,4,1]=>11340
[5,1,2,3,4,6,9,7,10,8]=>[5,4,1]=>181440
[1,2,3,4,11,5,6,7,8,10,9]=>[6,1,1,1,1,1]=>55440
[1,4,2,3,5,6,9,8,7]=>[3,2,1,1,1,1]=>2520
[1,5,2,3,6,8,7,4]=>[6,1,1]=>3360
[4,1,9,5,2,3,6,8,7]=>[4,4,1]=>11340
[4,1,2,3,10,5,6,9,7,8]=>[6,4]=>151200
[1,3,2,4,5,6,9,8,7]=>[2,2,1,1,1,1,1]=>378
[3,4,1,2,5,6,8,9,7]=>[3,2,2,1,1]=>7560
[3,1,2,4,5,10,6,9,7,8]=>[5,3,1,1]=>120960
[2,3,1,4,9,5,6,8,7]=>[4,3,1,1]=>15120
[1,2,3,4,5,6,7,8,11,10,9]=>[2,1,1,1,1,1,1,1,1,1]=>55
[3,5,7,4,1,8,2,6]=>[5,2,1]=>4032
[8,6,4,7,5,1,2,3]=>[7,1]=>5760
[8,6,4,1,2,5,3,7]=>[5,3]=>2688
[2,8,4,3,1,6,5,7]=>[5,2,1]=>4032
[3,8,4,6,1,5,2,7]=>[5,3]=>2688
[8,3,5,6,1,4,7,2]=>[5,2,1]=>4032
[6,8,7,3,5,4,2,1]=>[7,1]=>5760
[3,1,2,8,5,7,4,6]=>[4,3,1]=>3360
[8,1,2,3,4,6,9,5,7]=>[6,2,1]=>30240
[8,1,2,4,6,9,3,5,7]=>[8,1]=>45360
[6,1,2,3,4,5,9,8,7]=>[6,2,1]=>30240
[5,1,2,3,4,8,6,9,7]=>[5,4]=>18144
[4,1,2,3,9,6,8,5,7]=>[4,4,1]=>11340
[9,1,2,3,4,5,7,10,6,8]=>[7,2,1]=>259200
[7,3,1,2,5,8,4,6]=>[5,2,1]=>4032
[3,1,2,8,4,6,9,5,7]=>[3,3,2,1]=>10080
[8,3,5,7,2,1,4,6]=>[3,3,2]=>1120
[2,1,3,8,5,7,4,6]=>[4,2,1,1]=>2520
[2,1,9,4,6,8,3,5,7]=>[3,3,2,1]=>10080
[9,1,2,3,5,7,10,4,6,8]=>[9,1]=>403200
[1,8,2,4,6,9,3,5,7]=>[7,1,1]=>25920
[9,1,3,5,7,10,2,4,6,8]=>[9,1]=>403200
[7,3,1,2,8,4,5,6]=>[8]=>5040
[2,1,4,7,6,3,5,8]=>[5,2,1]=>4032
[7,2,4,5,3,8,1,6]=>[3,2,2,1]=>1680
[8,4,2,5,6,7,3,1]=>[6,2]=>3360
[5,4,1,6,3,7,8,2]=>[5,3]=>2688
[4,5,1,3,6,7,8,2]=>[5,3]=>2688
[5,1,7,6,3,4,8,2]=>[6,2]=>3360
[6,1,7,5,4,8,2,3]=>[6,2]=>3360
[3,7,2,1,6,8,4,5]=>[5,3]=>2688
[1,5,8,2,4,7,6,3]=>[3,2,2,1]=>1680
[5,8,1,6,4,7,3,2]=>[6,2]=>3360
[3,8,6,5,7,2,4,1]=>[5,3]=>2688
[6,8,1,4,7,3,5,2]=>[3,2,2,1]=>1680
[1,6,8,2,7,4,5,3]=>[3,2,2,1]=>1680
[5,7,2,1,8,4,3,6]=>[5,3]=>2688
[5,7,1,6,8,3,2,4]=>[6,2]=>3360
[5,6,2,1,8,3,4,7]=>[5,3]=>2688
[6,4,1,7,3,8,2,5]=>[5,3]=>2688
[8,2,5,6,7,1,4,3]=>[7,1]=>5760
[7,2,4,6,8,3,1,5]=>[3,2,2,1]=>1680
[6,2,4,7,8,1,3,5]=>[3,2,2,1]=>1680
[6,1,4,3,2,8,5,7]=>[6,2]=>3360
[2,7,4,8,6,1,5,3]=>[5,3]=>2688
[2,4,8,6,5,7,3,1]=>[7,1]=>5760
[3,7,8,6,4,2,5,1]=>[5,3]=>2688
[6,2,8,4,7,5,1,3]=>[4,2,1,1]=>2520
[1,4,7,2,6,8,5,3]=>[5,2,1]=>4032
[4,2,8,5,1,6,3,7]=>[3,3,1,1]=>1120
[6,5,8,1,4,2,3,7]=>[5,3]=>2688
[2,3,8,4,1,6,5,7]=>[6,1,1]=>3360
[4,5,7,3,1,6,2,8]=>[6,1,1]=>3360
[5,1,8,7,4,6,3,2]=>[7,1]=>5760
[2,4,8,7,5,1,3,6]=>[7,1]=>5760
[3,5,7,6,1,8,4,2]=>[8]=>5040
[3,5,7,6,2,8,4,1]=>[6,2]=>3360
[1,5,3,2,8,7,6,4]=>[4,2,1,1]=>2520
[6,1,4,3,8,7,5,2]=>[6,2]=>3360
[6,3,1,8,7,4,2,5]=>[8]=>5040
[5,3,6,2,8,7,4,1]=>[5,3]=>2688
[6,3,5,2,1,8,7,4]=>[7,1]=>5760
[2,8,4,1,3,7,6,5]=>[6,2]=>3360
[3,8,1,4,7,6,5,2]=>[2,2,2,1,1]=>420
[6,2,3,8,7,5,4,1]=>[6,1,1]=>3360
[4,1,3,5,8,7,6,2]=>[5,2,1]=>4032
[3,4,7,5,8,1,2,6]=>[8]=>5040
[2,7,8,3,4,1,5,6]=>[8]=>5040
[2,8,6,7,5,4,3,1]=>[4,3,1]=>3360
[7,2,6,8,1,4,3,5]=>[7,1]=>5760
[5,3,6,2,8,4,7,1]=>[4,3,1]=>3360
[8,1,6,3,7,4,5,2]=>[3,3,2]=>1120
[2,4,3,7,1,8,6,5]=>[7,1]=>5760
[2,6,5,7,3,8,4,1]=>[4,2,2]=>1260
[6,8,2,7,4,1,5,3]=>[3,3,2]=>1120
[6,1,7,8,5,3,2,4]=>[5,2,1]=>4032
[2,6,5,4,7,1,8,3]=>[4,3,1]=>3360
[5,8,3,4,6,1,7,2]=>[3,2,1,1,1]=>1120
[6,1,7,4,2,5,8,3]=>[4,3,1]=>3360
[6,8,7,1,5,4,2,3]=>[4,3,1]=>3360
[4,8,3,1,5,7,6,2]=>[2,2,2,1,1]=>420
[5,3,8,2,7,1,6,4]=>[4,4]=>1260
[8,3,4,5,2,7,1,6]=>[4,4]=>1260
[7,1,5,2,6,3,4,8]=>[4,3,1]=>3360
[3,7,1,5,2,6,8,4]=>[5,2,1]=>4032
[6,7,1,8,3,4,5,2]=>[8]=>5040
[3,7,1,6,8,4,5,2]=>[4,2,2]=>1260
[3,8,5,2,6,7,1,4]=>[5,3]=>2688
[3,6,5,2,7,1,4,8]=>[7,1]=>5760
[6,8,3,4,7,1,5,2]=>[2,2,2,1,1]=>420
[3,7,1,6,5,2,8,4]=>[5,2,1]=>4032
[8,3,5,2,7,1,6,4]=>[8]=>5040
[7,1,8,4,6,3,5,2]=>[7,1]=>5760
[3,7,1,4,5,2,8,6]=>[4,2,1,1]=>2520
[2,3,7,6,5,8,1,4]=>[4,3,1]=>3360
[4,3,5,6,7,8,9,1,2]=>[5,4]=>18144
[6,7,8,5,4,3,2,1,9]=>[4,2,2,1]=>11340
[6,5,7,8,4,3,2,1,9]=>[8,1]=>45360
[6,5,4,7,8,3,2,1,9]=>[8,1]=>45360
[6,5,4,3,7,8,2,1,9]=>[3,3,2,1]=>10080
[6,5,4,3,2,7,8,1,9]=>[4,2,2,1]=>11340
[7,8,9,5,4,3,2,1,6]=>[4,3,2]=>15120
[7,8,9,6,5,4,3,2,1,10]=>[4,2,2,1,1]=>56700
[6,7,8,9,4,3,2,1,5]=>[4,3,2]=>15120
[7,6,8,9,5,4,3,2,1,10]=>[8,1,1]=>226800
[6,5,7,8,9,3,2,1,4]=>[9]=>40320
[7,6,5,8,9,4,3,2,1,10]=>[5,4,1]=>181440
[6,5,4,7,8,9,2,1,3]=>[9]=>40320
[7,6,5,4,8,9,3,2,1,10]=>[8,1,1]=>226800
[6,5,4,3,7,8,9,1,2]=>[4,3,2]=>15120
[7,6,5,4,3,8,9,2,1,10]=>[3,3,2,1,1]=>50400
[6,5,4,3,2,7,8,9,1]=>[5,2,2]=>9072
[7,6,5,4,3,2,8,9,1,10]=>[4,2,2,1,1]=>56700
[3,5,7,6,8,2,1,4]=>[5,3]=>2688
[4,2,5,3,7,6,1,8]=>[5,1,1,1]=>1344
[6,2,4,3,7,5,1,8]=>[4,2,1,1]=>2520
[1,3,6,4,7,5,2,8]=>[5,1,1,1]=>1344
[8,2,5,3,6,4,1,7]=>[4,3,1]=>3360
[7,2,5,3,6,4,1,8]=>[4,2,1,1]=>2520
[6,2,5,3,7,4,1,8]=>[6,1,1]=>3360
[4,2,6,3,7,5,1,8]=>[6,1,1]=>3360
[5,2,7,3,6,4,1,8]=>[6,1,1]=>3360
[7,3,6,2,5,4,1,8]=>[4,2,1,1]=>2520
[6,3,8,2,5,4,1,7]=>[7,1]=>5760
[7,3,1,4,6,5,2,8]=>[4,2,1,1]=>2520
[8,3,7,2,5,4,1,6]=>[7,1]=>5760
[5,2,8,3,6,4,1,7]=>[7,1]=>5760
[3,2,8,4,6,5,1,7]=>[4,2,1,1]=>2520
[1,4,7,3,6,5,2,8]=>[4,2,1,1]=>2520
[8,2,5,4,1,6,3,7]=>[5,1,1,1]=>1344
[8,2,6,4,1,5,3,7]=>[6,1,1]=>3360
[1,4,8,3,7,5,2,6]=>[7,1]=>5760
[6,2,1,4,8,5,3,7]=>[6,1,1]=>3360
[5,2,1,4,8,6,3,7]=>[5,1,1,1]=>1344
[3,2,1,5,8,6,4,7]=>[4,2,1,1]=>2520
[4,2,8,3,7,5,1,6]=>[7,1]=>5760
[5,2,8,3,7,4,1,6]=>[4,3,1]=>3360
[8,3,7,2,6,4,1,5]=>[8]=>5040
[7,3,1,4,8,5,2,6]=>[4,3,1]=>3360
[1,3,7,4,8,5,2,6]=>[3,3,1,1]=>1120
[8,2,6,3,7,4,1,5]=>[4,3,1]=>3360
[7,2,6,3,8,4,1,5]=>[3,2,2,1]=>1680
[5,2,7,3,8,4,1,6]=>[7,1]=>5760
[3,2,7,4,8,5,1,6]=>[3,3,1,1]=>1120
[5,2,6,3,8,4,1,7]=>[4,3,1]=>3360
[6,2,5,3,8,4,1,7]=>[7,1]=>5760
[7,2,5,3,8,4,1,6]=>[5,2,1]=>4032
[8,2,5,3,7,4,1,6]=>[7,1]=>5760
[1,3,6,4,8,5,2,7]=>[6,1,1]=>3360
[1,3,5,4,8,6,2,7]=>[5,1,1,1]=>1344
[8,2,4,3,7,5,1,6]=>[5,2,1]=>4032
[7,2,4,3,8,5,1,6]=>[3,2,2,1]=>1680
[6,2,4,3,8,5,1,7]=>[5,2,1]=>4032
[5,2,4,3,8,6,1,7]=>[4,2,1,1]=>2520
[4,2,5,3,8,6,1,7]=>[6,1,1]=>3360
[4,2,5,3,1,7,6,8]=>[4,2,1,1]=>2520
[6,2,4,3,1,7,5,8]=>[4,2,1,1]=>2520
[7,2,4,3,1,6,5,8]=>[3,2,1,1,1]=>1120
[8,5,1,3,6,4,2,7]=>[8]=>5040
[8,4,1,3,6,5,2,7]=>[6,2]=>3360
[1,5,2,4,7,6,3,8]=>[4,1,1,1,1]=>420
[7,2,5,3,1,6,4,8]=>[5,1,1,1]=>1344
[6,2,5,3,1,7,4,8]=>[6,1,1]=>3360
[4,2,6,3,1,7,5,8]=>[6,1,1]=>3360
[3,2,6,4,1,7,5,8]=>[5,1,1,1]=>1344
[3,2,7,4,1,6,5,8]=>[4,1,1,1,1]=>420
[4,2,7,3,1,6,5,8]=>[5,1,1,1]=>1344
[5,2,7,3,1,6,4,8]=>[3,2,1,1,1]=>1120
[6,2,7,3,1,5,4,8]=>[3,3,1,1]=>1120
[7,2,6,3,1,5,4,8]=>[6,1,1]=>3360
[1,5,2,4,8,6,3,7]=>[5,1,1,1]=>1344
[8,4,1,3,7,5,2,6]=>[8]=>5040
[6,2,1,5,3,7,4,8]=>[6,1,1]=>3360
[3,2,1,6,4,7,5,8]=>[4,2,1,1]=>2520
[3,2,8,5,1,6,4,7]=>[6,1,1]=>3360
[6,2,8,4,1,5,3,7]=>[3,3,1,1]=>1120
[8,3,7,4,1,5,2,6]=>[4,3,1]=>3360
[7,1,3,2,5,6,4,8]=>[4,1,1,1,1]=>420
[6,3,5,2,4,8,1,7]=>[4,4]=>1260
[1,5,2,8,7,4,3,6]=>[4,3,1]=>3360
[5,7,2,8,1,4,3,6]=>[3,3,2]=>1120
[5,8,2,7,1,4,3,6]=>[6,2]=>3360
[4,8,3,1,5,2,7,6]=>[3,2,1,1,1]=>1120
[7,1,5,3,2,6,8,4]=>[7,1]=>5760
[9,8,7,6,4,3,2,1,5,10]=>[9,1]=>403200
[8,6,2,3,1,5,7,4]=>[7,1]=>5760
[1,4,2,7,3,6,8,5]=>[6,1,1]=>3360
[7,3,4,2,1,5,8,6]=>[5,3]=>2688
[1,6,3,2,4,7,8,5]=>[6,1,1]=>3360
[1,8,5,3,2,4,7,6]=>[6,1,1]=>3360
[4,7,8,1,5,6,2,3]=>[2,2,2,1,1]=>420
[3,6,7,1,8,4,2,5]=>[6,2]=>3360
[1,3,7,6,2,4,5,8]=>[4,2,1,1]=>2520
[2,7,3,8,4,5,6,1]=>[7,1]=>5760
[7,1,4,3,8,5,6,2]=>[6,2]=>3360
[5,6,2,7,8,3,4,1]=>[3,3,2]=>1120
[7,4,1,8,5,6,2,3]=>[6,1,1]=>3360
[7,2,5,8,1,6,3,4]=>[4,2,1,1]=>2520
[6,4,8,1,5,7,2,3]=>[5,2,1]=>4032
[6,2,1,4,7,5,8,3]=>[6,1,1]=>3360
[6,8,7,9,5,4,3,2,1]=>[4,2,2,1]=>11340
[5,8,7,6,9,4,3,2,1]=>[3,2,2,2]=>2520
[4,8,7,6,5,9,3,2,1]=>[4,2,2,1]=>11340
[3,8,7,6,5,4,9,2,1]=>[4,2,2,1]=>11340
[2,8,7,6,5,4,3,9,1]=>[4,2,2,1]=>11340
[2,6,1,5,4,7,3,8]=>[5,2,1]=>4032
[2,3,6,8,4,1,7,5]=>[4,3,1]=>3360
[1,7,2,8,6,3,5,4]=>[5,2,1]=>4032
[8,4,2,3,7,1,6,5]=>[5,3]=>2688
[5,2,4,8,7,3,1,6]=>[4,3,1]=>3360
[8,3,2,6,7,4,1,5]=>[4,2,2]=>1260
[3,2,4,6,7,8,1,5]=>[7,1]=>5760
[5,2,6,8,1,3,7,4]=>[2,2,2,1,1]=>420
[4,8,1,6,3,7,5,2]=>[6,2]=>3360
[7,1,5,2,6,4,3,8]=>[7,1]=>5760
[8,3,5,2,6,1,4,7]=>[8]=>5040
[1,8,5,6,2,7,4,3]=>[4,3,1]=>3360
[8,3,2,4,6,7,1,5]=>[5,2,1]=>4032
[4,2,7,6,1,8,5,3]=>[7,1]=>5760
[7,2,4,8,6,3,5,1]=>[7,1]=>5760
[7,3,2,1,8,5,4,6]=>[3,3,2]=>1120
[7,3,2,1,6,4,8,5]=>[6,2]=>3360
[3,6,5,2,1,8,4,7]=>[5,3]=>2688
[6,7,2,4,3,5,8,1]=>[7,1]=>5760
[4,3,8,2,1,5,7,6]=>[7,1]=>5760
[4,3,2,8,1,6,7,5]=>[4,2,1,1]=>2520
[4,5,8,3,2,7,1,6]=>[6,2]=>3360
[6,8,5,2,7,3,4,1]=>[8]=>5040
[5,4,7,8,2,3,6,1]=>[5,3]=>2688
[4,3,8,2,1,6,7,5]=>[6,1,1]=>3360
[5,3,7,6,2,4,8,1]=>[6,2]=>3360
[4,6,7,2,5,3,8,1]=>[7,1]=>5760
[6,4,7,8,3,1,5,2]=>[3,3,2]=>1120
[8,4,7,3,1,5,6,2]=>[8]=>5040
[5,8,1,7,6,4,2,3]=>[8]=>5040
[5,6,7,1,8,3,4,2]=>[8]=>5040
[7,1,8,6,2,5,4,3]=>[6,2]=>3360
[1,5,8,2,6,4,7,3]=>[4,2,1,1]=>2520
[1,5,7,4,6,8,3,2]=>[4,2,1,1]=>2520
[1,4,7,5,6,8,3,2]=>[5,2,1]=>4032
[5,6,7,4,8,1,3,2]=>[5,2,1]=>4032
[8,1,2,6,4,5,7,3]=>[4,3,1]=>3360
[4,8,1,7,2,5,6,3]=>[8]=>5040
[2,6,7,1,5,4,8,3]=>[4,3,1]=>3360
[1,2,7,4,5,8,3,6]=>[2,2,1,1,1,1]=>210
[6,7,3,2,5,8,1,4]=>[6,1,1]=>3360
[6,1,8,4,5,3,7,2]=>[5,1,1,1]=>1344
[7,8,9,4,5,6,3,1,2]=>[6,1,1,1]=>10080
[4,6,2,5,1,8,7,3]=>[4,3,1]=>3360
[5,1,4,6,2,8,7,3]=>[4,3,1]=>3360
[7,3,5,2,1,6,8,4]=>[7,1]=>5760
[8,5,1,2,6,3,7,4]=>[7,1]=>5760
[1,5,8,7,4,6,3,2]=>[6,1,1]=>3360
[5,7,2,1,3,6,8,4]=>[7,1]=>5760
[3,7,2,6,8,1,5,4]=>[8]=>5040
[7,4,8,6,5,1,3,2]=>[7,1]=>5760
[2,7,6,8,5,1,4,3]=>[7,1]=>5760
[1,6,4,5,7,3,8,2]=>[7,1]=>5760
[1,5,4,7,8,6,2,3]=>[6,1,1]=>3360
[7,3,1,6,8,2,5,4]=>[8]=>5040
[7,1,6,8,5,2,4,3]=>[7,1]=>5760
[3,5,8,7,6,4,1,2]=>[8]=>5040
[1,5,7,8,6,2,4,3]=>[4,3,1]=>3360
[6,8,2,7,5,4,3,1]=>[7,1]=>5760
[5,8,1,7,6,4,3,2]=>[6,2]=>3360
[10,6,1,2,3,4,9,5,7,8]=>[5,3,2]=>120960
[10,7,1,2,3,4,9,5,6,8]=>[5,5]=>72576
[9,10,1,2,3,4,8,5,6,7]=>[10]=>362880
[10,1,5,2,3,4,6,7,8,9]=>[8,2]=>226800
[10,1,2,5,3,4,6,7,8,9]=>[10]=>362880
[5,1,2,3,10,4,6,7,8,9]=>[10]=>362880
[7,1,2,3,4,5,11,6,8,9,10]=>[11]=>3628800
[7,6,1,2,3,4,10,9,5,8]=>[7,3]=>172800
[11,1,2,3,4,5,8,6,7,9,10]=>[11]=>3628800
[9,7,1,2,3,4,8,5,10,6]=>[10]=>362880
[5,9,1,2,3,4,6,7,10,8]=>[7,3]=>172800
[10,8,4,9,1,2,3,5,6,7]=>[10]=>362880
[11,10,5,1,2,3,4,6,7,8,9]=>[6,5]=>1330560
[2,10,1,5,3,4,6,7,8,9]=>[10]=>362880
[11,10,1,5,2,3,4,6,7,8,9]=>[11]=>3628800
[3,1,5,2,10,4,6,7,8,9]=>[10]=>362880
[5,11,1,2,10,3,4,6,7,8,9]=>[6,5]=>1330560
[4,1,2,10,3,5,6,7,8,9]=>[10]=>362880
[5,11,1,2,3,10,4,6,7,8,9]=>[5,3,3]=>443520
[4,1,5,6,7,8,9,2,3]=>[5,4]=>18144
[2,3,4,5,8,9,1,6,7]=>[9]=>40320
[2,3,6,7,1,8,9,4,5]=>[9]=>40320
[2,4,5,6,7,8,9,10,11,1,3]=>[6,5]=>1330560
[3,4,5,6,7,8,9,10,11,1,2]=>[11]=>3628800
[8,6,3,2,1,5,4,7]=>[7,1]=>5760
[8,5,3,2,4,1,7,6]=>[3,3,1,1]=>1120
[7,5,2,4,3,6,8,1]=>[3,3,1,1]=>1120
[8,5,1,4,6,3,2,7]=>[7,1]=>5760
[8,5,1,6,3,4,2,7]=>[6,2]=>3360
[8,4,3,6,1,5,2,7]=>[7,1]=>5760
[8,4,3,5,2,1,7,6]=>[3,3,1,1]=>1120
[6,4,3,2,8,7,1,5]=>[3,2,2,1]=>1680
[8,5,1,4,3,7,2,6]=>[7,1]=>5760
[8,5,4,2,1,3,7,6]=>[7,1]=>5760
[4,7,3,6,1,8,5,2]=>[7,1]=>5760
[7,6,2,4,1,5,8,3]=>[7,1]=>5760
[8,1,6,3,7,4,2,5]=>[5,3]=>2688
[5,3,8,2,6,7,1,4]=>[4,4]=>1260
[8,2,5,1,7,6,3,4]=>[3,3,1,1]=>1120
[8,2,4,6,3,7,1,5]=>[7,1]=>5760
[7,2,6,4,3,5,8,1]=>[3,3,1,1]=>1120
[7,3,6,2,4,5,8,1]=>[5,3]=>2688
[8,3,7,2,1,4,6,5]=>[5,3]=>2688
[7,6,4,1,3,2,8,5]=>[6,2]=>3360
[7,3,8,2,1,5,6,4]=>[4,4]=>1260
[6,2,5,7,4,3,8,1]=>[7,1]=>5760
[6,2,5,4,8,7,1,3]=>[3,3,1,1]=>1120
[7,2,4,8,5,1,6,3]=>[3,3,1,1]=>1120
[4,2,7,6,8,5,1,3]=>[7,1]=>5760
[7,1,6,2,8,5,4,3]=>[4,4]=>1260
[7,1,6,3,8,5,2,4]=>[5,3]=>2688
[7,2,6,8,1,3,5,4]=>[3,2,2,1]=>1680
[7,2,8,5,1,3,6,4]=>[7,1]=>5760
[7,1,8,5,3,2,6,4]=>[4,4]=>1260
[7,1,8,2,5,6,4,3]=>[4,2,1,1]=>2520
[6,1,5,8,7,2,4,3]=>[5,3]=>2688
[6,1,5,7,4,8,3,2]=>[4,4]=>1260
[6,1,5,7,8,3,4,2]=>[6,2]=>3360
[4,6,7,3,1,8,5,2]=>[5,3]=>2688
[6,1,4,2,5,8,7,3]=>[6,1,1]=>3360
[1,5,3,8,4,6,2,7]=>[5,1,1,1]=>1344
[7,6,4,2,8,5,1,3]=>[6,2]=>3360
[4,1,8,5,7,6,2,3]=>[5,2,1]=>4032
[6,7,5,1,3,2,4,8]=>[5,2,1]=>4032
[7,8,4,5,1,3,6,2]=>[6,2]=>3360
[1,5,8,3,6,4,7,2]=>[6,1,1]=>3360
[6,3,8,1,4,2,7,5]=>[7,1]=>5760
[8,1,4,2,3,5,7,6]=>[7,1]=>5760
[5,1,8,3,7,4,6,2]=>[8]=>5040
[8,3,7,1,5,4,6,2]=>[7,1]=>5760
[8,4,7,1,5,3,6,2]=>[4,3,1]=>3360
[7,2,5,3,4,6,1,8]=>[3,2,1,1,1]=>1120
[7,6,4,2,5,3,1,8]=>[4,2,1,1]=>2520
[5,8,4,3,6,2,7,1]=>[5,2,1]=>4032
[1,7,2,6,3,4,8,5]=>[5,2,1]=>4032
[7,5,1,6,3,2,4,8]=>[7,1]=>5760
[7,1,2,6,3,4,5,8]=>[5,2,1]=>4032
[7,1,6,5,4,2,3,8]=>[5,2,1]=>4032
[3,6,8,5,2,4,7,1]=>[4,3,1]=>3360
[5,7,8,4,3,2,6,1]=>[4,3,1]=>3360
[1,3,8,4,7,2,6,5]=>[6,1,1]=>3360
[6,7,1,3,2,8,5,4]=>[5,3]=>2688
[1,5,3,2,6,8,4,7]=>[6,1,1]=>3360
[5,4,3,1,7,2,8,6]=>[7,1]=>5760
[3,7,6,5,8,2,4,1]=>[8]=>5040
[5,7,4,2,8,6,1,3]=>[7,1]=>5760
[5,4,3,7,8,2,6,1]=>[4,3,1]=>3360
[3,8,5,7,6,2,4,1]=>[6,2]=>3360
[1,3,6,8,7,2,5,4]=>[3,2,2,1]=>1680
[5,8,7,1,4,2,3,6]=>[3,3,2]=>1120
[2,6,3,7,1,4,5,8]=>[6,1,1]=>3360
[1,7,6,5,3,2,4,8]=>[6,1,1]=>3360
[2,7,6,5,4,1,3,8]=>[5,2,1]=>4032
[6,2,3,5,8,4,1,7]=>[6,1,1]=>3360
[4,7,6,1,5,8,3,2]=>[5,2,1]=>4032
[9,8,7,6,5,4,2,3,1]=>[4,2,2,1]=>11340
[2,3,9,8,7,6,5,4,1]=>[4,2,2,1]=>11340
[9,1,3,2,4,5,6,7,8]=>[8,1]=>45360
[6,8,7,1,5,4,3,2]=>[3,2,2,1]=>1680
[9,10,1,8,7,6,5,4,3,2]=>[3,2,2,2,1]=>25200
[2,4,3,6,5,8,7,1,9]=>[5,1,1,1,1]=>3024
[3,2,5,4,7,6,9,8,1,10]=>[5,1,1,1,1,1]=>6048
[2,4,3,6,5,8,7,10,9,1]=>[6,1,1,1,1]=>25200
[7,2,6,1,5,8,3,4]=>[6,1,1]=>3360
[4,7,3,6,8,2,1,5]=>[5,2,1]=>4032
[5,4,7,3,8,2,1,6]=>[8]=>5040
[8,7,2,4,6,3,5,1]=>[5,2,1]=>4032
[1,7,2,8,5,4,3,6]=>[3,3,1,1]=>1120
[5,4,8,3,6,2,1,7]=>[8]=>5040
[6,8,2,5,7,1,4,3]=>[3,3,2]=>1120
[3,8,6,2,7,5,1,4]=>[5,3]=>2688
[5,8,4,2,7,3,6,1]=>[8]=>5040
[8,2,7,3,4,5,1,6]=>[7,1]=>5760
[8,1,5,2,4,6,3,7]=>[7,1]=>5760
[8,6,1,3,4,5,7,2]=>[7,1]=>5760
[8,5,1,2,4,6,7,3]=>[3,3,1,1]=>1120
[2,6,8,7,3,4,5,1]=>[8]=>5040
[1,7,8,5,6,4,2,3]=>[3,2,2,1]=>1680
[8,3,1,2,4,6,7,5]=>[6,1,1]=>3360
[3,1,7,5,8,2,4,6]=>[8]=>5040
[8,1,3,2,4,6,5,7]=>[6,1,1]=>3360
[8,1,5,6,4,2,3,7]=>[8]=>5040
[8,1,6,5,4,3,2,7]=>[4,2,2]=>1260
[2,6,8,1,5,4,3,7]=>[4,3,1]=>3360
[3,5,8,2,1,4,7,6]=>[7,1]=>5760
[4,2,8,5,3,7,6,1]=>[5,2,1]=>4032
[4,2,7,5,3,8,6,1]=>[7,1]=>5760
[6,4,5,1,8,3,2,7]=>[8]=>5040
[5,4,7,8,3,1,2,6]=>[8]=>5040
[4,5,8,1,3,7,2,6]=>[6,2]=>3360
[1,5,3,6,8,7,2,4]=>[6,1,1]=>3360
[7,6,2,8,1,4,3,5]=>[8]=>5040
[4,7,2,6,8,3,5,1]=>[8]=>5040
[6,3,2,8,7,4,5,1]=>[4,2,2]=>1260
[7,4,3,8,5,6,2,1]=>[5,1,1,1]=>1344
[3,1,5,8,7,6,2,4]=>[5,2,1]=>4032
[8,2,1,6,5,7,3,4]=>[6,1,1]=>3360
[3,1,8,6,5,7,2,4]=>[7,1]=>5760
[1,2,7,6,4,5,8,3]=>[3,3,1,1]=>1120
[7,2,6,5,1,8,3,4]=>[7,1]=>5760
[4,2,8,5,6,3,1,7]=>[7,1]=>5760
[4,7,3,2,5,1,6,8]=>[5,1,1,1]=>1344
[4,2,5,3,8,7,1,6]=>[7,1]=>5760
[7,2,5,3,8,4,6,1]=>[7,1]=>5760
[8,7,3,2,5,4,6,1]=>[4,2,1,1]=>2520
[7,5,6,1,8,3,2,4]=>[6,2]=>3360
[4,5,6,2,7,3,1,8]=>[5,2,1]=>4032
[3,5,1,4,6,8,2,7]=>[5,2,1]=>4032
[8,5,7,4,2,1,3,6]=>[3,2,2,1]=>1680
[4,6,2,7,5,8,1,3]=>[4,3,1]=>3360
[7,8,1,4,2,3,5,6]=>[7,1]=>5760
[6,5,2,4,8,7,1,3]=>[4,3,1]=>3360
[8,5,2,4,1,3,7,6]=>[6,1,1]=>3360
[5,1,2,4,3,6,8,7]=>[4,2,1,1]=>2520
[4,3,8,1,5,2,6,7]=>[5,2,1]=>4032
[4,1,3,6,7,2,8,5]=>[4,3,1]=>3360
[3,5,1,2,4,7,6,9,8]=>[3,2,2,2]=>2520
[7,8,1,6,5,2,4,3]=>[7,1]=>5760
[7,4,8,6,5,1,2,3]=>[5,2,1]=>4032
[3,7,8,6,5,1,2,4]=>[5,2,1]=>4032
[8,4,5,7,2,6,3,1]=>[5,2,1]=>4032
[6,5,8,2,7,3,1,4]=>[8]=>5040
[6,4,8,2,7,3,1,5]=>[6,2]=>3360
[4,5,7,8,3,2,1,6]=>[8]=>5040
[5,7,3,4,2,6,8,1]=>[5,1,1,1]=>1344
[5,7,4,2,3,6,8,1]=>[7,1]=>5760
[5,4,7,3,2,8,1,6]=>[6,2]=>3360
[6,8,3,2,4,5,1,7]=>[7,1]=>5760
[5,8,3,4,6,1,2,7]=>[3,3,1,1]=>1120
[6,4,3,8,5,1,2,7]=>[4,2,1,1]=>2520
[6,4,8,2,3,5,1,7]=>[6,2]=>3360
[5,4,6,8,2,3,1,7]=>[6,2]=>3360
[5,6,8,4,1,2,3,7]=>[3,2,2,1]=>1680
[6,4,8,5,1,2,3,7]=>[5,3]=>2688
[7,4,8,3,1,2,5,6]=>[5,3]=>2688
[5,7,8,2,3,1,4,6]=>[5,3]=>2688
[5,4,7,8,2,1,3,6]=>[6,2]=>3360
[5,8,6,3,1,2,4,7]=>[6,2]=>3360
[6,8,5,2,1,3,4,7]=>[4,4]=>1260
[5,6,1,3,2,4,8,7]=>[6,2]=>3360
[4,3,8,1,2,5,7,6]=>[5,2,1]=>4032
[5,3,7,2,1,8,6,4]=>[6,2]=>3360
[5,4,8,3,7,2,1,6]=>[5,3]=>2688
[3,6,8,5,2,1,7,4]=>[7,1]=>5760
[6,1,5,4,7,2,8,3]=>[4,3,1]=>3360
[5,4,8,3,2,7,1,6]=>[8]=>5040
[5,4,3,7,2,1,6,8]=>[6,1,1]=>3360
[5,4,3,7,8,2,1,6]=>[7,1]=>5760
[3,4,5,6,7,8,2,9,1]=>[9]=>40320
[3,4,5,6,7,8,9,2,10,1]=>[6,4]=>151200
[1,4,5,6,7,8,3,9,2]=>[5,3,1]=>24192
[3,4,5,6,7,2,1,9,8]=>[4,3,2]=>15120
[2,1,5,6,7,8,9,4,3]=>[4,3,2]=>15120
[2,4,5,6,7,8,3,1,9]=>[5,3,1]=>24192
[2,4,5,6,7,8,9,10,3,1]=>[6,4]=>151200
[1,4,8,6,3,2,7,5]=>[3,3,1,1]=>1120
[4,1,8,6,2,5,7,3]=>[5,2,1]=>4032
[6,7,2,5,3,8,4,1]=>[5,3]=>2688
[6,3,4,8,1,2,7,5]=>[7,1]=>5760
[2,6,3,1,5,8,7,4]=>[5,1,1,1]=>1344
[7,1,3,2,6,5,8,4]=>[5,2,1]=>4032
[8,7,6,4,5,3,2,9,1]=>[3,2,2,1,1]=>7560
[2,9,8,7,5,6,4,3,1]=>[3,2,2,1,1]=>7560
[6,1,3,5,8,7,4,2]=>[7,1]=>5760
[3,5,8,7,4,6,2,1]=>[4,3,1]=>3360
[6,8,5,7,3,4,2,1]=>[6,2]=>3360
[5,3,6,8,4,2,1,7]=>[5,3]=>2688
[5,1,6,8,4,7,3,2]=>[5,3]=>2688
[6,2,8,3,4,1,5,7]=>[5,2,1]=>4032
[2,4,1,8,7,6,3,5]=>[7,1]=>5760
[1,3,5,8,4,7,2,6]=>[7,1]=>5760
[2,3,8,7,5,1,6,4]=>[7,1]=>5760
[8,5,4,7,6,1,3,2]=>[5,3]=>2688
[5,8,7,2,4,1,3,6]=>[6,2]=>3360
[4,1,3,5,6,2,8,7]=>[5,2,1]=>4032
[6,3,8,5,1,7,4,2]=>[5,3]=>2688
[8,2,4,6,1,3,7,5]=>[3,3,1,1]=>1120
[6,4,8,7,3,5,2,1]=>[5,3]=>2688
[8,2,3,5,6,1,4,7]=>[6,1,1]=>3360
[4,3,5,6,8,2,7,1]=>[7,1]=>5760
[8,2,3,4,6,1,7,5]=>[4,1,1,1,1]=>420
[1,7,4,3,5,2,8,6]=>[4,2,1,1]=>2520
[2,7,4,3,8,1,5,6]=>[6,2]=>3360
[3,8,2,7,6,4,1,5]=>[8]=>5040
[5,3,6,2,1,8,4,7]=>[6,2]=>3360
[4,3,8,6,2,7,1,5]=>[4,4]=>1260
[8,2,1,4,6,3,7,5]=>[5,1,1,1]=>1344
[3,1,6,8,2,7,5,4]=>[6,2]=>3360
[5,3,8,6,7,2,1,4]=>[5,3]=>2688
[5,8,7,2,4,6,1,3]=>[7,1]=>5760
[1,5,2,8,7,6,4,3]=>[6,1,1]=>3360
[2,7,1,4,6,5,3,8]=>[4,2,1,1]=>2520
[4,7,1,2,6,5,8,3]=>[6,2]=>3360
[4,2,5,6,8,7,3,1]=>[7,1]=>5760
[6,5,8,3,7,4,2,1]=>[5,3]=>2688
[8,2,5,1,6,3,7,4]=>[3,3,1,1]=>1120
[8,3,4,5,1,6,7,2]=>[6,1,1]=>3360
[7,8,1,3,5,4,6,2]=>[5,2,1]=>4032
[3,5,7,6,4,8,1,2]=>[5,3]=>2688
[1,3,7,8,5,4,6,2]=>[6,1,1]=>3360
[1,3,2,7,8,5,4,6]=>[3,2,2,1]=>1680
[1,5,7,6,8,3,4,2]=>[4,3,1]=>3360
[6,5,8,4,3,7,1,2]=>[4,3,1]=>3360
[6,7,3,1,5,2,4,8]=>[5,1,1,1]=>1344
[2,1,7,4,3,8,5,6]=>[3,2,2,1]=>1680
[7,2,3,8,5,4,1,6]=>[3,2,1,1,1]=>1120
[4,1,5,7,6,3,8,2]=>[5,3]=>2688
[3,2,5,4,7,6,1,10,8,9]=>[4,3,1,1,1]=>50400
[3,2,5,4,9,8,6,7,1,10]=>[4,3,1,1,1]=>50400
[3,2,5,4,1,8,6,10,7,9]=>[5,3,1,1]=>120960
[3,2,5,4,1,10,9,6,7,8]=>[3,3,2,1,1]=>50400
[3,2,7,6,4,5,9,8,1,10]=>[4,3,1,1,1]=>50400
[3,2,7,6,4,5,1,10,8,9]=>[3,3,3,1]=>22400
[3,2,9,6,4,8,5,7,1,10]=>[5,3,1,1]=>120960
[3,2,1,6,4,8,5,10,7,9]=>[7,2,1]=>259200
[3,2,1,6,4,10,9,5,7,8]=>[5,2,2,1]=>90720
[3,2,9,8,7,4,5,6,1,10]=>[3,3,2,1,1]=>50400
[3,2,1,8,7,4,5,10,6,9]=>[5,2,2,1]=>90720
[3,2,1,10,7,4,9,5,6,8]=>[7,2,1]=>259200
[3,2,1,10,9,8,4,5,6,7]=>[4,3,2,1]=>151200
[5,4,2,3,7,6,9,8,1,10]=>[4,3,1,1,1]=>50400
[5,4,2,3,7,6,1,10,8,9]=>[3,3,3,1]=>22400
[5,4,2,3,9,8,6,7,1,10]=>[3,3,3,1]=>22400
[5,4,2,3,1,8,6,10,7,9]=>[5,3,2]=>120960
[5,4,2,3,1,10,9,6,7,8]=>[3,3,2,2]=>25200
[7,4,2,6,3,5,9,8,1,10]=>[5,3,1,1]=>120960
[7,4,2,6,3,5,1,10,8,9]=>[5,3,2]=>120960
[9,4,2,6,3,8,5,7,1,10]=>[7,2,1]=>259200
[1,4,2,6,3,8,5,10,7,9]=>[9,1]=>403200
[1,4,2,6,3,10,9,5,7,8]=>[7,2,1]=>259200
[9,4,2,8,7,3,5,6,1,10]=>[5,2,2,1]=>90720
[1,4,2,8,7,3,5,10,6,9]=>[7,2,1]=>259200
[1,4,2,10,7,3,9,5,6,8]=>[9,1]=>403200
[1,4,2,10,9,8,3,5,6,7]=>[5,4,1]=>181440
[7,6,5,2,3,4,9,8,1,10]=>[3,3,2,1,1]=>50400
[7,6,5,2,3,4,1,10,8,9]=>[3,3,2,2]=>25200
[9,6,5,2,3,8,4,7,1,10]=>[5,2,2,1]=>90720
[1,6,5,2,3,8,4,10,7,9]=>[7,2,1]=>259200
[1,6,5,2,3,10,9,4,7,8]=>[5,2,2,1]=>90720
[9,8,5,2,7,3,4,6,1,10]=>[7,2,1]=>259200
[1,8,5,2,7,3,4,10,6,9]=>[9,1]=>403200
[1,10,5,2,7,3,9,4,6,8]=>[5,4,1]=>181440
[1,10,5,2,9,8,3,4,6,7]=>[9,1]=>403200
[9,8,7,6,2,3,4,5,1,10]=>[4,3,2,1]=>151200
[1,8,7,6,2,3,4,10,5,9]=>[5,4,1]=>181440
[1,10,7,6,2,3,9,4,5,8]=>[9,1]=>403200
[1,10,9,6,2,8,3,4,5,7]=>[6,3,1]=>201600
[1,10,9,8,7,2,3,4,5,6]=>[4,3,2,1]=>151200
[3,2,5,4,7,6,1,10,8,12,9,11]=>[5,4,1,1,1]=>3991680
[3,2,5,4,9,8,6,7,1,12,10,11]=>[4,3,3,1,1]=>3326400
[3,2,5,4,11,8,6,10,7,9,1,12]=>[5,4,1,1,1]=>3991680
[3,2,5,4,1,8,6,12,11,7,9,10]=>[5,3,2,1,1]=>7983360
[3,2,5,4,1,10,9,6,7,12,8,11]=>[5,3,2,1,1]=>7983360
[3,2,5,4,1,12,11,10,6,7,8,9]=>[4,3,3,1,1]=>3326400
[3,2,7,6,4,5,9,8,1,12,10,11]=>[4,3,3,1,1]=>3326400
[3,2,7,6,4,5,11,10,8,9,1,12]=>[4,3,3,1,1]=>3326400
[3,2,7,6,4,5,1,10,8,12,9,11]=>[5,3,3,1]=>5322240
[3,2,7,6,4,5,1,12,11,8,9,10]=>[3,3,3,2,1]=>1478400
[3,2,9,6,4,8,5,7,11,10,1,12]=>[5,4,1,1,1]=>3991680
[3,2,9,6,4,8,5,7,1,12,10,11]=>[5,3,3,1]=>5322240
[3,2,11,6,4,10,9,5,7,8,1,12]=>[5,3,2,1,1]=>7983360
[3,2,1,6,4,12,11,10,5,7,8,9]=>[5,4,2,1]=>11975040
[3,2,9,8,7,4,5,6,1,12,10,11]=>[3,3,3,2,1]=>1478400
[3,2,11,8,7,4,5,10,6,9,1,12]=>[5,3,2,1,1]=>7983360
[3,2,1,8,7,4,5,12,11,6,9,10]=>[5,2,2,2,1]=>1995840
[3,2,1,12,7,4,9,5,11,6,8,10]=>[5,4,2,1]=>11975040
[3,2,11,10,9,8,4,5,6,7,1,12]=>[4,3,3,1,1]=>3326400
[3,2,1,10,9,8,4,5,6,12,7,11]=>[5,4,2,1]=>11975040
[3,2,1,12,11,10,9,4,5,6,7,8]=>[4,3,2,2,1]=>4989600
[5,4,2,3,7,6,9,8,1,12,10,11]=>[4,3,3,1,1]=>3326400
[5,4,2,3,7,6,11,10,8,9,1,12]=>[4,3,3,1,1]=>3326400
[5,4,2,3,7,6,1,10,8,12,9,11]=>[5,3,3,1]=>5322240
[5,4,2,3,7,6,1,12,11,8,9,10]=>[3,3,3,2,1]=>1478400
[5,4,2,3,9,8,6,7,11,10,1,12]=>[4,3,3,1,1]=>3326400
[5,4,2,3,9,8,6,7,1,12,10,11]=>[3,3,3,3]=>246400
[5,4,2,3,11,8,6,10,7,9,1,12]=>[5,3,3,1]=>5322240
[5,4,2,3,1,8,6,12,11,7,9,10]=>[5,3,2,2]=>3991680
[5,4,2,3,11,10,9,6,7,8,1,12]=>[3,3,3,2,1]=>1478400
[5,4,2,3,1,10,9,6,7,12,8,11]=>[5,3,2,2]=>3991680
[5,4,2,3,1,12,11,10,6,7,8,9]=>[4,3,3,2]=>3326400
[7,4,2,6,3,5,9,8,11,10,1,12]=>[5,4,1,1,1]=>3991680
[7,4,2,6,3,5,9,8,1,12,10,11]=>[5,3,3,1]=>5322240
[7,4,2,6,3,5,11,10,8,9,1,12]=>[5,3,3,1]=>5322240
[7,4,2,6,3,5,1,10,8,12,9,11]=>[5,5,2]=>4790016
[7,4,2,6,3,5,1,12,11,8,9,10]=>[5,3,2,2]=>3991680
[1,4,2,6,3,8,5,10,7,12,9,11]=>[11,1]=>43545600
[1,4,2,6,3,12,9,5,11,7,8,10]=>[11,1]=>43545600
[1,4,2,6,3,12,11,10,5,7,8,9]=>[7,4,1]=>17107200
[9,4,2,8,7,3,5,6,11,10,1,12]=>[5,3,2,1,1]=>7983360
[9,4,2,8,7,3,5,6,1,12,10,11]=>[5,3,2,2]=>3991680
[1,4,2,10,7,3,9,5,6,12,8,11]=>[11,1]=>43545600
[1,4,2,12,7,3,11,10,5,6,8,9]=>[11,1]=>43545600
[11,4,2,10,9,8,3,5,6,7,1,12]=>[5,4,2,1]=>11975040
[1,4,2,10,9,8,3,5,6,12,7,11]=>[7,4,1]=>17107200
[1,4,2,12,9,8,3,5,11,6,7,10]=>[11,1]=>43545600
[1,4,2,12,11,10,9,3,5,6,7,8]=>[5,4,2,1]=>11975040
[7,6,5,2,3,4,9,8,1,12,10,11]=>[3,3,3,2,1]=>1478400
[7,6,5,2,3,4,11,10,8,9,1,12]=>[3,3,3,2,1]=>1478400
[7,6,5,2,3,4,1,10,8,12,9,11]=>[5,3,2,2]=>3991680
[7,6,5,2,3,4,1,12,11,8,9,10]=>[3,3,2,2,2]=>554400
[9,6,5,2,3,8,4,7,11,10,1,12]=>[5,3,2,1,1]=>7983360
[9,6,5,2,3,8,4,7,1,12,10,11]=>[5,3,2,2]=>3991680
[11,6,5,2,3,10,9,4,7,8,1,12]=>[5,2,2,2,1]=>1995840
[1,6,5,2,3,12,11,10,4,7,8,9]=>[5,4,2,1]=>11975040
[1,8,5,2,7,3,4,10,6,12,9,11]=>[11,1]=>43545600
[11,10,5,2,7,3,9,4,6,8,1,12]=>[5,4,2,1]=>11975040
[1,12,5,2,7,3,9,4,11,6,8,10]=>[11,1]=>43545600
[1,12,5,2,7,3,11,10,4,6,8,9]=>[7,4,1]=>17107200
[1,10,5,2,9,8,3,4,6,12,7,11]=>[11,1]=>43545600
[1,12,5,2,11,8,3,10,4,6,7,9]=>[4,4,3,1]=>4989600
[9,8,7,6,2,3,4,5,11,10,1,12]=>[4,3,3,1,1]=>3326400
[9,8,7,6,2,3,4,5,1,12,10,11]=>[4,3,3,2]=>3326400
[11,8,7,6,2,3,4,10,5,9,1,12]=>[5,4,2,1]=>11975040
[1,8,7,6,2,3,4,10,5,12,9,11]=>[7,4,1]=>17107200
[1,8,7,6,2,3,4,12,11,5,9,10]=>[5,4,2,1]=>11975040
[1,10,7,6,2,3,9,4,5,12,8,11]=>[11,1]=>43545600
[1,12,7,6,2,3,9,4,11,5,8,10]=>[7,4,1]=>17107200
[1,12,7,6,2,3,11,10,4,5,8,9]=>[11,1]=>43545600
[1,12,9,6,2,8,3,4,11,5,7,10]=>[4,4,3,1]=>4989600
[1,12,11,6,2,10,9,3,4,5,7,8]=>[11,1]=>43545600
[11,10,9,8,7,2,3,4,5,6,1,12]=>[4,3,2,2,1]=>4989600
[1,10,9,8,7,2,3,4,5,12,6,11]=>[5,4,2,1]=>11975040
[1,12,11,8,7,2,3,10,4,5,6,9]=>[11,1]=>43545600
[1,12,11,10,9,8,2,3,4,5,6,7]=>[4,4,3,1]=>4989600
[1,4,8,2,3,6,5,7]=>[4,2,1,1]=>2520
[1,7,3,2,4,5,6,8]=>[5,1,1,1]=>1344
[1,7,3,2,4,5,8,6]=>[6,1,1]=>3360
[1,6,4,3,2,5,7,8]=>[3,2,1,1,1]=>1120
[4,2,6,5,3,1,7,8]=>[5,1,1,1]=>1344
[5,2,1,6,8,7,4,3]=>[4,3,1]=>3360
[1,3,5,8,6,2,7,4]=>[4,2,1,1]=>2520
[3,7,8,5,4,2,6,1]=>[3,3,2]=>1120
[1,3,8,5,7,4,2,6]=>[7,1]=>5760
[1,2,3,7,5,4,6,8]=>[3,1,1,1,1,1]=>112
[1,4,2,8,6,3,5,7]=>[7,1]=>5760
[2,8,6,3,5,7,4,1]=>[4,3,1]=>3360
[6,1,8,2,5,3,4,7]=>[7,1]=>5760
[1,5,4,2,3,6,8,7]=>[4,2,1,1]=>2520
[6,1,5,2,3,4,8,7]=>[4,2,2]=>1260
[3,1,2,4,8,6,7,5]=>[3,2,1,1,1]=>1120
[3,1,2,5,8,7,4,6]=>[5,3]=>2688
[6,5,2,1,8,4,7,3]=>[4,3,1]=>3360
[3,7,5,2,8,1,4,6]=>[5,3]=>2688
[5,1,4,7,3,2,8,6]=>[8]=>5040
[5,4,8,6,3,7,1,2]=>[8]=>5040
[6,4,7,5,3,8,1,2]=>[8]=>5040
[5,7,4,8,3,1,6,2]=>[8]=>5040
[2,5,3,6,1,8,4,7]=>[4,3,1]=>3360
[2,5,6,8,3,1,7,4]=>[5,2,1]=>4032
[7,1,4,5,3,6,2,8]=>[3,3,1,1]=>1120
[1,7,2,4,5,3,6,8]=>[4,1,1,1,1]=>420
[1,7,4,5,3,2,6,8]=>[3,3,1,1]=>1120
[1,6,4,7,3,5,2,8]=>[6,1,1]=>3360
[3,5,6,4,8,2,1,7]=>[7,1]=>5760
[1,6,4,7,5,2,3,8]=>[3,2,1,1,1]=>1120
[1,5,2,6,7,4,3,8]=>[4,2,1,1]=>2520
[8,5,6,1,4,3,7,2]=>[5,2,1]=>4032
[2,5,4,7,8,3,1,6]=>[8]=>5040
[6,4,5,8,2,3,1,7]=>[8]=>5040
[8,6,1,3,2,5,7,4]=>[4,3,1]=>3360
[7,5,8,1,4,6,3,2]=>[7,1]=>5760
[4,2,6,7,8,1,5,3]=>[7,1]=>5760
[3,4,6,7,8,1,5,2]=>[5,3]=>2688
[4,7,3,8,5,1,6,2]=>[6,1,1]=>3360
[4,3,2,7,5,8,1,6]=>[3,2,2,1]=>1680
[4,8,5,3,2,6,1,7]=>[7,1]=>5760
[2,8,4,5,3,6,1,7]=>[4,3,1]=>3360
[8,1,5,3,2,4,7,6]=>[7,1]=>5760
[7,8,4,1,3,6,5,2]=>[5,2,1]=>4032
[8,6,1,3,2,7,4,5]=>[8]=>5040
[6,2,3,7,8,1,5,4]=>[4,2,1,1]=>2520
[6,3,7,8,1,5,4,2]=>[5,3]=>2688
[2,6,3,7,8,1,5,4]=>[4,3,1]=>3360
[7,5,8,1,6,4,2,3]=>[6,2]=>3360
[8,1,4,3,7,5,6,2]=>[3,3,2]=>1120
[1,4,8,5,3,2,6,7]=>[7,1]=>5760
[8,2,7,6,4,1,5,3]=>[7,1]=>5760
[2,7,4,3,8,5,1,6]=>[3,3,2]=>1120
[6,8,2,7,3,1,5,4]=>[6,2]=>3360
[8,2,6,3,4,1,7,5]=>[6,1,1]=>3360
[6,1,2,8,5,3,7,4]=>[4,2,1,1]=>2520
[4,1,5,8,3,6,7,2]=>[4,2,1,1]=>2520
[7,5,2,8,1,6,3,4]=>[5,2,1]=>4032
[3,4,7,2,1,5,8,6]=>[6,2]=>3360
[4,8,2,7,1,3,6,5]=>[8]=>5040
[8,2,1,7,4,6,3,5]=>[6,1,1]=>3360
[4,2,5,8,3,6,7,1]=>[3,2,1,1,1]=>1120
[5,1,6,8,3,2,7,4]=>[5,2,1]=>4032
[4,1,5,6,8,2,7,3]=>[4,3,1]=>3360
[4,5,2,8,7,3,1,6]=>[8]=>5040
[4,8,5,3,1,6,7,2]=>[4,2,1,1]=>2520
[6,2,3,1,7,8,5,4]=>[4,2,1,1]=>2520
[5,2,3,6,8,4,7,1]=>[3,2,1,1,1]=>1120
[6,2,1,7,8,4,3,5]=>[5,2,1]=>4032
[5,2,1,3,8,4,7,6]=>[6,1,1]=>3360
[5,2,7,8,4,1,6,3]=>[7,1]=>5760
[6,2,7,8,3,5,4,1]=>[7,1]=>5760
[5,2,8,6,4,1,7,3]=>[4,2,1,1]=>2520
[5,1,2,8,4,3,7,6]=>[7,1]=>5760
[6,7,8,3,2,5,4,1]=>[8]=>5040
[5,7,2,6,4,8,1,3]=>[8]=>5040
[6,2,3,4,7,8,5,1]=>[3,2,1,1,1]=>1120
[7,2,1,8,4,3,5,6]=>[7,1]=>5760
[6,2,1,3,7,5,8,4]=>[7,1]=>5760
[6,8,7,3,4,5,1,2]=>[6,2]=>3360
[6,2,3,7,8,1,4,5]=>[2,2,2,1,1]=>420
[7,4,3,2,5,8,1,6]=>[2,2,2,1,1]=>420
[7,2,4,3,5,8,1,6]=>[2,2,2,1,1]=>420
[1,7,6,4,2,3,5,8]=>[3,2,1,1,1]=>1120
[1,3,2,5,8,6,4,7]=>[4,2,1,1]=>2520
[6,1,4,7,2,8,5,3]=>[8]=>5040
[1,6,7,2,4,8,5,3]=>[7,1]=>5760
[5,7,2,4,3,6,8,1]=>[6,1,1]=>3360
[5,7,3,4,6,2,8,1]=>[6,1,1]=>3360
[2,8,3,6,1,7,4,5]=>[4,3,1]=>3360
[4,3,1,8,5,2,6,7]=>[7,1]=>5760
[1,8,4,5,6,2,7,3]=>[6,1,1]=>3360
[7,3,8,2,1,4,5,6]=>[5,3]=>2688
[8,2,5,3,1,7,4,6]=>[7,1]=>5760
[6,3,5,8,1,7,4,2]=>[8]=>5040
[3,5,4,8,6,1,7,2]=>[7,1]=>5760
[7,5,2,3,8,4,6,1]=>[8]=>5040
[2,7,5,1,4,8,3,6]=>[6,2]=>3360
[5,7,6,1,2,8,3,4]=>[8]=>5040
[7,4,6,5,1,8,2,3]=>[5,3]=>2688
[7,1,3,2,6,8,4,5]=>[4,3,1]=>3360
[4,3,5,2,8,1,6,7]=>[8]=>5040
[1,7,3,8,2,4,6,5]=>[6,1,1]=>3360
[2,7,4,8,5,3,1,6]=>[4,3,1]=>3360
[6,1,3,8,4,2,7,5]=>[3,3,1,1]=>1120
[5,4,1,8,6,2,7,3]=>[7,1]=>5760
[5,4,6,8,1,3,2,7]=>[4,2,2]=>1260
[3,6,1,5,8,4,7,2]=>[5,2,1]=>4032
[6,4,8,3,5,7,2,1]=>[7,1]=>5760
[3,5,8,2,4,1,7,6]=>[4,3,1]=>3360
[7,2,8,4,1,3,6,5]=>[6,1,1]=>3360
[5,8,1,2,4,3,6,7]=>[8]=>5040
[8,4,3,5,7,2,6,1]=>[5,2,1]=>4032
[4,1,5,2,3,8,7,6]=>[3,2,2,1]=>1680
[6,3,5,8,2,4,7,1]=>[4,3,1]=>3360
[2,8,7,1,4,6,3,5]=>[5,2,1]=>4032
[1,8,5,3,7,4,2,6]=>[7,1]=>5760
[7,5,6,2,8,4,3,1]=>[8]=>5040
[5,7,6,2,8,1,4,3]=>[5,3]=>2688
[6,3,8,1,2,5,4,7]=>[8]=>5040
[7,6,4,8,5,3,2,1]=>[7,1]=>5760
[8,6,9,7,5,4,3,2,1]=>[8,1]=>45360
[3,2,5,4,7,6,1,10,9,8]=>[4,2,1,1,1,1]=>18900
[3,2,5,4,9,8,7,6,1,10]=>[4,2,1,1,1,1]=>18900
[3,2,5,4,1,8,7,10,9,6]=>[3,3,1,1,1,1]=>8400
[3,2,5,4,1,10,9,8,7,6]=>[3,2,2,1,1,1]=>25200
[3,2,7,6,5,4,9,8,1,10]=>[4,2,1,1,1,1]=>18900
[3,2,7,6,5,4,1,10,9,8]=>[3,2,2,1,1,1]=>25200
[3,2,9,6,5,8,7,4,1,10]=>[3,3,1,1,1,1]=>8400
[3,2,1,6,5,8,7,10,9,4]=>[4,2,1,1,1,1]=>18900
[3,2,1,6,5,10,9,8,7,4]=>[3,2,2,1,1,1]=>25200
[3,2,1,8,7,6,5,10,9,4]=>[3,2,2,1,1,1]=>25200
[3,2,1,10,7,6,9,8,5,4]=>[3,2,2,1,1,1]=>25200
[5,4,3,2,7,6,9,8,1,10]=>[4,2,1,1,1,1]=>18900
[5,4,3,2,7,6,1,10,9,8]=>[3,2,2,1,1,1]=>25200
[5,4,3,2,9,8,7,6,1,10]=>[3,2,2,1,1,1]=>25200
[5,4,3,2,1,8,7,10,9,6]=>[3,2,2,1,1,1]=>25200
[7,4,3,6,5,2,9,8,1,10]=>[3,3,1,1,1,1]=>8400
[7,4,3,6,5,2,1,10,9,8]=>[3,2,2,1,1,1]=>25200
[9,4,3,6,5,8,7,2,1,10]=>[4,2,1,1,1,1]=>18900
[1,4,3,6,5,8,7,10,9,2]=>[5,1,1,1,1,1]=>6048
[1,4,3,6,5,10,9,8,7,2]=>[4,2,1,1,1,1]=>18900
[9,4,3,8,7,6,5,2,1,10]=>[3,2,2,1,1,1]=>25200
[1,4,3,8,7,6,5,10,9,2]=>[4,2,1,1,1,1]=>18900
[1,4,3,10,7,6,9,8,5,2]=>[3,3,1,1,1,1]=>8400
[1,4,3,10,9,8,7,6,5,2]=>[3,2,2,1,1,1]=>25200
[7,6,5,4,3,2,9,8,1,10]=>[3,2,2,1,1,1]=>25200
[9,6,5,4,3,8,7,2,1,10]=>[3,2,2,1,1,1]=>25200
[1,6,5,4,3,8,7,10,9,2]=>[4,2,1,1,1,1]=>18900
[1,6,5,4,3,10,9,8,7,2]=>[3,2,2,1,1,1]=>25200
[9,8,5,4,7,6,3,2,1,10]=>[3,2,2,1,1,1]=>25200
[1,8,5,4,7,6,3,10,9,2]=>[3,3,1,1,1,1]=>8400
[1,10,5,4,7,6,9,8,3,2]=>[4,2,1,1,1,1]=>18900
[1,10,5,4,9,8,7,6,3,2]=>[3,2,2,1,1,1]=>25200
[1,10,7,6,5,4,9,8,3,2]=>[3,2,2,1,1,1]=>25200
[1,10,9,6,5,8,7,4,3,2]=>[3,2,2,1,1,1]=>25200
[1,5,7,2,4,3,6,8]=>[3,3,1,1]=>1120
[1,6,5,3,2,4,7,8]=>[5,1,1,1]=>1344
[1,7,2,4,6,5,3,8]=>[3,2,1,1,1]=>1120
[1,4,7,2,6,5,3,8]=>[2,2,2,1,1]=>420
[1,2,6,8,7,4,3,5]=>[6,1,1]=>3360
[1,2,7,4,3,5,8,6]=>[5,1,1,1]=>1344
[1,6,2,8,7,4,3,5]=>[7,1]=>5760
[1,7,4,2,3,5,8,6]=>[7,1]=>5760
[1,8,5,2,3,6,4,7]=>[4,2,1,1]=>2520
[1,7,4,8,5,2,3,6]=>[6,1,1]=>3360
[1,4,7,5,2,8,6,3]=>[4,3,1]=>3360
[1,6,3,7,4,2,8,5]=>[4,2,1,1]=>2520
[1,8,5,2,7,4,3,6]=>[4,3,1]=>3360
[1,4,8,7,5,3,2,6]=>[3,3,1,1]=>1120
[1,2,5,8,6,3,7,4]=>[3,2,1,1,1]=>1120
[1,2,4,7,5,8,6,3]=>[5,1,1,1]=>1344
[1,5,8,7,6,2,4,3]=>[3,2,2,1]=>1680
[1,3,5,8,7,6,2,4]=>[4,2,1,1]=>2520
[1,5,2,4,3,6,8,7]=>[3,2,1,1,1]=>1120
[1,6,8,7,5,3,2,4]=>[6,1,1]=>3360
[1,2,5,7,4,3,8,6]=>[6,1,1]=>3360
[1,5,3,2,6,8,7,4]=>[5,1,1,1]=>1344
[1,4,2,6,8,7,5,3]=>[7,1]=>5760
[1,5,8,6,3,2,7,4]=>[6,1,1]=>3360
[1,8,5,2,6,3,4,7]=>[4,3,1]=>3360
[1,7,4,6,3,2,8,5]=>[7,1]=>5760
[1,6,3,2,8,5,4,7]=>[6,1,1]=>3360
[1,3,8,6,4,2,5,7]=>[7,1]=>5760
[1,5,7,4,2,3,8,6]=>[4,2,1,1]=>2520
[6,3,7,5,4,2,8,1]=>[6,2]=>3360
[7,5,2,6,3,4,8,1]=>[3,3,2]=>1120
[3,8,2,7,5,4,1,6]=>[7,1]=>5760
[5,4,8,6,7,1,2,3]=>[6,2]=>3360
[2,7,3,6,8,5,4,1]=>[7,1]=>5760
[3,7,2,8,1,6,4,5]=>[7,1]=>5760
[8,5,2,4,6,7,3,1]=>[5,2,1]=>4032
[2,5,8,7,1,4,3,6]=>[5,3]=>2688
[3,4,6,5,8,2,7,1]=>[7,1]=>5760
[5,2,4,1,6,7,8,3]=>[7,1]=>5760
[5,2,8,6,4,7,1,3]=>[5,2,1]=>4032
[6,1,3,4,7,2,8,5]=>[3,3,1,1]=>1120
[8,3,4,5,2,1,7,6]=>[4,3,1]=>3360
[8,6,1,4,7,3,5,2]=>[5,2,1]=>4032
[5,3,6,7,2,8,4,1]=>[6,2]=>3360
[5,3,6,7,2,4,8,1]=>[8]=>5040
[1,5,8,2,6,7,4,3]=>[5,2,1]=>4032
[7,1,3,6,5,2,8,4]=>[6,1,1]=>3360
[8,2,1,4,5,7,6,3]=>[3,2,1,1,1]=>1120
[1,4,7,5,2,3,8,6]=>[4,3,1]=>3360
[6,1,7,5,4,2,8,3]=>[3,3,2]=>1120
[2,7,3,6,5,1,8,4]=>[6,1,1]=>3360
[8,6,5,1,3,7,4,2]=>[6,2]=>3360
[5,7,6,2,4,8,1,3]=>[5,3]=>2688
[3,7,5,6,4,8,1,2]=>[8]=>5040
[7,6,8,1,3,5,4,2]=>[5,3]=>2688
[2,8,4,6,1,7,5,3]=>[8]=>5040
[2,8,6,4,7,3,5,1]=>[3,2,2,1]=>1680
[8,7,1,4,6,5,3,2]=>[5,2,1]=>4032
[3,5,8,6,7,1,4,2]=>[8]=>5040
[1,2,4,6,8,5,3,7]=>[6,1,1]=>3360
[3,1,5,8,6,2,4,7]=>[5,3]=>2688
[2,5,4,6,8,1,3,7]=>[8]=>5040
[6,5,2,4,7,8,1,3]=>[7,1]=>5760
[7,2,5,8,6,4,1,3]=>[5,2,1]=>4032
[5,2,8,3,4,7,6,1]=>[5,2,1]=>4032
[2,4,3,8,7,1,6,5]=>[7,1]=>5760
[1,5,8,7,4,2,6,3]=>[5,2,1]=>4032
[6,8,7,5,4,3,1,2]=>[4,2,2]=>1260
[5,6,4,7,3,8,2,9,1]=>[9]=>40320
[5,6,4,7,3,9,2,8,1]=>[8,1]=>45360
[5,3,4,8,6,2,7,1]=>[7,1]=>5760
[5,4,6,3,7,2,8,1,9]=>[4,4,1]=>11340
[6,5,7,4,8,3,9,2,10,1]=>[6,3,1]=>201600
[6,5,7,4,8,3,10,2,9,1]=>[5,3,1,1]=>120960
[3,4,5,8,6,2,7,1]=>[7,1]=>5760
[5,6,4,7,3,8,2,9,1,10]=>[9,1]=>403200
[5,4,2,3,6,1,8,7]=>[3,3,2]=>1120
[5,1,7,4,3,6,8,2]=>[6,1,1]=>3360
[4,3,7,6,8,2,1,5]=>[6,2]=>3360
[8,1,4,7,2,3,5,6]=>[8]=>5040
[6,1,8,5,2,7,3,4]=>[8]=>5040
[8,7,2,6,3,1,4,5]=>[8]=>5040
[8,7,1,6,4,5,2,3]=>[3,3,2]=>1120
[5,4,1,3,7,2,8,6]=>[8]=>5040
[3,1,8,7,5,2,4,6]=>[5,2,1]=>4032
[6,5,8,7,2,4,3,1]=>[6,2]=>3360
[4,3,6,5,8,2,1,7]=>[5,3]=>2688
[7,6,3,2,8,5,4,1]=>[7,1]=>5760
[4,3,7,1,8,5,2,6]=>[3,3,2]=>1120
[3,2,8,5,6,7,1,4]=>[7,1]=>5760
[8,3,2,1,4,7,5,6]=>[6,2]=>3360
[4,7,3,1,8,5,2,6]=>[3,2,2,1]=>1680
[3,7,8,2,5,6,1,4]=>[6,1,1]=>3360
[7,5,1,4,2,3,6,8]=>[4,2,1,1]=>2520
[7,8,6,1,2,4,5,3]=>[8]=>5040
[1,5,3,4,7,8,6,2]=>[5,1,1,1]=>1344
[5,1,2,4,7,8,6,3]=>[7,1]=>5760
[5,1,7,8,6,2,3,4]=>[4,2,2]=>1260
[8,5,1,6,7,2,3,4]=>[8]=>5040
[7,5,1,2,4,6,8,3]=>[4,3,1]=>3360
[6,1,5,2,7,3,4,8]=>[7,1]=>5760
[7,1,2,6,4,5,8,3]=>[5,3]=>2688
[1,7,3,6,4,5,8,2]=>[3,3,1,1]=>1120
[1,8,3,6,4,5,7,2]=>[3,2,1,1,1]=>1120
[8,1,6,2,7,3,4,5]=>[6,2]=>3360
[7,1,6,2,5,3,4,8]=>[4,2,1,1]=>2520
[8,1,6,2,5,3,4,7]=>[5,2,1]=>4032
[8,1,7,2,5,3,4,6]=>[7,1]=>5760
[8,1,2,7,4,5,6,3]=>[4,4]=>1260
[1,8,3,7,4,5,6,2]=>[4,2,1,1]=>2520
[8,1,6,7,5,2,3,4]=>[7,1]=>5760
[7,3,1,2,6,4,5,8]=>[7,1]=>5760
[3,1,2,8,5,6,7,4]=>[3,2,1,1,1]=>1120
[6,3,1,2,7,4,5,8]=>[5,2,1]=>4032
[6,1,7,4,2,3,5,8]=>[6,1,1]=>3360
[1,7,3,4,6,8,5,2]=>[5,1,1,1]=>1344
[1,7,3,8,4,5,6,2]=>[6,1,1]=>3360
[7,1,8,2,5,3,4,6]=>[4,3,1]=>3360
[6,1,7,2,5,3,4,8]=>[6,1,1]=>3360
[5,1,7,2,6,3,4,8]=>[7,1]=>5760
[5,1,8,2,6,3,4,7]=>[8]=>5040
[1,6,3,7,4,5,8,2]=>[6,1,1]=>3360
[2,4,7,3,5,1,6,8]=>[6,1,1]=>3360
[2,4,8,6,3,5,1,7]=>[8]=>5040
[2,3,7,5,4,1,6,8]=>[5,2,1]=>4032
[3,4,6,2,1,5,8,7]=>[4,2,2]=>1260
[3,4,7,2,1,6,5,8]=>[4,2,1,1]=>2520
[2,6,8,3,5,1,4,7]=>[4,3,1]=>3360
[2,3,6,1,5,8,4,7]=>[7,1]=>5760
[2,3,7,1,6,5,8,4]=>[6,2]=>3360
[2,4,7,1,3,6,8,5]=>[4,3,1]=>3360
[5,4,7,8,1,3,2,6]=>[6,2]=>3360
[2,5,7,1,4,6,3,8]=>[4,2,1,1]=>2520
[2,4,7,1,6,3,5,8]=>[4,3,1]=>3360
[2,3,7,1,6,5,4,8]=>[5,2,1]=>4032
[2,5,7,1,4,3,6,8]=>[4,3,1]=>3360
[2,5,7,3,1,4,6,8]=>[4,3,1]=>3360
[3,4,7,2,1,6,8,5]=>[5,2,1]=>4032
[4,6,3,7,1,5,2,8]=>[6,1,1]=>3360
[5,7,3,2,8,1,4,6]=>[4,3,1]=>3360
[2,6,5,7,1,8,4,3]=>[6,2]=>3360
[3,6,8,5,4,1,7,2]=>[5,2,1]=>4032
[5,4,7,8,1,3,6,2]=>[3,3,2]=>1120
[2,5,7,1,4,6,8,3]=>[4,3,1]=>3360
[2,4,7,1,6,3,8,5]=>[5,3]=>2688
[2,4,7,1,6,8,3,5]=>[3,3,2]=>1120
[1,8,3,4,5,6,7,9,2]=>[3,1,1,1,1,1,1]=>168
[7,2,3,4,5,6,1,9,8]=>[2,2,1,1,1,1,1]=>378
[2,1,9,4,5,6,7,8,3]=>[2,2,1,1,1,1,1]=>378
[2,8,3,4,5,6,7,1,9]=>[3,1,1,1,1,1,1]=>168
[8,6,5,1,2,4,3,7]=>[8]=>5040
[7,6,1,4,2,3,5,8]=>[6,1,1]=>3360
[6,5,1,4,8,3,2,7]=>[4,3,1]=>3360
[8,7,5,1,4,2,3,6]=>[8]=>5040
[8,4,1,2,5,3,6,7]=>[5,2,1]=>4032
[8,7,5,1,4,2,6,3]=>[5,3]=>2688
[8,6,1,4,2,5,3,7]=>[4,3,1]=>3360
[8,7,1,4,3,2,6,5]=>[4,3,1]=>3360
[2,8,3,7,4,5,6,1]=>[4,3,1]=>3360
[8,7,5,2,4,3,6,1]=>[6,2]=>3360
[4,2,5,7,3,1,6,8]=>[4,2,1,1]=>2520
[8,2,4,5,3,1,6,7]=>[4,3,1]=>3360
[8,4,5,1,3,2,6,7]=>[6,2]=>3360
[4,3,7,5,2,1,6,8]=>[7,1]=>5760
[1,6,7,4,3,2,5,8]=>[3,2,1,1,1]=>1120
[1,4,5,7,3,2,6,8]=>[4,2,1,1]=>2520
[3,5,1,4,7,2,6,8]=>[4,2,1,1]=>2520
[2,5,1,4,7,8,3,6]=>[5,2,1]=>4032
[4,3,7,1,5,2,6,8]=>[4,2,1,1]=>2520
[3,5,1,6,4,2,7,8]=>[4,2,1,1]=>2520
[6,4,3,1,7,2,5,8]=>[4,2,1,1]=>2520
[6,2,7,4,3,1,5,8]=>[3,2,1,1,1]=>1120
[2,6,4,1,7,3,5,8]=>[5,2,1]=>4032
[6,3,2,7,4,5,1,8]=>[5,2,1]=>4032
[7,2,4,1,3,6,8,5]=>[6,1,1]=>3360
[6,3,2,5,7,1,4,8]=>[3,2,2,1]=>1680
[3,2,6,5,7,1,4,8]=>[3,3,1,1]=>1120
[1,7,3,2,5,6,4,8]=>[3,1,1,1,1,1]=>112
[2,1,7,3,5,6,8,4]=>[4,2,1,1]=>2520
[2,1,6,3,5,7,8,4]=>[5,2,1]=>4032
[1,6,3,2,5,7,4,8]=>[4,1,1,1,1]=>420
[1,4,6,5,2,7,3,8]=>[3,3,1,1]=>1120
[5,6,2,1,4,3,7,8]=>[3,3,1,1]=>1120
[2,5,1,6,4,3,7,8]=>[6,1,1]=>3360
[2,5,4,1,6,3,7,8]=>[6,1,1]=>3360
[4,6,1,5,2,7,3,8]=>[7,1]=>5760
[1,6,5,3,7,2,4,8]=>[4,2,1,1]=>2520
[1,2,5,3,4,8,7,6]=>[3,2,1,1,1]=>1120
[5,2,7,6,1,8,4,3]=>[5,2,1]=>4032
[5,8,2,6,1,7,4,3]=>[3,3,2]=>1120
[1,5,8,3,6,2,7,4]=>[3,3,1,1]=>1120
[1,2,6,4,7,3,8,5]=>[3,2,1,1,1]=>1120
[1,2,7,8,3,5,6,4]=>[4,2,1,1]=>2520
[2,7,4,5,8,1,6,3]=>[4,4]=>1260
[5,8,6,2,3,4,1,7]=>[8]=>5040
[5,8,6,2,1,4,3,7]=>[6,2]=>3360
[6,4,7,5,8,2,1,3]=>[8]=>5040
[6,3,7,4,2,5,8,1]=>[7,1]=>5760
[7,5,6,2,4,3,8,1]=>[3,3,2]=>1120
[4,6,2,5,7,3,8,1]=>[5,3]=>2688
[8,1,7,4,5,6,2,3]=>[5,1,1,1]=>1344
[2,1,7,8,4,5,6,3]=>[6,2]=>3360
[8,2,1,4,3,7,6,5]=>[4,2,1,1]=>2520
[7,6,5,3,1,2,8,4]=>[6,2]=>3360
[5,4,1,6,2,8,3,7]=>[8]=>5040
[3,1,8,6,7,2,4,5]=>[8]=>5040
[4,2,5,1,8,6,7,3]=>[3,2,1,1,1]=>1120
[4,5,3,7,1,6,8,2]=>[6,1,1]=>3360
[2,8,6,3,5,4,7,1]=>[3,3,1,1]=>1120
[3,5,2,8,6,4,7,1]=>[7,1]=>5760
[7,3,5,1,6,4,8,2]=>[8]=>5040
[5,1,4,7,2,6,8,3]=>[4,3,1]=>3360
[1,8,2,5,6,4,7,3]=>[3,3,1,1]=>1120
[2,7,1,4,8,5,6,3]=>[7,1]=>5760
[2,8,4,6,1,3,7,5]=>[4,3,1]=>3360
[8,4,6,2,5,3,7,1]=>[2,2,2,1,1]=>420
[8,3,7,6,2,1,5,4]=>[4,4]=>1260
[8,5,2,7,6,1,4,3]=>[6,2]=>3360
[5,8,2,7,6,1,4,3]=>[3,3,2]=>1120
[8,3,7,6,2,5,1,4]=>[8]=>5040
[7,3,8,6,5,1,4,2]=>[4,3,1]=>3360
[2,6,3,7,5,4,8,1]=>[6,1,1]=>3360
[5,4,7,1,3,8,6,2]=>[8]=>5040
[2,8,5,1,4,7,3,6]=>[8]=>5040
[7,2,6,5,8,4,3,1]=>[7,1]=>5760
[5,8,2,3,4,6,1,7]=>[7,1]=>5760
[1,5,6,3,2,4,7,8]=>[3,2,1,1,1]=>1120
[2,4,5,7,3,6,1,8]=>[4,2,1,1]=>2520
[1,7,8,4,5,3,6,2]=>[5,1,1,1]=>1344
[5,7,4,2,1,6,3,8]=>[4,2,1,1]=>2520
[7,4,8,6,3,5,2,1]=>[8]=>5040
[4,7,6,3,5,2,1,8]=>[6,1,1]=>3360
[1,6,5,8,7,4,2,3]=>[7,1]=>5760
[1,7,4,5,2,8,6,3]=>[7,1]=>5760
[7,5,4,2,1,8,6,3]=>[8]=>5040
[7,8,2,6,4,5,3,1]=>[5,3]=>2688
[7,6,8,5,4,1,3,2]=>[6,2]=>3360
[4,1,3,8,6,2,7,5]=>[6,1,1]=>3360
[5,6,3,2,8,1,7,4]=>[6,1,1]=>3360
[8,2,6,3,1,5,7,4]=>[6,1,1]=>3360
[8,2,5,6,7,4,3,1]=>[3,2,2,1]=>1680
[8,2,5,3,4,7,6,1]=>[3,2,2,1]=>1680
[7,5,3,2,4,1,8,6]=>[4,3,1]=>3360
[7,1,2,3,6,8,4,5]=>[5,3]=>2688
[6,7,2,8,3,4,5,1]=>[4,4]=>1260
[3,1,8,4,6,5,7,2]=>[4,2,1,1]=>2520
[6,1,2,3,8,4,7,5]=>[5,2,1]=>4032
[8,1,6,7,4,2,3,5]=>[8]=>5040
[8,1,6,4,5,2,3,7]=>[6,1,1]=>3360
[8,6,4,1,2,3,7,5]=>[7,1]=>5760
[8,6,1,4,2,5,7,3]=>[3,3,1,1]=>1120
[8,6,4,2,5,3,7,1]=>[4,2,1,1]=>2520
[8,6,4,1,5,7,2,3]=>[4,3,1]=>3360
[8,6,1,4,7,2,5,3]=>[3,2,2,1]=>1680
[8,6,4,1,5,2,3,7]=>[5,2,1]=>4032
[8,6,7,1,4,5,2,3]=>[8]=>5040
[3,4,7,5,8,2,6,1]=>[8]=>5040
[8,7,1,4,6,5,2,3]=>[3,2,2,1]=>1680
[8,3,7,6,4,5,1,2]=>[5,3]=>2688
[5,3,8,6,4,1,7,2]=>[4,3,1]=>3360
[8,10,1,2,3,4,5,9,6,7]=>[10]=>362880
[10,8,1,9,2,3,4,5,6,7]=>[7,3]=>172800
[8,7,1,2,3,4,5,9,10,6]=>[10]=>362880
[10,11,1,9,2,3,4,5,6,7,8]=>[7,4]=>1425600
[6,1,2,3,4,5,7,8,9]=>[6,1,1,1]=>10080
[5,1,2,3,4,6,7,8,9]=>[5,1,1,1,1]=>3024
[4,1,2,3,5,6,7,8,9]=>[4,1,1,1,1,1]=>756
[2,10,1,5,6,7,8,9,3,4]=>[10]=>362880
[2,3,4,5,6,7,8,9,10,11,12,1]=>[12]=>39916800
[7,4,5,1,2,8,6,3]=>[8]=>5040
[6,4,7,1,8,5,2,3]=>[8]=>5040
[5,7,4,2,3,8,6,1]=>[8]=>5040
[3,8,2,5,1,7,4,6]=>[8]=>5040
[5,8,4,2,3,7,1,6]=>[8]=>5040
[4,8,5,2,1,7,3,6]=>[8]=>5040
[8,5,7,6,1,2,4,3]=>[8]=>5040
[6,8,7,5,2,4,1,3]=>[8]=>5040
[5,7,6,8,4,1,3,2]=>[8]=>5040
[7,3,1,6,8,5,4,2]=>[8]=>5040
[5,3,1,7,4,8,6,2]=>[8]=>5040
[7,3,1,8,6,4,5,2]=>[8]=>5040
[8,6,4,1,7,3,2,5]=>[8]=>5040
[4,6,8,3,7,1,2,5]=>[8]=>5040
[3,5,2,8,4,7,1,6]=>[8]=>5040
[6,4,8,3,7,2,1,5]=>[8]=>5040
[3,6,2,8,7,4,1,5]=>[8]=>5040
[6,8,4,2,7,3,1,5]=>[8]=>5040
[9,8,2,3,4,5,6,7,1]=>[7,2]=>25920
[8,9,2,3,4,5,6,7,1]=>[9]=>40320
[9,8,7,6,4,5,3,2,1]=>[3,2,2,2]=>2520
[5,6,7,9,8,4,3,2,1]=>[7,2]=>25920
[5,6,7,8,9,1,4,3,2]=>[5,4]=>18144
[10,9,2,3,4,5,6,7,8,1]=>[8,2]=>226800
[3,4,7,8,5,1,2,6]=>[7,1]=>5760
[4,7,3,2,5,6,8,1]=>[5,1,1,1]=>1344
[3,2,7,6,4,5,8,1]=>[4,3,1]=>3360
[1,7,3,6,8,4,2,5]=>[2,2,2,1,1]=>420
[2,3,6,5,1,8,7,4]=>[7,1]=>5760
[8,3,1,2,6,4,7,5]=>[7,1]=>5760
[1,7,8,2,4,3,5,6]=>[4,3,1]=>3360
[3,6,4,7,1,2,8,5]=>[6,2]=>3360
[5,7,4,8,1,3,2,6]=>[4,2,2]=>1260
[4,3,7,8,1,5,2,6]=>[5,3]=>2688
[8,5,4,2,6,1,7,3]=>[7,1]=>5760
[3,2,6,8,7,4,1,5]=>[7,1]=>5760
[2,3,7,5,1,8,6,4]=>[8]=>5040
[6,3,1,2,8,7,4,5]=>[6,2]=>3360
[5,2,1,3,8,7,6,4]=>[5,2,1]=>4032
[7,2,1,5,3,8,4,6]=>[5,2,1]=>4032
[1,5,8,2,4,3,6,7]=>[4,3,1]=>3360
[4,3,6,8,1,5,2,7]=>[8]=>5040
[5,4,6,8,3,1,7,2]=>[4,3,1]=>3360
[3,6,8,4,5,1,7,2]=>[5,1,1,1]=>1344
[8,6,1,7,2,4,3,5]=>[8]=>5040
[7,3,1,2,8,6,4,5]=>[5,2,1]=>4032
[2,3,7,6,1,8,5,4]=>[5,3]=>2688
[3,2,7,8,6,4,1,5]=>[4,3,1]=>3360
[6,2,8,3,1,4,7,5]=>[6,1,1]=>3360
[3,1,2,8,7,4,5,6]=>[3,3,2]=>1120
[2,1,3,8,7,4,6,5]=>[5,2,1]=>4032
[2,1,3,8,7,4,5,6]=>[3,2,2,1]=>1680
[1,6,8,3,2,4,7,5]=>[6,1,1]=>3360
[8,5,1,7,2,4,3,6]=>[6,2]=>3360
[8,4,1,7,3,2,5,6]=>[8]=>5040
[8,3,1,6,2,7,5,4]=>[8]=>5040
[1,3,2,8,7,6,4,5]=>[4,2,1,1]=>2520
[2,1,3,8,7,6,4,5]=>[4,2,1,1]=>2520
[2,4,3,1,6,5,8,7,10,9]=>[3,2,2,2,1]=>25200
[1,6,3,7,2,5,4,8]=>[3,2,1,1,1]=>1120
[1,7,2,4,6,3,5,8]=>[5,1,1,1]=>1344
[5,6,2,8,4,1,3,7]=>[8]=>5040
[3,5,8,4,2,1,6,7]=>[5,2,1]=>4032
[2,5,8,3,1,4,6,7]=>[5,3]=>2688
[2,8,1,3,5,7,4,6]=>[7,1]=>5760
[5,4,7,8,3,2,6,1]=>[8]=>5040
[3,4,8,5,7,1,2,6]=>[4,4]=>1260
[3,6,8,2,5,1,4,7]=>[7,1]=>5760
[3,6,8,7,2,5,4,1]=>[3,3,2]=>1120
[3,4,6,5,8,2,1,7]=>[8]=>5040
[2,4,6,7,8,3,5,1]=>[6,2]=>3360
[1,4,2,5,7,6,3,8]=>[5,1,1,1]=>1344
[1,4,2,6,8,5,3,7]=>[7,1]=>5760
[1,2,6,8,3,5,4,7]=>[3,3,1,1]=>1120
[1,6,8,3,5,4,2,7]=>[6,1,1]=>3360
[1,5,3,2,4,6,8,7]=>[3,2,1,1,1]=>1120
[1,5,8,7,6,3,2,4]=>[7,1]=>5760
[1,5,7,6,3,2,4,8]=>[6,1,1]=>3360
[1,6,3,2,4,7,5,8]=>[5,1,1,1]=>1344
[1,6,3,2,4,8,7,5]=>[5,1,1,1]=>1344
[1,2,7,6,4,3,5,8]=>[5,1,1,1]=>1344
[1,8,7,5,2,4,6,3]=>[7,1]=>5760
[1,7,5,2,4,6,3,8]=>[5,1,1,1]=>1344
[1,7,4,2,5,3,6,8]=>[5,1,1,1]=>1344
[1,8,4,7,5,2,6,3]=>[6,1,1]=>3360
[1,7,5,2,3,6,4,8]=>[3,2,1,1,1]=>1120
[1,7,5,2,6,3,4,8]=>[3,3,1,1]=>1120
[1,6,3,7,4,2,5,8]=>[3,2,1,1,1]=>1120
[1,6,3,2,7,5,4,8]=>[5,1,1,1]=>1344
[1,4,7,5,2,6,3,8]=>[3,2,1,1,1]=>1120
[1,3,6,4,8,7,5,2]=>[6,1,1]=>3360
[1,3,7,6,4,2,5,8]=>[6,1,1]=>3360
[1,3,2,4,8,5,7,6]=>[3,2,1,1,1]=>1120
[1,3,8,7,5,2,4,6]=>[4,2,1,1]=>2520
[1,4,6,3,2,7,5,8]=>[6,1,1]=>3360
[1,4,6,3,2,8,7,5]=>[6,1,1]=>3360
[1,5,7,6,4,2,3,8]=>[4,2,1,1]=>2520
[1,6,3,2,8,4,7,5]=>[3,2,1,1,1]=>1120
[1,6,3,5,2,7,4,8]=>[5,1,1,1]=>1344
[1,6,3,5,2,8,7,4]=>[5,1,1,1]=>1344
[1,8,3,7,5,2,4,6]=>[3,2,1,1,1]=>1120
[6,4,7,1,5,3,8,2]=>[7,1]=>5760
[5,3,8,2,6,4,7,1]=>[7,1]=>5760
[4,3,8,2,6,5,7,1]=>[5,2,1]=>4032
[5,7,1,4,8,2,3,6]=>[7,1]=>5760
[6,5,7,1,4,3,8,2]=>[8]=>5040
[5,7,6,1,2,4,8,3]=>[8]=>5040
[4,8,3,5,7,6,2,1]=>[6,1,1]=>3360
[5,7,6,2,4,8,3,1]=>[8]=>5040
[6,7,5,2,3,8,4,1]=>[3,3,2]=>1120
[6,7,5,3,8,4,2,1]=>[6,2]=>3360
[7,3,1,4,2,6,5,8]=>[5,1,1,1]=>1344
[5,4,1,8,2,6,3,7]=>[7,1]=>5760
[5,3,1,8,2,6,4,7]=>[4,3,1]=>3360
[4,7,1,5,2,6,3,8]=>[6,1,1]=>3360
[6,5,1,4,2,7,3,8]=>[4,2,1,1]=>2520
[1,8,7,3,4,5,2,6]=>[7,1]=>5760
[1,8,7,4,5,2,3,6]=>[3,2,1,1,1]=>1120
[1,2,6,8,7,3,4,5]=>[4,2,1,1]=>2520
[1,3,4,5,6,7,8,9,10,11,12,2]=>[11,1]=>43545600
[8,4,2,3,1,6,5,7]=>[4,3,1]=>3360
[6,4,5,2,8,1,7,3]=>[3,2,2,1]=>1680
[4,8,6,2,3,1,7,5]=>[7,1]=>5760
[6,4,2,1,8,5,3,7]=>[8]=>5040
[6,4,2,3,5,8,1,7]=>[4,3,1]=>3360
[2,8,6,4,5,1,7,3]=>[5,1,1,1]=>1344
[8,2,4,6,7,1,5,3]=>[5,2,1]=>4032
[2,6,3,1,7,4,8,5]=>[4,3,1]=>3360
[6,5,1,8,3,2,7,4]=>[5,2,1]=>4032
[1,4,3,7,2,8,6,5]=>[6,1,1]=>3360
[1,8,7,4,5,3,2,6]=>[5,1,1,1]=>1344
[6,1,7,2,8,4,5,3]=>[4,4]=>1260
[3,2,6,7,8,4,5,1]=>[7,1]=>5760
[1,7,4,6,3,8,2,5]=>[5,2,1]=>4032
[5,6,4,1,3,8,2,7]=>[4,4]=>1260
[4,5,3,1,8,7,6,2]=>[3,2,2,1]=>1680
[6,3,4,2,7,8,5,1]=>[3,3,2]=>1120
[8,7,4,5,1,6,3,2]=>[7,1]=>5760
[6,2,7,8,1,3,5,4]=>[5,2,1]=>4032
[5,1,8,4,3,7,2,6]=>[7,1]=>5760
[7,2,8,1,4,5,6,3]=>[5,2,1]=>4032
[2,1,4,3,6,5,8,10,9,7]=>[3,2,2,2,1]=>25200
[2,1,4,3,6,8,7,5,10,9]=>[3,2,2,2,1]=>25200
[2,1,4,3,8,10,7,9,5,6]=>[3,2,2,2,1]=>25200
[2,1,4,3,6,7,10,8,9,5]=>[4,2,2,1,1]=>56700
[2,1,4,6,5,3,8,7,10,9]=>[3,2,2,2,1]=>25200
[2,1,4,6,5,3,8,10,9,7]=>[3,3,2,1,1]=>50400
[2,1,6,8,5,7,3,4,10,9]=>[3,2,2,2,1]=>25200
[2,1,8,7,5,10,4,9,3,6]=>[3,2,2,2,1]=>25200
[2,1,6,7,5,10,8,4,9,3]=>[3,3,2,1,1]=>50400
[2,1,4,5,8,6,7,3,10,9]=>[4,2,2,1,1]=>56700
[2,1,8,5,10,6,7,9,3,4]=>[3,3,2,1,1]=>50400
[2,1,4,7,10,6,9,8,3,5]=>[4,2,2,1,1]=>56700
[2,1,4,5,6,10,7,8,9,3]=>[5,2,1,1,1]=>60480
[2,4,3,1,6,5,8,10,9,7]=>[3,3,2,1,1]=>50400
[2,4,3,1,6,8,7,5,10,9]=>[3,3,2,1,1]=>50400
[2,4,3,1,8,10,7,9,5,6]=>[3,3,2,1,1]=>50400
[2,4,3,1,6,7,10,8,9,5]=>[4,3,1,1,1]=>50400
[4,6,3,5,1,2,8,7,10,9]=>[3,2,2,2,1]=>25200
[4,6,3,5,1,2,8,10,9,7]=>[3,3,2,1,1]=>50400
[6,5,3,8,2,7,1,4,10,9]=>[3,2,2,2,1]=>25200
[8,5,3,7,2,10,4,9,1,6]=>[3,2,2,2,1]=>25200
[6,5,3,7,2,10,8,4,9,1]=>[3,3,2,1,1]=>50400
[4,5,3,8,6,2,7,1,10,9]=>[3,3,2,1,1]=>50400
[8,6,3,5,10,2,7,9,1,4]=>[3,3,2,1,1]=>50400
[4,7,3,6,10,1,9,8,2,5]=>[3,3,2,1,1]=>50400
[4,5,3,6,10,7,1,8,9,2]=>[4,3,1,1,1]=>50400
[2,3,6,4,5,1,8,7,10,9]=>[4,2,2,1,1]=>56700
[2,3,6,4,5,1,8,10,9,7]=>[4,3,1,1,1]=>50400
[6,3,8,4,5,7,1,2,10,9]=>[3,3,2,1,1]=>50400
[8,3,7,4,5,10,2,9,1,6]=>[3,3,2,1,1]=>50400
[6,3,7,4,5,10,8,2,9,1]=>[4,3,1,1,1]=>50400
[2,5,8,4,7,6,1,3,10,9]=>[4,2,2,1,1]=>56700
[8,5,10,4,7,6,2,9,1,3]=>[3,3,2,1,1]=>50400
[2,7,10,4,8,6,9,5,1,3]=>[4,2,2,1,1]=>56700
[2,5,6,4,10,8,7,3,9,1]=>[4,3,1,1,1]=>50400
[2,3,4,8,5,6,7,1,10,9]=>[5,2,1,1,1]=>60480
[8,3,4,10,5,6,7,9,1,2]=>[4,3,1,1,1]=>50400
[2,7,4,10,5,6,9,8,1,3]=>[4,3,1,1,1]=>50400
[2,3,6,10,5,9,7,8,1,4]=>[5,2,1,1,1]=>60480
[2,3,4,5,10,6,7,8,9,1]=>[6,1,1,1,1]=>25200
[2,1,4,3,6,5,8,7,10,12,11,9]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,6,5,8,10,9,7,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,6,5,10,12,9,11,7,8]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,6,8,7,5,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,6,8,7,5,10,12,11,9]=>[3,3,2,2,1,1]=>1663200
[2,1,4,3,8,10,7,9,5,6,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,10,9,7,12,6,11,5,8]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,8,9,7,12,10,6,11,5]=>[3,3,2,2,1,1]=>1663200
[2,1,4,3,10,7,12,8,9,11,5,6]=>[3,3,2,2,1,1]=>1663200
[2,1,4,3,6,7,8,12,9,10,11,5]=>[5,2,2,1,1,1]=>1995840
[2,1,4,6,5,3,8,7,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,6,5,3,8,7,10,12,11,9]=>[3,3,2,2,1,1]=>1663200
[2,1,4,6,5,3,8,10,9,7,12,11]=>[3,3,2,2,1,1]=>1663200
[2,1,4,6,5,3,10,12,9,11,7,8]=>[3,3,2,2,1,1]=>1663200
[2,1,6,8,5,7,3,4,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,6,8,5,7,3,4,10,12,11,9]=>[3,3,2,2,1,1]=>1663200
[2,1,8,7,5,10,4,9,3,6,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,10,7,5,9,4,12,6,11,3,8]=>[3,2,2,2,2,1]=>415800
[2,1,8,7,5,9,4,12,10,6,11,3]=>[3,3,2,2,1,1]=>1663200
[2,1,6,7,5,10,8,4,9,3,12,11]=>[3,3,2,2,1,1]=>1663200
[2,1,10,8,5,7,12,4,9,11,3,6]=>[3,3,2,2,1,1]=>1663200
[2,1,6,9,5,8,12,3,11,10,4,7]=>[3,3,2,2,1,1]=>1663200
[2,1,8,5,10,6,7,9,3,4,12,11]=>[3,3,2,2,1,1]=>1663200
[2,1,10,5,9,6,7,12,4,11,3,8]=>[3,3,2,2,1,1]=>1663200
[2,1,10,7,12,6,9,8,4,11,3,5]=>[3,3,2,2,1,1]=>1663200
[2,1,4,5,6,10,7,8,9,3,12,11]=>[5,2,2,1,1,1]=>1995840
[2,1,4,5,8,12,7,11,9,10,3,6]=>[5,2,2,1,1,1]=>1995840
[2,4,3,1,6,5,8,7,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,4,3,1,6,5,8,7,10,12,11,9]=>[3,3,2,2,1,1]=>1663200
[2,4,3,1,6,5,8,10,9,7,12,11]=>[3,3,2,2,1,1]=>1663200
[2,4,3,1,6,5,10,12,9,11,7,8]=>[3,3,2,2,1,1]=>1663200
[2,4,3,1,6,8,7,5,10,9,12,11]=>[3,3,2,2,1,1]=>1663200
[2,4,3,1,8,10,7,9,5,6,12,11]=>[3,3,2,2,1,1]=>1663200
[2,4,3,1,10,9,7,12,6,11,5,8]=>[3,3,2,2,1,1]=>1663200
[4,6,3,5,1,2,8,7,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[4,6,3,5,1,2,8,7,10,12,11,9]=>[3,3,2,2,1,1]=>1663200
[4,6,3,5,1,2,8,10,9,7,12,11]=>[3,3,2,2,1,1]=>1663200
[4,6,3,5,1,2,10,12,9,11,7,8]=>[3,3,2,2,1,1]=>1663200
[6,5,3,8,2,7,1,4,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[6,5,3,8,2,7,1,4,10,12,11,9]=>[3,3,2,2,1,1]=>1663200
[8,5,3,7,2,10,4,9,1,6,12,11]=>[3,2,2,2,2,1]=>415800
[10,5,3,7,2,9,4,12,6,11,1,8]=>[3,2,2,2,2,1]=>415800
[8,5,3,7,2,9,4,12,10,6,11,1]=>[3,3,2,2,1,1]=>1663200
[6,5,3,7,2,10,8,4,9,1,12,11]=>[3,3,2,2,1,1]=>1663200
[10,5,3,8,2,7,12,4,9,11,1,6]=>[3,3,2,2,1,1]=>1663200
[6,5,3,9,2,8,12,1,11,10,4,7]=>[3,3,2,2,1,1]=>1663200
[4,5,3,8,6,2,7,1,10,9,12,11]=>[3,3,2,2,1,1]=>1663200
[8,6,3,5,10,2,7,9,1,4,12,11]=>[3,3,2,2,1,1]=>1663200
[10,6,3,5,9,2,7,12,4,11,1,8]=>[3,3,2,2,1,1]=>1663200
[4,7,3,6,10,1,9,8,2,5,12,11]=>[3,3,2,2,1,1]=>1663200
[10,6,3,7,12,2,9,8,4,11,1,5]=>[3,3,2,2,1,1]=>1663200
[4,9,3,6,12,1,10,8,11,7,2,5]=>[3,3,2,2,1,1]=>1663200
[6,3,8,4,5,7,1,2,10,9,12,11]=>[3,3,2,2,1,1]=>1663200
[8,3,7,4,5,10,2,9,1,6,12,11]=>[3,3,2,2,1,1]=>1663200
[10,3,7,4,5,9,2,12,6,11,1,8]=>[3,3,2,2,1,1]=>1663200
[8,5,10,4,7,6,2,9,1,3,12,11]=>[3,3,2,2,1,1]=>1663200
[10,5,9,4,7,6,2,12,3,11,1,8]=>[3,3,2,2,1,1]=>1663200
[10,7,12,4,8,6,9,5,2,11,1,3]=>[3,3,2,2,1,1]=>1663200
[2,3,4,8,5,6,7,1,10,9,12,11]=>[5,2,2,1,1,1]=>1995840
[2,3,6,10,5,9,7,8,1,4,12,11]=>[5,2,2,1,1,1]=>1995840
[2,3,8,12,5,10,7,11,9,6,1,4]=>[5,2,2,1,1,1]=>1995840
[8,1,6,7,2,5,4,3]=>[6,2]=>3360
[7,5,2,3,6,8,4,1]=>[8]=>5040
[8,1,4,6,5,3,2,7]=>[4,3,1]=>3360
[8,1,4,7,6,5,2,3]=>[6,2]=>3360
[8,1,2,7,6,5,4,3]=>[4,2,2]=>1260
[4,5,8,1,6,7,2,3]=>[4,2,2]=>1260
[3,2,8,6,1,5,7,4]=>[6,1,1]=>3360
[3,7,2,5,8,4,6,1]=>[8]=>5040
[6,7,8,4,1,5,2,3]=>[3,2,2,1]=>1680
[6,2,8,3,5,1,4,7]=>[4,2,1,1]=>2520
[6,8,2,5,3,4,1,7]=>[8]=>5040
[6,8,7,5,4,1,2,3]=>[4,2,2]=>1260
[7,4,5,6,1,8,2,3]=>[8]=>5040
[6,1,8,7,4,5,2,3]=>[6,2]=>3360
[1,3,2,6,8,7,4,5]=>[3,2,2,1]=>1680
[1,3,8,2,5,4,6,7]=>[6,1,1]=>3360
[1,6,2,5,8,7,3,4]=>[4,3,1]=>3360
[1,6,8,7,2,3,5,4]=>[7,1]=>5760
[1,6,8,7,2,5,3,4]=>[4,3,1]=>3360
[1,5,2,4,8,3,6,7]=>[6,1,1]=>3360
[1,2,4,5,8,6,3,7]=>[5,1,1,1]=>1344
[1,2,8,3,5,4,7,6]=>[4,1,1,1,1]=>420
[1,3,8,2,5,4,7,6]=>[5,1,1,1]=>1344
[1,6,7,5,2,4,8,3]=>[4,3,1]=>3360
[1,5,6,4,7,2,3,8]=>[5,1,1,1]=>1344
[1,7,4,2,5,8,3,6]=>[4,2,1,1]=>2520
[1,6,4,3,7,5,2,8]=>[4,2,1,1]=>2520
[1,6,5,4,7,2,3,8]=>[3,2,1,1,1]=>1120
[1,7,3,2,6,4,8,5]=>[6,1,1]=>3360
[1,5,8,2,3,6,7,4]=>[5,1,1,1]=>1344
[1,3,2,6,8,5,4,7]=>[5,2,1]=>4032
[1,6,3,2,7,4,5,8]=>[3,2,1,1,1]=>1120
[1,7,8,5,4,2,3,6]=>[5,2,1]=>4032
[1,8,4,2,3,6,5,7]=>[6,1,1]=>3360
[1,4,2,7,5,3,8,6]=>[6,1,1]=>3360
[1,5,7,6,2,4,3,8]=>[2,2,2,1,1]=>420
[1,8,4,7,3,2,6,5]=>[7,1]=>5760
[1,3,8,4,2,6,5,7]=>[5,1,1,1]=>1344
[1,7,4,2,6,5,8,3]=>[5,2,1]=>4032
[1,6,5,8,3,7,4,2]=>[5,2,1]=>4032
[1,7,4,8,3,2,5,6]=>[7,1]=>5760
[1,4,8,3,2,7,5,6]=>[7,1]=>5760
[1,8,3,6,4,5,2,7]=>[3,3,1,1]=>1120
[1,6,4,7,3,2,8,5]=>[5,2,1]=>4032
[8,2,3,7,4,5,6,1]=>[4,2,1,1]=>2520
[8,5,7,2,3,6,4,1]=>[5,2,1]=>4032
[7,5,2,1,6,8,3,4]=>[8]=>5040
[7,6,1,5,4,8,2,3]=>[6,2]=>3360
[7,6,3,2,1,8,4,5]=>[7,1]=>5760
[2,8,7,3,4,6,1,5]=>[7,1]=>5760
[6,5,1,3,7,2,8,4]=>[8]=>5040
[8,1,7,3,4,5,2,6]=>[8]=>5040
[7,1,8,3,4,5,2,6]=>[5,3]=>2688
[6,8,7,3,4,2,1,5]=>[8]=>5040
[3,8,7,1,2,4,5,6]=>[8]=>5040
[1,8,5,3,4,6,2,7]=>[3,3,1,1]=>1120
[7,1,6,5,4,3,8,2]=>[4,2,2]=>1260
[7,1,3,6,4,5,8,2]=>[4,3,1]=>3360
[7,1,5,3,6,4,8,2]=>[4,4]=>1260
[6,1,5,3,7,8,2,4]=>[8]=>5040
[5,8,7,1,2,6,3,4]=>[5,2,1]=>4032
[6,8,2,3,4,7,1,5]=>[5,3]=>2688
[5,1,7,3,8,6,2,4]=>[7,1]=>5760
[6,1,3,2,4,7,8,5]=>[7,1]=>5760
[6,2,1,3,4,7,8,5]=>[7,1]=>5760
[3,4,5,6,1,8,9,2,7]=>[4,3,2]=>15120
[3,4,5,6,8,1,9,2,7]=>[7,2]=>25920
[3,4,5,6,8,9,1,2,7]=>[9]=>40320
[2,4,5,1,6,7,8,9,3]=>[6,3]=>20160
[2,3,4,1,6,7,8,9,5]=>[5,4]=>18144
[2,3,4,5,6,1,8,9,10,7]=>[6,4]=>151200
[3,4,5,6,1,2,9,7,8]=>[3,3,3]=>2240
[3,4,5,6,8,1,2,7,9]=>[8,1]=>45360
[2,3,4,5,6,8,9,1,10,7]=>[7,3]=>172800
[3,4,5,1,6,7,8,2,9]=>[8,1]=>45360
[5,6,1,7,8,9,2,3,4]=>[5,4]=>18144
[4,5,6,1,7,8,9,10,2,3]=>[4,4,2]=>56700
[1,3,5,2,6,7,8,9,4]=>[8,1]=>45360
[3,5,6,1,7,8,9,10,2,4]=>[6,4]=>151200
[2,1,4,3,6,7,8,9,5]=>[5,2,2]=>9072
[3,4,6,1,7,8,9,10,2,5]=>[10]=>362880
[2,3,1,5,6,7,8,9,4]=>[6,3]=>20160
[3,4,5,1,7,8,9,10,2,6]=>[7,3]=>172800
[3,2,5,8,7,4,1,6]=>[4,3,1]=>3360
[4,2,5,8,7,3,1,6]=>[7,1]=>5760
[8,3,4,1,6,5,2,7]=>[6,2]=>3360
[3,4,8,5,7,2,1,6]=>[8]=>5040
[3,6,4,8,5,7,2,1]=>[4,3,1]=>3360
[5,8,4,7,3,6,2,1]=>[7,1]=>5760
[4,2,8,7,3,1,6,5]=>[4,3,1]=>3360
[6,5,8,2,1,7,4,3]=>[6,2]=>3360
[6,1,4,3,8,7,2,5]=>[4,2,2]=>1260
[5,1,3,2,6,8,7,4]=>[6,1,1]=>3360
[6,1,3,8,7,2,4,5]=>[4,3,1]=>3360
[1,2,8,4,5,7,3,6]=>[4,1,1,1,1]=>420
[4,2,1,8,7,6,3,5]=>[6,1,1]=>3360
[3,2,5,8,7,1,4,6]=>[7,1]=>5760
[5,6,3,8,7,2,1,4]=>[3,2,2,1]=>1680
[2,5,8,4,7,1,6,3]=>[5,2,1]=>4032
[1,6,2,4,8,5,7,3]=>[5,1,1,1]=>1344
[3,1,6,5,8,7,2,4]=>[5,3]=>2688
[4,8,5,3,6,7,1,2]=>[6,2]=>3360
[1,8,5,3,4,7,6,2]=>[3,2,2,1]=>1680
[2,7,1,3,6,4,5,8]=>[7,1]=>5760
[8,1,7,3,5,4,6,2]=>[4,3,1]=>3360
[8,1,2,4,7,5,6,3]=>[4,3,1]=>3360
[8,6,2,1,5,7,3,4]=>[4,3,1]=>3360
[4,6,2,8,5,3,7,1]=>[3,3,1,1]=>1120
[8,7,2,4,1,5,3,6]=>[4,3,1]=>3360
[7,5,3,4,8,6,2,1]=>[5,1,1,1]=>1344
[2,8,3,1,4,6,7,5]=>[5,1,1,1]=>1344
[4,3,6,5,1,2,7,8]=>[3,3,1,1]=>1120
[5,8,3,7,6,4,2,1]=>[7,1]=>5760
[1,3,8,7,6,5,2,4]=>[5,2,1]=>4032
[4,8,7,2,6,3,1,5]=>[8]=>5040
[1,8,7,2,6,3,5,4]=>[4,3,1]=>3360
[8,7,2,1,4,3,5,6]=>[8]=>5040
[2,8,7,1,6,3,4,5]=>[8]=>5040
[4,2,8,7,6,5,1,3]=>[3,2,2,1]=>1680
[6,3,8,7,4,5,2,1]=>[8]=>5040
[2,8,3,4,1,5,6,7]=>[6,1,1]=>3360
[1,3,7,5,4,8,6,2]=>[5,2,1]=>4032
[4,5,6,3,1,8,2,7]=>[8]=>5040
[1,5,6,3,8,4,2,7]=>[4,3,1]=>3360
[2,6,5,3,8,4,1,7]=>[8]=>5040
[5,7,3,8,4,2,6,1]=>[4,3,1]=>3360
[5,3,6,2,8,4,1,7]=>[4,4]=>1260
[2,3,6,5,4,8,1,7]=>[6,2]=>3360
[3,7,5,4,8,2,6,1]=>[4,3,1]=>3360
[5,3,7,1,2,8,4,6]=>[6,2]=>3360
[6,3,8,7,2,5,4,1]=>[6,2]=>3360
[9,7,8,5,4,3,2,1,6]=>[5,2,2]=>9072
[1,2,3,4,6,5,7,8,9]=>[2,1,1,1,1,1,1,1]=>36
[1,2,3,5,4,6,7,8,9]=>[2,1,1,1,1,1,1,1]=>36
[6,8,4,1,7,5,2,3]=>[8]=>5040
[8,1,4,6,7,5,2,3]=>[8]=>5040
[2,6,8,1,4,7,5,3]=>[6,2]=>3360
[6,4,8,1,2,7,5,3]=>[6,2]=>3360
[8,2,1,6,7,4,5,3]=>[3,2,2,1]=>1680
[4,2,8,1,6,7,5,3]=>[3,2,2,1]=>1680
[8,1,2,6,4,7,5,3]=>[4,4]=>1260
[8,4,1,6,2,7,5,3]=>[5,3]=>2688
[4,8,1,2,6,7,5,3]=>[5,3]=>2688
[4,8,2,1,6,7,5,3]=>[3,3,2]=>1120
[8,2,4,6,1,7,5,3]=>[7,1]=>5760
[2,1,4,3,6,5,8,9,10,7]=>[4,2,2,2]=>18900
[2,1,4,3,6,7,8,5,10,9]=>[4,2,2,2]=>18900
[2,1,4,3,8,7,9,10,5,6]=>[6,2,2]=>75600
[2,1,4,3,6,7,8,9,10,5]=>[6,2,2]=>75600
[2,1,4,5,6,3,8,7,10,9]=>[4,2,2,2]=>18900
[2,1,4,5,6,3,8,9,10,7]=>[4,4,2]=>56700
[2,1,6,5,7,8,3,4,10,9]=>[6,2,2]=>75600
[2,1,8,5,9,7,3,10,6,4]=>[8,2]=>226800
[2,1,6,5,7,8,9,10,3,4]=>[8,2]=>226800
[2,1,4,5,6,7,8,3,10,9]=>[6,2,2]=>75600
[2,1,8,5,6,7,9,10,3,4]=>[8,2]=>226800
[2,1,4,7,6,8,9,3,10,5]=>[8,2]=>226800
[2,1,4,5,6,7,8,9,10,3]=>[8,2]=>226800
[2,3,4,1,6,5,8,7,10,9]=>[4,2,2,2]=>18900
[2,3,4,1,6,5,8,9,10,7]=>[4,4,2]=>56700
[2,3,4,1,6,7,8,5,10,9]=>[4,4,2]=>56700
[2,3,4,1,8,7,9,10,5,6]=>[6,4]=>151200
[2,3,4,1,6,7,8,9,10,5]=>[6,4]=>151200
[4,3,5,6,1,2,8,7,10,9]=>[6,2,2]=>75600
[4,3,5,6,1,2,8,9,10,7]=>[6,4]=>151200
[6,3,7,5,1,8,4,2,10,9]=>[8,2]=>226800
[8,3,9,5,1,7,4,10,6,2]=>[10]=>362880
[6,3,7,5,1,8,9,10,4,2]=>[10]=>362880
[4,3,5,6,7,8,1,2,10,9]=>[8,2]=>226800
[8,3,9,5,6,7,1,10,4,2]=>[10]=>362880
[4,3,7,8,6,10,9,2,5,1]=>[10]=>362880
[4,3,5,6,7,8,9,10,1,2]=>[10]=>362880
[2,3,4,5,6,1,8,7,10,9]=>[6,2,2]=>75600
[6,3,4,5,7,8,1,2,10,9]=>[8,2]=>226800
[8,3,4,5,9,7,1,10,6,2]=>[10]=>362880
[6,3,4,5,7,8,9,10,1,2]=>[10]=>362880
[2,5,4,6,7,1,8,3,10,9]=>[8,2]=>226800
[8,5,4,6,7,1,9,10,3,2]=>[10]=>362880
[2,7,4,8,6,1,9,5,10,3]=>[10]=>362880
[2,5,4,6,7,8,9,1,10,3]=>[10]=>362880
[2,3,4,5,6,7,8,1,10,9]=>[8,2]=>226800
[8,3,4,5,6,7,9,10,1,2]=>[10]=>362880
[2,7,4,5,6,8,9,1,10,3]=>[10]=>362880
[2,3,6,5,7,8,1,9,10,4]=>[10]=>362880
[2,1,4,3,6,7,8,5,10,11,12,9]=>[4,4,2,2]=>1871100
[2,1,4,5,6,3,8,7,10,11,12,9]=>[4,4,2,2]=>1871100
[2,1,4,5,6,3,8,9,10,7,12,11]=>[4,4,2,2]=>1871100
[2,1,4,5,6,3,10,9,11,12,7,8]=>[6,4,2]=>9979200
[2,1,4,5,6,3,8,9,10,11,12,7]=>[6,4,2]=>9979200
[2,1,6,5,7,8,3,4,10,11,12,9]=>[6,4,2]=>9979200
[2,1,4,5,6,7,8,3,10,11,12,9]=>[6,4,2]=>9979200
[2,3,4,1,6,5,8,7,10,11,12,9]=>[4,4,2,2]=>1871100
[2,3,4,1,6,5,8,9,10,7,12,11]=>[4,4,2,2]=>1871100
[2,3,4,1,6,5,10,9,11,12,7,8]=>[6,4,2]=>9979200
[2,3,4,1,6,5,8,9,10,11,12,7]=>[6,4,2]=>9979200
[2,3,4,1,6,7,8,5,10,9,12,11]=>[4,4,2,2]=>1871100
[2,3,4,1,6,7,8,5,10,11,12,9]=>[4,4,4]=>1247400
[2,3,4,1,8,7,9,10,5,6,12,11]=>[6,4,2]=>9979200
[2,3,4,1,6,7,8,9,10,5,12,11]=>[6,4,2]=>9979200
[4,3,5,6,1,2,8,7,10,11,12,9]=>[6,4,2]=>9979200
[4,3,5,6,1,2,8,9,10,7,12,11]=>[6,4,2]=>9979200
[4,3,5,6,1,2,10,9,11,12,7,8]=>[6,6]=>6652800
[4,3,5,6,1,2,8,9,10,11,12,7]=>[6,6]=>6652800
[10,3,11,5,1,7,4,9,6,12,8,2]=>[12]=>39916800
[8,3,9,5,1,7,4,10,11,12,6,2]=>[12]=>39916800
[10,3,11,5,1,7,8,9,4,12,6,2]=>[12]=>39916800
[6,3,9,5,2,10,8,12,11,4,7,1]=>[12]=>39916800
[6,3,7,5,1,8,9,10,11,12,4,2]=>[12]=>39916800
[10,3,11,5,6,7,1,9,4,12,8,2]=>[12]=>39916800
[8,3,9,5,6,7,1,10,11,12,4,2]=>[12]=>39916800
[10,3,11,7,6,8,9,4,1,12,5,2]=>[12]=>39916800
[4,3,9,10,6,12,8,2,11,7,5,1]=>[12]=>39916800
[4,3,7,8,6,9,10,12,11,5,1,2]=>[12]=>39916800
[10,3,11,5,6,7,8,9,1,12,4,2]=>[12]=>39916800
[4,3,9,10,6,7,8,12,11,2,5,1]=>[12]=>39916800
[4,3,5,8,9,7,12,10,1,11,6,2]=>[12]=>39916800
[4,3,5,6,7,8,9,10,11,12,1,2]=>[12]=>39916800
[2,3,4,5,6,1,8,7,10,11,12,9]=>[6,4,2]=>9979200
[2,3,4,5,6,1,8,9,10,7,12,11]=>[6,4,2]=>9979200
[2,3,4,5,6,1,10,9,11,12,7,8]=>[6,6]=>6652800
[2,3,4,5,6,1,8,9,10,11,12,7]=>[6,6]=>6652800
[10,3,4,5,11,7,1,9,6,12,8,2]=>[12]=>39916800
[8,3,4,5,9,7,1,10,11,12,6,2]=>[12]=>39916800
[10,3,4,5,11,7,8,9,1,12,6,2]=>[12]=>39916800
[6,3,4,5,9,10,8,12,11,2,7,1]=>[12]=>39916800
[6,3,4,5,7,8,9,10,11,12,1,2]=>[12]=>39916800
[10,5,4,6,7,1,11,9,3,12,8,2]=>[12]=>39916800
[8,5,4,6,7,1,9,10,11,12,3,2]=>[12]=>39916800
[10,7,4,8,6,1,9,5,11,12,3,2]=>[12]=>39916800
[2,9,4,10,6,1,8,5,11,7,12,3]=>[12]=>39916800
[2,7,4,8,6,1,9,10,11,5,12,3]=>[12]=>39916800
[10,5,4,6,7,8,9,1,11,12,3,2]=>[12]=>39916800
[2,9,4,10,6,7,8,1,11,5,12,3]=>[12]=>39916800
[2,5,4,8,9,7,11,10,3,6,12,1]=>[12]=>39916800
[2,5,4,6,7,8,9,10,11,1,12,3]=>[12]=>39916800
[10,3,4,5,6,7,11,9,1,12,8,2]=>[12]=>39916800
[8,3,4,5,6,7,9,10,11,12,1,2]=>[12]=>39916800
[10,7,4,5,6,8,9,1,11,12,3,2]=>[12]=>39916800
[2,9,4,5,6,10,8,1,11,7,12,3]=>[12]=>39916800
[2,7,4,5,6,8,9,10,11,1,12,3]=>[12]=>39916800
[10,3,6,5,7,8,1,9,11,12,4,2]=>[12]=>39916800
[2,9,6,5,7,8,1,10,11,4,12,3]=>[12]=>39916800
[2,3,8,5,9,7,1,10,6,11,12,4]=>[12]=>39916800
[2,3,6,5,7,8,9,10,1,11,12,4]=>[12]=>39916800
[10,3,4,5,6,7,8,9,11,12,1,2]=>[12]=>39916800
[2,9,4,5,6,7,8,10,11,1,12,3]=>[12]=>39916800
[2,3,8,5,6,7,9,10,1,11,12,4]=>[12]=>39916800
[2,3,4,7,6,8,9,1,10,11,12,5]=>[12]=>39916800
[5,4,7,6,3,1,2,8]=>[7,1]=>5760
[3,6,4,8,1,5,2,7]=>[8]=>5040
[3,6,8,4,1,5,2,7]=>[7,1]=>5760
[8,7,1,4,2,3,5,6]=>[4,3,1]=>3360
[3,8,6,4,1,5,2,7]=>[4,3,1]=>3360
[7,1,4,8,2,3,6,5]=>[8]=>5040
[4,5,3,6,7,1,8,2]=>[4,3,1]=>3360
[4,6,1,3,5,2,8,7]=>[3,2,2,1]=>1680
[2,5,1,4,8,3,7,6]=>[6,1,1]=>3360
[6,1,2,5,4,8,7,3]=>[5,2,1]=>4032
[8,4,1,7,3,5,6,2]=>[8]=>5040
[8,4,1,2,5,7,3,6]=>[5,2,1]=>4032
[2,4,5,6,8,3,1,7]=>[8]=>5040
[3,4,5,8,6,2,1,7]=>[8]=>5040
[4,5,1,8,6,3,7,2]=>[7,1]=>5760
[1,8,2,3,4,5,9,6,7]=>[6,2,1]=>30240
[1,3,4,5,6,8,9,2,7]=>[6,2,1]=>30240
[8,3,7,2,1,6,5,4]=>[7,1]=>5760
[8,4,7,6,2,5,1,3]=>[4,4]=>1260
[8,4,7,3,6,2,1,5]=>[8]=>5040
[3,8,7,5,6,4,1,2]=>[3,3,2]=>1120
[3,8,7,5,6,2,1,4]=>[5,3]=>2688
[3,8,7,5,6,2,4,1]=>[8]=>5040
[2,8,7,5,6,4,1,3]=>[5,3]=>2688
[4,5,2,3,6,7,8,9,1]=>[9]=>40320
[4,3,2,5,6,7,8,9,1]=>[7,2]=>25920
[5,6,7,2,3,4,8,9,1]=>[6,3]=>20160
[5,3,6,2,4,7,8,9,1]=>[9]=>40320
[5,4,3,2,6,7,8,9,1]=>[6,2,1]=>30240
[6,3,7,8,2,4,5,9,1]=>[5,4]=>18144
[6,7,4,5,2,3,8,9,1]=>[9]=>40320
[6,4,3,7,2,5,8,9,1]=>[8,1]=>45360
[7,8,4,5,9,2,3,6,1]=>[6,3]=>20160
[7,4,3,8,9,2,5,6,1]=>[4,4,1]=>11340
[7,5,8,3,6,2,4,9,1]=>[6,3]=>20160
[7,5,4,3,8,2,6,9,1]=>[7,2]=>25920
[7,6,5,4,3,2,8,9,1]=>[4,2,2,1]=>11340
[8,6,4,9,3,7,2,5,1]=>[6,3]=>20160
[8,6,5,4,3,9,2,7,1]=>[6,2,1]=>30240
[4,5,2,3,6,7,8,9,10,1]=>[10]=>362880
[4,3,2,5,6,7,8,9,10,1]=>[8,2]=>226800
[5,6,7,2,3,4,8,9,10,1]=>[7,3]=>172800
[5,3,6,2,4,7,8,9,10,1]=>[10]=>362880
[5,4,3,2,6,7,8,9,10,1]=>[7,2,1]=>259200
[6,7,8,9,2,3,4,5,10,1]=>[10]=>362880
[6,3,7,8,2,4,5,9,10,1]=>[6,4]=>151200
[6,7,4,5,2,3,8,9,10,1]=>[10]=>362880
[6,4,3,7,2,5,8,9,10,1]=>[9,1]=>403200
[6,5,4,3,2,7,8,9,10,1]=>[6,2,2]=>75600
[7,8,9,10,1,3,4,5,6,2]=>[7,3]=>172800
[7,3,8,9,10,2,4,5,6,1]=>[10]=>362880
[7,4,3,8,9,2,5,6,10,1]=>[5,4,1]=>181440
[7,5,8,3,6,2,4,9,10,1]=>[7,3]=>172800
[7,5,4,3,8,2,6,9,10,1]=>[8,2]=>226800
[7,6,5,4,3,2,8,9,10,1]=>[5,2,2,1]=>90720
[8,5,9,3,6,10,2,4,7,1]=>[10]=>362880
[8,5,4,3,9,10,2,6,7,1]=>[4,4,2]=>56700
[8,9,6,7,4,5,2,3,10,1]=>[10]=>362880
[8,6,4,9,3,7,2,5,10,1]=>[7,3]=>172800
[8,6,5,4,3,9,2,7,10,1]=>[7,2,1]=>259200
[8,7,6,5,4,3,2,9,10,1]=>[4,2,2,2]=>18900
[9,7,5,4,10,3,8,2,6,1]=>[6,3,1]=>201600
[9,7,6,5,4,3,10,2,8,1]=>[6,2,2]=>75600
[10,1,9,2,8,3,7,4,6,5]=>[6,3,1]=>201600
[1,5,6,3,8,2,7,4]=>[6,1,1]=>3360
[2,6,3,8,4,7,1,5]=>[4,3,1]=>3360
[2,6,3,5,7,8,1,4]=>[7,1]=>5760
[1,5,6,3,7,2,8,4]=>[7,1]=>5760
[1,7,5,3,6,2,8,4]=>[7,1]=>5760
[1,5,7,3,4,2,8,6]=>[7,1]=>5760
[1,5,8,3,4,2,7,6]=>[6,1,1]=>3360
[1,4,5,3,7,2,8,6]=>[7,1]=>5760
[1,4,5,3,8,2,7,6]=>[6,1,1]=>3360
[6,5,1,4,2,7,8,3]=>[5,2,1]=>4032
[6,5,1,4,2,8,7,3]=>[4,2,1,1]=>2520
[1,7,5,4,2,8,6,3]=>[6,1,1]=>3360
[5,1,6,8,3,7,2,4]=>[6,2]=>3360
[1,2,3,4,5,6,7,8,9,10,11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[2,4,1,5,3,6,7,8,9]=>[5,1,1,1,1]=>3024
[1,4,8,2,6,5,3,7]=>[3,2,2,1]=>1680
[8,5,1,3,6,2,4,7]=>[5,3]=>2688
[5,2,8,1,7,4,3,6]=>[7,1]=>5760
[1,2,5,6,8,7,3,4]=>[6,1,1]=>3360
[1,5,6,8,2,7,4,3]=>[5,2,1]=>4032
[2,6,7,3,4,1,8,5]=>[5,3]=>2688
[1,6,5,7,8,2,4,3]=>[3,2,2,1]=>1680
[1,5,6,7,2,8,4,3]=>[3,2,2,1]=>1680
[3,7,6,1,8,2,4,5]=>[6,2]=>3360
[1,3,7,2,6,4,8,5]=>[7,1]=>5760
[1,5,8,6,7,3,4,2]=>[7,1]=>5760
[1,6,5,8,7,2,4,3]=>[5,2,1]=>4032
[1,5,7,6,2,8,3,4]=>[3,2,2,1]=>1680
[1,2,5,8,6,7,4,3]=>[6,1,1]=>3360
[1,2,6,5,7,3,8,4]=>[4,2,1,1]=>2520
[1,7,5,8,6,4,2,3]=>[5,2,1]=>4032
[3,6,5,8,1,2,7,4]=>[3,2,2,1]=>1680
[5,4,7,8,1,6,3,2]=>[3,2,2,1]=>1680
[4,6,5,8,3,2,7,1]=>[3,2,2,1]=>1680
[4,7,5,8,3,6,2,1]=>[3,2,2,1]=>1680
[7,3,6,8,5,2,1,4]=>[3,2,2,1]=>1680
[2,4,7,8,5,6,3,1]=>[4,2,1,1]=>2520
[6,8,4,7,5,1,3,2]=>[3,2,2,1]=>1680
[4,5,6,7,8,3,9,1,2]=>[7,2]=>25920
[8,9,2,3,4,5,1,6,7]=>[9]=>40320
[5,6,7,4,8,9,1,2,3]=>[8,1]=>45360
[7,8,9,2,3,1,4,5,6]=>[9]=>40320
[6,5,7,8,9,1,2,3,4]=>[7,2]=>25920
[7,6,1,2,3,5,4,8]=>[7,1]=>5760
[2,8,7,5,1,6,3,4]=>[5,2,1]=>4032
[8,7,6,4,2,1,5,3]=>[4,3,1]=>3360
[3,8,7,5,2,6,4,1]=>[7,1]=>5760
[3,8,7,5,1,2,6,4]=>[8]=>5040
[5,8,3,7,1,4,6,2]=>[3,2,2,1]=>1680
[3,8,7,4,2,6,5,1]=>[6,1,1]=>3360
[5,8,3,2,4,7,6,1]=>[5,2,1]=>4032
[5,3,8,2,4,6,1,7]=>[7,1]=>5760
[5,8,2,1,4,6,3,7]=>[4,3,1]=>3360
[3,2,7,1,8,5,4,6]=>[4,3,1]=>3360
[6,2,7,8,1,5,3,4]=>[3,2,2,1]=>1680
[2,7,1,3,8,5,4,6]=>[5,3]=>2688
[7,1,2,3,4,5,8,6,9]=>[8,1]=>45360
[6,1,2,3,4,7,5,8,9]=>[7,1,1]=>25920
[5,1,2,3,6,4,7,8,9]=>[6,1,1,1]=>10080
[4,1,2,5,3,6,7,8,9]=>[5,1,1,1,1]=>3024
[7,1,2,6,3,8,4,5]=>[8]=>5040
[8,1,2,6,5,3,7,4]=>[6,1,1]=>3360
[8,5,4,6,1,2,7,3]=>[7,1]=>5760
[7,4,1,8,2,5,3,6]=>[5,3]=>2688
[7,4,8,3,1,2,6,5]=>[8]=>5040
[8,4,5,3,1,6,7,2]=>[6,1,1]=>3360
[7,2,6,8,4,1,3,5]=>[4,3,1]=>3360
[7,2,5,1,6,8,3,4]=>[7,1]=>5760
[6,2,1,7,4,8,3,5]=>[7,1]=>5760
[1,7,4,3,2,5,6,8]=>[4,2,1,1]=>2520
[1,7,4,3,6,2,5,8]=>[4,2,1,1]=>2520
[3,7,5,8,2,4,6,1]=>[8]=>5040
[5,2,1,6,3,4,8,7]=>[3,2,2,1]=>1680
[5,1,3,4,6,2,8,7]=>[4,2,1,1]=>2520
[3,8,4,5,7,2,6,1]=>[8]=>5040
[3,8,4,7,5,6,2,1]=>[6,1,1]=>3360
[4,2,8,6,3,7,5,1]=>[7,1]=>5760
[4,1,7,6,3,8,5,2]=>[5,3]=>2688
[7,4,1,8,5,3,6,2]=>[4,3,1]=>3360
[3,5,6,8,4,7,1,2]=>[4,4]=>1260
[5,4,1,8,6,7,2,3]=>[8]=>5040
[6,2,8,4,5,3,7,1]=>[4,1,1,1,1]=>420
[4,5,2,1,8,7,3,6]=>[6,2]=>3360
[4,7,3,8,2,6,5,1]=>[3,3,1,1]=>1120
[4,7,3,1,8,6,2,5]=>[2,2,2,1,1]=>420
[6,2,1,3,7,4,8,5]=>[4,3,1]=>3360
[6,3,7,1,2,5,8,4]=>[8]=>5040
[5,1,4,7,8,2,6,3]=>[8]=>5040
[7,2,5,8,1,3,6,4]=>[5,2,1]=>4032
[8,3,6,7,2,4,5,1]=>[6,2]=>3360
[3,8,7,5,2,1,6,4]=>[4,4]=>1260
[3,8,5,6,2,7,4,1]=>[5,3]=>2688
[3,6,5,8,4,2,7,1]=>[5,2,1]=>4032
[6,8,3,2,5,7,4,1]=>[6,1,1]=>3360
[4,1,5,6,8,7,3,2]=>[8]=>5040
[8,4,2,3,6,7,5,1]=>[3,3,2]=>1120
[6,1,2,4,5,7,8,3]=>[6,1,1]=>3360
[4,5,1,3,7,6,8,2]=>[4,3,1]=>3360
[3,5,4,8,6,2,7,1]=>[4,3,1]=>3360
[3,6,2,4,5,8,7,1]=>[5,1,1,1]=>1344
[9,1,2,3,8,5,6,7,4]=>[5,4]=>18144
[8,1,3,7,4,5,6,2]=>[4,3,1]=>3360
[10,1,2,3,4,9,6,7,8,5]=>[6,4]=>151200
[10,1,9,3,4,5,6,7,8,2]=>[7,3]=>172800
[8,1,5,3,6,4,7,2]=>[4,3,1]=>3360
[2,6,4,8,3,1,5,7]=>[5,3]=>2688
[2,6,4,1,5,8,7,3]=>[6,1,1]=>3360
[3,6,4,5,2,8,1,7]=>[8]=>5040
[8,1,5,4,7,3,6,2]=>[4,3,1]=>3360
[7,6,5,4,1,8,2,3]=>[7,1]=>5760
[8,1,5,4,7,6,3,2]=>[3,3,1,1]=>1120
[2,5,1,4,6,7,3,8]=>[6,1,1]=>3360
[3,6,4,1,5,7,8,2]=>[4,3,1]=>3360
[7,6,5,2,8,4,1,3]=>[3,3,2]=>1120
[3,1,6,5,2,8,7,4]=>[7,1]=>5760
[1,7,2,4,3,5,8,6]=>[6,1,1]=>3360
[3,8,1,7,4,2,6,5]=>[6,2]=>3360
[8,1,7,4,3,5,6,2]=>[4,3,1]=>3360
[6,8,2,4,5,3,7,1]=>[5,1,1,1]=>1344
[4,8,5,3,6,1,7,2]=>[5,2,1]=>4032
[2,8,3,1,4,7,5,6]=>[7,1]=>5760
[8,6,3,2,7,4,1,5]=>[4,3,1]=>3360
[2,7,3,1,8,4,5,6]=>[7,1]=>5760
[1,2,8,3,5,6,4,7]=>[4,1,1,1,1]=>420
[2,8,1,3,5,4,6,7]=>[7,1]=>5760
[1,5,2,8,6,4,3,7]=>[7,1]=>5760
[7,4,8,6,3,1,2,5]=>[5,3]=>2688
[3,6,8,4,1,2,5,7]=>[5,2,1]=>4032
[4,7,8,5,2,1,3,6]=>[8]=>5040
[6,1,5,2,8,7,3,4]=>[8]=>5040
[8,1,3,5,7,4,2,6]=>[7,1]=>5760
[3,1,8,5,4,7,2,6]=>[6,2]=>3360
[3,1,6,4,8,5,2,7]=>[7,1]=>5760
[5,1,3,4,2,6,8,7]=>[3,2,1,1,1]=>1120
[3,2,6,4,1,5,7,8]=>[4,1,1,1,1]=>420
[5,4,2,1,8,3,6,7]=>[8]=>5040
[4,2,5,1,8,7,3,6]=>[5,2,1]=>4032
[6,8,2,7,1,4,3,5]=>[8]=>5040
[1,8,4,7,3,2,5,6]=>[4,3,1]=>3360
[8,6,3,1,5,7,2,4]=>[3,3,1,1]=>1120
[5,8,3,1,4,7,6,2]=>[3,2,2,1]=>1680
[1,2,5,4,7,8,3,6]=>[3,2,1,1,1]=>1120
[1,8,3,2,6,4,7,5]=>[5,1,1,1]=>1344
[4,7,1,2,5,3,6,8]=>[6,1,1]=>3360
[6,8,4,1,3,7,2,5]=>[8]=>5040
[3,2,6,1,7,8,5,4]=>[5,2,1]=>4032
[7,6,4,1,8,3,5,2]=>[8]=>5040
[5,4,1,6,7,3,2,8]=>[7,1]=>5760
[7,4,1,6,5,8,2,3]=>[7,1]=>5760
[8,5,4,1,6,7,3,2]=>[8]=>5040
[5,2,1,6,4,7,8,3]=>[7,1]=>5760
[1,6,2,3,5,7,8,4]=>[6,1,1]=>3360
[1,3,4,8,5,2,6,7]=>[6,1,1]=>3360
[8,2,4,6,1,7,3,5]=>[4,3,1]=>3360
[1,5,7,2,3,6,8,4]=>[6,1,1]=>3360
[7,3,1,4,2,5,8,6]=>[7,1]=>5760
[3,2,5,7,8,4,1,6]=>[7,1]=>5760
[4,3,5,1,6,2,7,8]=>[4,2,1,1]=>2520
[8,6,3,5,4,1,2,7]=>[5,2,1]=>4032
[8,3,2,6,1,5,4,7]=>[6,2]=>3360
[8,5,1,7,4,6,2,3]=>[4,3,1]=>3360
[4,8,1,7,6,3,5,2]=>[6,2]=>3360
[8,5,1,7,4,3,6,2]=>[8]=>5040
[8,5,7,6,2,1,3,4]=>[4,2,2]=>1260
[5,4,8,3,1,7,2,6]=>[6,2]=>3360
[5,1,4,8,3,2,7,6]=>[7,1]=>5760
[4,8,1,7,6,5,2,3]=>[6,2]=>3360
[4,3,8,7,2,6,1,5]=>[4,3,1]=>3360
[3,8,7,2,6,4,1,5]=>[5,3]=>2688
[8,2,5,7,4,3,6,1]=>[5,2,1]=>4032
[3,8,7,4,6,1,2,5]=>[7,1]=>5760
[8,7,6,3,5,4,1,2]=>[4,3,1]=>3360
[2,8,4,7,6,1,5,3]=>[8]=>5040
[2,5,4,8,3,1,7,6]=>[7,1]=>5760
[5,4,8,2,1,3,7,6]=>[3,2,2,1]=>1680
[3,8,7,2,6,1,5,4]=>[5,3]=>2688
[1,8,4,7,6,3,5,2]=>[5,2,1]=>4032
[1,8,3,7,6,5,2,4]=>[4,2,1,1]=>2520
[1,4,3,8,7,2,6,5]=>[6,1,1]=>3360
[7,1,5,4,6,2,3,8]=>[6,1,1]=>3360
[7,4,1,3,6,2,5,8]=>[7,1]=>5760
[5,4,3,1,7,6,2,8]=>[5,1,1,1]=>1344
[2,6,8,3,1,7,4,5]=>[8]=>5040
[2,5,4,8,1,7,3,6]=>[5,3]=>2688
[7,2,6,5,8,3,4,1]=>[5,2,1]=>4032
[5,6,3,1,4,2,7,8]=>[3,2,1,1,1]=>1120
[2,6,5,3,4,8,7,1]=>[4,3,1]=>3360
[2,6,1,5,3,4,7,8]=>[6,1,1]=>3360
[3,4,7,8,5,1,6,2]=>[4,3,1]=>3360
[5,3,6,4,8,7,2,1]=>[4,3,1]=>3360
[1,5,4,8,6,2,7,3]=>[3,3,1,1]=>1120
[4,5,2,7,6,3,8,1]=>[4,4]=>1260
[5,8,3,1,2,7,6,4]=>[5,2,1]=>4032
[7,6,2,5,3,8,4,1]=>[8]=>5040
[8,4,6,1,3,7,2,5]=>[8]=>5040
[4,8,5,1,2,3,6,7]=>[6,2]=>3360
[8,6,2,4,5,1,3,7]=>[6,1,1]=>3360
[4,5,1,3,8,6,2,7]=>[4,3,1]=>3360
[2,1,6,7,4,8,3,5]=>[6,2]=>3360
[7,5,8,1,6,2,4,3]=>[3,3,2]=>1120
[7,8,3,1,6,2,5,4]=>[7,1]=>5760
[7,5,2,8,1,4,6,3]=>[8]=>5040
[6,7,8,2,5,4,3,1]=>[7,1]=>5760
[7,8,1,6,2,5,4,3]=>[8]=>5040
[5,1,6,8,3,4,7,2]=>[7,1]=>5760
[7,1,6,8,5,4,3,2]=>[7,1]=>5760
[5,6,8,1,2,3,7,4]=>[7,1]=>5760
[4,8,1,2,7,6,5,3]=>[5,2,1]=>4032
[4,6,1,2,8,5,7,3]=>[7,1]=>5760
[6,4,7,3,5,2,1,8]=>[6,1,1]=>3360
[5,7,8,4,2,1,3,6]=>[7,1]=>5760
[3,1,6,2,5,7,8,4]=>[7,1]=>5760
[1,6,4,5,2,7,3,8]=>[6,1,1]=>3360
[6,2,1,4,5,3,7,8]=>[3,1,1,1,1,1]=>112
[6,2,1,5,7,3,4,8]=>[3,3,1,1]=>1120
[1,2,3,4,5,8,9,6,7]=>[2,2,1,1,1,1,1]=>378
[1,2,4,6,8,3,7,5]=>[3,2,1,1,1]=>1120
[3,9,1,4,5,6,7,8,2]=>[2,2,1,1,1,1,1]=>378
[6,1,3,7,2,8,5,4]=>[7,1]=>5760
[8,1,4,3,6,7,2,5]=>[6,2]=>3360
[2,6,8,4,3,1,7,5]=>[3,3,1,1]=>1120
[8,1,5,2,6,4,3,7]=>[8]=>5040
[1,6,7,4,2,8,3,5]=>[4,2,1,1]=>2520
[1,4,7,2,3,6,8,5]=>[4,2,1,1]=>2520
[3,1,2,6,7,8,5,4]=>[3,3,2]=>1120
[3,8,1,6,4,2,7,5]=>[5,2,1]=>4032
[1,6,3,4,7,8,2,5]=>[5,1,1,1]=>1344
[3,1,5,7,6,2,8,4]=>[5,3]=>2688
[6,3,1,4,2,7,8,5]=>[7,1]=>5760
[2,4,3,7,6,1,8,5]=>[7,1]=>5760
[3,1,7,6,5,2,8,4]=>[7,1]=>5760
[1,4,7,6,8,3,2,5]=>[5,2,1]=>4032
[7,2,1,5,6,3,8,4]=>[7,1]=>5760
[4,3,1,8,6,2,7,5]=>[7,1]=>5760
[3,1,5,2,8,7,6,4]=>[6,2]=>3360
[1,2,8,4,3,7,6,5]=>[3,2,1,1,1]=>1120
[2,6,1,8,7,4,3,5]=>[8]=>5040
[7,5,1,8,3,2,6,4]=>[6,2]=>3360
[4,7,6,3,1,8,2,5]=>[6,2]=>3360
[5,3,1,8,6,2,4,7]=>[5,3]=>2688
[5,1,8,6,3,2,4,7]=>[8]=>5040
[1,5,4,2,8,6,3,7]=>[6,1,1]=>3360
[1,4,2,8,5,3,7,6]=>[5,1,1,1]=>1344
[8,3,1,6,4,2,5,7]=>[8]=>5040
[1,7,4,8,3,5,2,6]=>[5,2,1]=>4032
[7,3,2,4,8,5,1,6]=>[3,2,2,1]=>1680
[5,7,8,1,4,2,6,3]=>[3,3,2]=>1120
[2,6,3,8,1,7,5,4]=>[5,2,1]=>4032
[2,5,1,8,6,3,7,4]=>[5,2,1]=>4032
[2,8,6,4,1,7,3,5]=>[4,3,1]=>3360
[1,8,4,2,7,5,3,6]=>[7,1]=>5760
[6,5,1,7,2,8,4,3]=>[4,2,2]=>1260
[2,8,1,7,5,3,6,4]=>[7,1]=>5760
[1,2,8,7,6,4,3,5]=>[6,1,1]=>3360
[4,1,7,8,6,3,5,2]=>[4,4]=>1260
[1,6,5,7,8,4,2,3]=>[4,3,1]=>3360
[4,1,8,7,6,3,5,2]=>[8]=>5040
[4,8,2,6,3,5,1,7]=>[8]=>5040
[4,1,8,5,3,6,2,7]=>[7,1]=>5760
[3,1,5,8,2,7,4,6]=>[4,4]=>1260
[6,1,8,4,5,3,2,7]=>[6,1,1]=>3360
[6,3,8,4,5,1,7,2]=>[3,2,1,1,1]=>1120
[2,6,1,8,5,7,4,3]=>[7,1]=>5760
[6,3,8,4,5,2,1,7]=>[6,1,1]=>3360
[6,5,8,7,2,3,4,1]=>[4,2,2]=>1260
[6,3,8,4,5,2,7,1]=>[5,1,1,1]=>1344
[2,1,6,8,5,3,7,4]=>[2,2,2,1,1]=>420
[6,5,8,7,4,1,2,3]=>[4,2,2]=>1260
[6,5,8,7,4,2,1,3]=>[6,2]=>3360
[6,5,8,7,2,4,1,3]=>[4,2,2]=>1260
[6,2,8,4,5,7,1,3]=>[3,2,1,1,1]=>1120
[6,1,8,4,5,7,3,2]=>[6,1,1]=>3360
[10,1,11,2,3,4,5,6,7,8,9]=>[6,5]=>1330560
[1,9,2,10,3,4,5,6,7,8]=>[5,4,1]=>181440
[2,8,1,9,3,4,5,6,7]=>[9]=>40320
[10,11,1,2,3,4,5,6,7,8,9]=>[11]=>3628800
[3,6,1,8,5,7,4,2]=>[5,2,1]=>4032
[5,2,6,8,4,1,7,3]=>[6,1,1]=>3360
[7,5,1,6,3,2,8,4]=>[8]=>5040
[2,7,6,3,4,1,8,5]=>[8]=>5040
[5,7,6,3,1,2,8,4]=>[6,2]=>3360
[4,8,2,1,7,5,6,3]=>[3,3,2]=>1120
[6,3,8,5,7,2,4,1]=>[5,3]=>2688
[1,5,4,8,6,2,3,7]=>[4,3,1]=>3360
[8,2,1,7,5,3,6,4]=>[6,1,1]=>3360
[6,2,8,1,7,5,3,4]=>[7,1]=>5760
[1,4,2,3,6,5,8,7,9]=>[3,2,2,1,1]=>7560
[1,3,4,2,6,5,8,7,9]=>[3,2,2,1,1]=>7560
[1,4,2,3,6,5,8,7,10,9]=>[3,2,2,2,1]=>25200
[2,3,1,4,6,5,8,7,9]=>[3,2,2,1,1]=>7560
[4,6,1,2,3,5,8,7,9]=>[6,2,1]=>30240
[3,4,5,1,6,2,8,7,9]=>[6,2,1]=>30240
[3,1,2,4,6,5,8,7,9]=>[3,2,2,1,1]=>7560
[1,3,4,2,6,5,8,7,10,9]=>[3,2,2,2,1]=>25200
[3,1,4,2,6,5,8,7,10,9,11]=>[4,2,2,2,1]=>207900
[5,6,2,7,8,1,3,4]=>[8]=>5040
[4,7,8,3,5,6,1,2]=>[6,1,1]=>3360
[2,1,3,4,5,6,9,7,8]=>[3,2,1,1,1,1]=>2520
[1,2,3,4,5,6,7,8,10,9,11]=>[2,1,1,1,1,1,1,1,1,1]=>55
[1,2,3,4,5,7,8,6,9]=>[3,1,1,1,1,1,1]=>168
[2,1,3,4,5,6,7,10,8,9]=>[3,2,1,1,1,1,1]=>5040
[8,4,5,2,6,3,7,1]=>[3,2,2,1]=>1680
[4,7,3,1,6,8,2,5]=>[3,2,2,1]=>1680
[1,7,4,6,8,3,2,5]=>[3,2,2,1]=>1680
[4,7,2,5,6,3,1,8]=>[7,1]=>5760
[5,4,1,3,7,8,2,6]=>[6,2]=>3360
[6,1,5,8,3,7,2,4]=>[4,2,2]=>1260
[7,2,1,6,8,3,5,4]=>[7,1]=>5760
[5,6,4,1,8,3,2,7]=>[8]=>5040
[4,5,2,1,7,8,3,6]=>[4,2,2]=>1260
[1,2,6,7,4,3,5,8]=>[3,2,1,1,1]=>1120
[10,2,3,4,5,6,7,8,1,9]=>[3,1,1,1,1,1,1,1]=>240
[7,1,9,3,4,5,6,2,8]=>[9]=>40320
[5,8,6,3,4,1,2,7]=>[5,3]=>2688
[3,10,1,4,5,6,7,8,9,2]=>[2,2,1,1,1,1,1,1]=>630
[8,1,10,3,4,5,6,7,2,9]=>[10]=>362880
[7,2,1,9,4,5,6,3,8]=>[8,1]=>45360
[6,9,7,3,4,5,1,2,8]=>[6,3]=>20160
[6,2,3,1,8,5,4,7]=>[6,1,1]=>3360
[5,1,2,6,4,8,3,7]=>[8]=>5040
[8,6,2,3,7,5,1,4]=>[8]=>5040
[3,8,1,2,9,5,6,7,4]=>[7,2]=>25920
[8,7,9,1,2,3,4,5,6]=>[6,3]=>20160
[9,1,11,3,4,5,6,7,8,2,10]=>[11]=>3628800
[8,2,1,10,4,5,6,7,3,9]=>[9,1]=>403200
[7,10,8,3,4,5,6,1,2,9]=>[7,3]=>172800
[7,2,3,1,9,5,6,4,8]=>[7,1,1]=>25920
[6,1,2,7,4,5,9,3,8]=>[9]=>40320
[5,9,6,3,4,1,7,2,8]=>[5,3,1]=>24192
[4,5,2,8,6,1,3,7]=>[8]=>5040
[3,4,8,2,5,6,1,7]=>[4,2,1,1]=>2520
[3,8,1,4,2,9,6,7,5]=>[6,2,1]=>30240
[9,7,2,3,8,5,6,1,4]=>[9]=>40320
[3,9,1,2,10,5,6,7,8,4]=>[8,2]=>226800
[6,3,2,5,8,4,1,7]=>[6,2]=>3360
[5,6,7,2,8,4,1,3]=>[5,3]=>2688
[5,8,3,6,4,1,7,2]=>[4,2,1,1]=>2520
[4,3,8,5,2,7,1,6]=>[8]=>5040
[2,8,4,5,1,6,3,7]=>[7,1]=>5760
[2,5,8,1,3,4,7,6]=>[7,1]=>5760
[3,5,1,8,7,4,2,6]=>[3,3,2]=>1120
[4,6,1,3,8,2,7,5]=>[3,2,2,1]=>1680
[8,6,1,2,3,5,7,4]=>[7,1]=>5760
[5,1,7,8,3,2,4,6]=>[8]=>5040
[3,1,7,6,2,8,5,4]=>[5,3]=>2688
[5,3,6,7,4,2,8,1]=>[5,3]=>2688
[5,4,2,8,6,7,3,1]=>[8]=>5040
[6,1,4,2,8,7,3,5]=>[6,2]=>3360
[4,6,5,2,7,8,3,1]=>[5,3]=>2688
[5,4,6,2,7,8,3,1]=>[6,2]=>3360
[5,1,8,6,4,2,7,3]=>[5,2,1]=>4032
[6,2,1,8,5,7,4,3]=>[6,1,1]=>3360
[5,4,6,2,3,1,8,7]=>[4,2,2]=>1260
[6,5,7,8,1,3,4,2]=>[8]=>5040
[2,1,7,6,8,4,5,3]=>[4,2,2]=>1260
[6,4,7,2,8,3,1,5]=>[4,2,2]=>1260
[6,3,2,7,8,4,5,1]=>[6,2]=>3360
[4,7,3,1,5,2,8,6]=>[4,2,1,1]=>2520
[4,7,6,3,1,5,8,2]=>[5,3]=>2688
[2,4,7,3,8,5,1,6]=>[5,3]=>2688
[2,8,3,1,7,4,5,6]=>[5,2,1]=>4032
[7,6,8,9,1,2,3,4,5]=>[7,2]=>25920
[5,4,6,7,8,9,1,2,3]=>[6,3]=>20160
[1,2,6,8,3,4,7,5]=>[5,1,1,1]=>1344
[1,8,2,7,3,5,6,4]=>[7,1]=>5760
[1,7,4,8,6,5,3,2]=>[5,2,1]=>4032
[1,6,3,5,7,4,8,2]=>[6,1,1]=>3360
[1,5,4,7,2,8,3,6]=>[3,2,2,1]=>1680
[3,8,5,2,6,1,7,4]=>[4,3,1]=>3360
[3,7,4,8,5,2,6,1]=>[4,3,1]=>3360
[8,1,2,6,5,3,4,7]=>[7,1]=>5760
[3,7,4,2,5,6,1,8]=>[5,1,1,1]=>1344
[6,8,7,1,3,4,2,5]=>[5,3]=>2688
[3,4,2,8,6,7,5,1]=>[5,3]=>2688
[3,7,8,6,1,4,2,5]=>[4,2,2]=>1260
[7,1,6,8,3,4,2,5]=>[5,3]=>2688
[8,1,2,6,3,5,7,4]=>[7,1]=>5760
[6,2,8,4,7,1,3,5]=>[4,2,1,1]=>2520
[3,7,8,4,2,5,6,1]=>[4,3,1]=>3360
[3,4,2,8,5,1,6,7]=>[7,1]=>5760
[1,4,3,2,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]=>36
[6,8,2,7,5,4,1,3]=>[4,3,1]=>3360
[1,8,4,3,7,6,2,5]=>[4,2,1,1]=>2520
[4,3,8,7,1,2,6,5]=>[8]=>5040
[1,8,4,5,7,6,2,3]=>[6,1,1]=>3360
[4,3,8,5,7,1,6,2]=>[5,3]=>2688
[6,3,4,8,7,2,1,5]=>[8]=>5040
[5,3,8,4,7,1,6,2]=>[4,3,1]=>3360
[5,2,8,7,1,4,6,3]=>[3,2,2,1]=>1680
[3,2,8,7,1,6,4,5]=>[4,2,1,1]=>2520
[2,7,8,3,1,6,4,5]=>[7,1]=>5760
[2,7,8,5,1,4,6,3]=>[6,2]=>3360
[3,5,8,7,4,1,6,2]=>[8]=>5040
[7,4,6,8,3,5,1,2]=>[3,3,2]=>1120
[2,7,8,1,3,6,4,5]=>[4,3,1]=>3360
[2,7,8,1,5,4,6,3]=>[5,2,1]=>4032
[2,7,8,1,4,5,6,3]=>[6,2]=>3360
[3,6,7,8,2,4,1,5]=>[5,3]=>2688
[4,5,7,8,6,3,1,2]=>[8]=>5040
[5,4,6,8,7,3,1,2]=>[3,3,2]=>1120
[4,5,8,6,7,1,3,2]=>[5,3]=>2688
[5,7,6,8,2,1,3,4]=>[6,2]=>3360
[3,7,6,8,2,4,1,5]=>[8]=>5040
[5,4,7,8,6,3,1,2]=>[5,3]=>2688
[4,5,7,8,2,6,1,3]=>[5,2,1]=>4032
[4,5,6,8,7,3,1,2]=>[6,2]=>3360
[6,1,5,3,8,4,7,2]=>[7,1]=>5760
[1,8,6,2,5,4,7,3]=>[5,1,1,1]=>1344
[3,8,4,1,7,5,2,6]=>[5,3]=>2688
[6,2,7,4,8,3,1,5]=>[4,2,1,1]=>2520
[2,8,5,1,4,3,7,6]=>[7,1]=>5760
[6,8,2,7,5,1,4,3]=>[3,2,2,1]=>1680
[8,3,4,5,6,1,7,2]=>[7,1]=>5760
[5,3,6,4,7,2,1,8]=>[3,3,1,1]=>1120
[4,2,6,5,7,3,1,8]=>[4,2,1,1]=>2520
[5,4,6,2,7,3,1,8]=>[3,2,2,1]=>1680
[3,2,6,5,8,4,1,7]=>[7,1]=>5760
[3,2,6,5,8,7,1,4]=>[4,3,1]=>3360
[4,2,6,5,8,7,1,3]=>[7,1]=>5760
[5,2,6,4,8,7,1,3]=>[6,1,1]=>3360
[5,4,7,6,8,2,1,3]=>[5,3]=>2688
[6,4,7,5,8,3,1,2]=>[4,4]=>1260
[4,2,7,5,8,6,1,3]=>[6,1,1]=>3360
[3,2,7,5,8,4,1,6]=>[4,3,1]=>3360
[4,3,7,2,8,5,1,6]=>[5,3]=>2688
[4,3,6,2,8,5,1,7]=>[8]=>5040
[4,3,7,6,8,5,1,2]=>[8]=>5040
[5,3,7,6,8,2,1,4]=>[8]=>5040
[5,3,7,2,8,6,1,4]=>[7,1]=>5760
[3,2,6,4,8,7,1,5]=>[4,2,1,1]=>2520
[4,2,7,3,8,6,1,5]=>[4,2,1,1]=>2520
[5,2,7,6,8,3,1,4]=>[7,1]=>5760
[3,2,7,6,8,4,1,5]=>[3,2,2,1]=>1680
[3,2,7,6,8,5,1,4]=>[4,3,1]=>3360
[6,2,7,5,8,4,1,3]=>[7,1]=>5760
[4,8,1,7,3,2,5,6]=>[5,3]=>2688
[3,7,4,8,2,1,5,6]=>[5,3]=>2688
[3,7,8,2,5,4,6,1]=>[4,3,1]=>3360
[4,7,5,8,3,2,6,1]=>[3,3,2]=>1120
[6,7,1,3,2,5,8,4]=>[8]=>5040
[8,7,6,4,1,5,3,2]=>[7,1]=>5760
[3,8,5,2,6,4,7,1]=>[7,1]=>5760
[7,2,5,3,4,8,1,6]=>[3,2,2,1]=>1680
[4,2,5,3,7,8,6,1]=>[7,1]=>5760
[5,3,6,2,4,1,8,7]=>[6,2]=>3360
[7,8,6,2,3,5,4,1]=>[5,3]=>2688
[5,8,2,6,3,7,4,1]=>[5,3]=>2688
[4,8,2,3,7,5,6,1]=>[5,3]=>2688
[7,5,6,2,3,8,4,1]=>[8]=>5040
[2,7,5,6,4,3,8,1]=>[4,4]=>1260
[2,8,4,3,7,5,6,1]=>[3,3,2]=>1120
[3,8,5,7,6,4,2,1]=>[8]=>5040
[7,8,6,3,5,4,2,1]=>[4,3,1]=>3360
[2,7,6,3,8,5,4,1]=>[8]=>5040
[7,4,2,5,6,3,8,1]=>[5,3]=>2688
[6,2,7,5,3,8,4,1]=>[4,3,1]=>3360
[2,4,8,3,7,5,6,1]=>[5,3]=>2688
[4,8,3,7,5,6,2,1]=>[5,1,1,1]=>1344
[6,2,5,8,3,7,4,1]=>[5,2,1]=>4032
[4,7,3,8,2,5,6,1]=>[4,3,1]=>3360
[8,2,5,6,3,7,4,1]=>[3,2,2,1]=>1680
[4,5,3,7,1,2,6,8]=>[6,1,1]=>3360
[8,5,6,4,1,3,2,7]=>[5,2,1]=>4032
[6,7,2,8,4,3,1,5]=>[5,3]=>2688
[6,7,3,2,8,4,1,5]=>[5,2,1]=>4032
[4,7,8,3,1,5,2,6]=>[6,2]=>3360
[4,5,8,1,3,2,6,7]=>[6,2]=>3360
[4,7,8,1,6,3,2,5]=>[4,2,2]=>1260
[4,7,1,3,8,6,5,2]=>[4,3,1]=>3360
[5,7,2,8,3,4,6,1]=>[8]=>5040
[3,7,2,8,5,6,4,1]=>[6,1,1]=>3360
[3,1,5,8,6,4,7,2]=>[7,1]=>5760
[2,5,6,1,8,7,3,4]=>[5,3]=>2688
[3,6,2,8,4,7,5,1]=>[8]=>5040
[2,3,8,6,7,5,4,1]=>[4,4]=>1260
[8,5,6,3,1,4,2,7]=>[5,3]=>2688
[5,7,8,3,4,6,2,1]=>[5,2,1]=>4032
[3,5,1,8,6,4,2,7]=>[6,2]=>3360
[7,5,3,8,6,4,2,1]=>[7,1]=>5760
[5,1,3,8,6,4,2,7]=>[7,1]=>5760
[1,5,8,3,6,4,2,7]=>[7,1]=>5760
[7,5,8,3,6,4,2,1]=>[8]=>5040
[1,5,8,6,3,4,2,7]=>[5,2,1]=>4032
[3,7,5,8,2,6,4,1]=>[7,1]=>5760
[5,7,8,1,4,6,2,3]=>[3,2,2,1]=>1680
[1,3,7,8,4,2,6,5]=>[4,3,1]=>3360
[6,1,2,5,3,4,7,8]=>[6,1,1]=>3360
[1,4,6,5,7,2,3,8]=>[6,1,1]=>3360
[6,7,3,5,4,1,2,8]=>[2,2,2,1,1]=>420
[7,2,4,1,6,5,3,8]=>[4,2,1,1]=>2520
[4,2,5,1,3,7,6,8]=>[2,2,2,1,1]=>420
[1,3,2,6,8,4,7,5]=>[2,2,2,1,1]=>420
[8,1,7,5,4,2,6,3]=>[6,2]=>3360
[1,2,6,4,7,3,5,8]=>[2,2,1,1,1,1]=>210
[1,6,4,3,7,2,5,8]=>[2,2,2,1,1]=>420
[5,7,8,3,2,6,1,4]=>[4,3,1]=>3360
[2,3,4,5,6,9,8,7,1]=>[7,2]=>25920
[2,3,4,5,8,7,9,6,1]=>[9]=>40320
[2,3,6,5,7,8,9,4,1]=>[9]=>40320
[2,3,4,5,6,7,10,9,8,1]=>[8,2]=>226800
[2,3,4,5,8,9,7,6,1]=>[8,1]=>45360
[2,3,4,5,6,9,8,10,7,1]=>[10]=>362880
[8,4,5,1,3,7,6,2]=>[4,2,2]=>1260
[8,6,4,3,7,1,5,2]=>[4,2,2]=>1260
[7,3,1,8,6,5,2,4]=>[4,2,2]=>1260
[3,4,5,6,7,1,2,8,9]=>[7,1,1]=>25920
[2,7,3,1,4,8,6,5]=>[7,1]=>5760
[3,1,6,5,7,8,4,2]=>[5,3]=>2688
[4,3,1,5,8,7,6,2]=>[6,2]=>3360
[4,7,1,3,2,5,6,8]=>[4,3,1]=>3360
[1,7,2,5,6,8,4,3]=>[7,1]=>5760
[3,5,4,7,1,8,6,2]=>[8]=>5040
[7,1,5,4,2,3,6,8]=>[6,1,1]=>3360
[7,1,3,6,4,5,2,8]=>[3,3,1,1]=>1120
[6,1,3,8,4,5,2,7]=>[7,1]=>5760
[2,1,8,7,3,6,5,4]=>[5,2,1]=>4032
[5,8,6,3,1,2,7,4]=>[5,2,1]=>4032
[5,8,2,7,1,3,6,4]=>[6,2]=>3360
[2,6,5,4,1,3,7,8]=>[5,1,1,1]=>1344
[4,1,5,7,6,3,2,8]=>[4,3,1]=>3360
[4,5,1,7,6,3,2,8]=>[7,1]=>5760
[5,4,2,1,8,7,3,6]=>[8]=>5040
[6,2,1,5,4,3,8,7]=>[3,2,2,1]=>1680
[1,4,2,6,7,8,5,3]=>[5,2,1]=>4032
[1,4,2,5,6,8,7,3]=>[6,1,1]=>3360
[2,5,3,6,7,8,4,1]=>[7,1]=>5760
[1,8,6,2,4,3,5,7]=>[5,2,1]=>4032
[2,3,4,7,5,8,6,1]=>[7,1]=>5760
[6,5,2,8,7,4,3,1]=>[4,4]=>1260
[7,8,5,4,2,1,6,3]=>[4,3,1]=>3360
[7,5,2,8,6,4,3,1]=>[8]=>5040
[7,8,3,2,6,5,4,1]=>[5,2,1]=>4032
[8,2,6,3,7,5,1,4]=>[7,1]=>5760
[1,6,2,7,8,4,5,3]=>[7,1]=>5760
[8,6,2,7,5,4,1,3]=>[7,1]=>5760
[1,6,8,2,7,5,3,4]=>[7,1]=>5760
[7,6,3,2,8,1,5,4]=>[7,1]=>5760
[5,1,7,4,3,8,6,2]=>[7,1]=>5760
[8,6,3,7,2,4,1,5]=>[7,1]=>5760
[1,7,8,6,4,2,3,5]=>[7,1]=>5760
[1,5,3,7,4,2,6,8]=>[5,1,1,1]=>1344
[1,7,6,3,4,2,5,8]=>[6,1,1]=>3360
[1,2,7,4,3,8,6,5]=>[5,1,1,1]=>1344
[1,5,4,2,3,8,7,6]=>[4,2,1,1]=>2520
[1,5,3,2,4,6,7,8]=>[3,1,1,1,1,1]=>112
[1,5,4,2,3,7,8,6]=>[4,3,1]=>3360
[1,2,7,6,3,5,8,4]=>[6,1,1]=>3360
[8,1,3,2,6,5,7,4]=>[4,2,1,1]=>2520
[3,2,7,5,6,1,8,4]=>[7,1]=>5760
[7,4,5,1,6,3,8,2]=>[5,3]=>2688
[7,5,6,1,4,3,8,2]=>[6,2]=>3360
[3,2,6,4,8,5,7,1]=>[5,1,1,1]=>1344
[8,1,4,3,5,2,7,6]=>[4,2,1,1]=>2520
[7,2,8,1,6,3,5,4]=>[7,1]=>5760
[10,5,9,4,8,3,7,2,6,1]=>[3,3,2,1,1]=>50400
[1,3,5,2,4,7,6,9,8,10]=>[4,2,2,1,1]=>56700
[2,3,5,1,4,7,6,9,8]=>[5,2,2]=>9072
[3,4,1,5,2,7,6,9,8]=>[3,2,2,2]=>2520
[4,1,2,5,3,7,6,9,8]=>[5,2,2]=>9072
[1,4,2,5,3,7,6,9,8,10]=>[4,2,2,1,1]=>56700
[1,7,5,8,4,6,3,2]=>[6,1,1]=>3360
[6,5,7,1,2,8,3,4]=>[4,2,2]=>1260
[7,1,4,2,3,8,6,5]=>[8]=>5040
[8,1,2,5,3,7,6,4]=>[6,2]=>3360
[8,6,5,2,4,1,7,3]=>[7,1]=>5760
[3,6,5,2,4,1,7,8]=>[6,1,1]=>3360
[3,4,2,8,6,7,1,5]=>[8]=>5040
[4,6,7,2,5,1,8,3]=>[4,3,1]=>3360
[3,4,2,7,8,1,5,6]=>[8]=>5040
[3,1,11,5,6,7,8,9,10,2,4]=>[11]=>3628800
[10,3,1,5,6,7,8,9,2,4]=>[10]=>362880
[10,4,1,5,6,7,8,9,2,3]=>[7,3]=>172800
[12,3,4,5,6,7,8,9,10,11,1,2]=>[12]=>39916800
[7,1,4,2,5,8,6,3]=>[7,1]=>5760
[7,8,5,1,2,4,3,6]=>[8]=>5040
[5,8,1,4,3,6,7,2]=>[3,2,1,1,1]=>1120
[7,2,3,8,6,4,1,5]=>[4,2,1,1]=>2520
[5,2,3,8,7,4,1,6]=>[3,3,1,1]=>1120
[5,7,6,3,1,2,4,8]=>[5,2,1]=>4032
[4,2,6,8,1,3,5,7,9]=>[5,2,1,1]=>18144
[4,6,2,8,1,3,5,7,9]=>[5,3,1]=>24192
[4,6,8,2,1,3,5,7,9]=>[8,1]=>45360
[4,6,2,7,8,1,3,5]=>[6,2]=>3360
[4,6,8,2,9,1,3,5,7]=>[5,4]=>18144
[4,6,2,7,9,1,3,5,8]=>[6,3]=>20160
[6,2,3,7,1,4,5,8]=>[5,1,1,1]=>1344
[4,2,5,7,9,1,3,6,8]=>[8,1]=>45360
[2,3,5,7,9,1,4,6,8]=>[7,2]=>25920
[4,2,6,8,10,1,3,5,7,9]=>[9,1]=>403200
[6,4,2,8,1,3,5,7,9]=>[8,1]=>45360
[4,6,2,8,10,1,3,5,7,9]=>[10]=>362880
[8,4,6,2,1,3,5,7,9]=>[4,2,2,1]=>11340
[4,6,8,2,10,1,3,5,7,9]=>[6,4]=>151200
[4,6,8,9,2,1,3,5,7]=>[9]=>40320
[4,6,8,10,2,1,3,5,7,9]=>[10]=>362880
[4,6,7,8,2,1,3,5]=>[6,2]=>3360
[4,6,2,7,1,3,5,8,9]=>[4,3,1,1]=>15120
[4,6,8,2,9,1,3,5,7,10]=>[5,4,1]=>181440
[4,8,2,5,9,1,3,6,7]=>[9]=>40320
[4,6,2,7,9,1,3,5,8,10]=>[6,3,1]=>201600
[6,2,3,7,9,1,4,5,8]=>[3,2,2,1,1]=>7560
[4,2,5,7,9,1,3,6,8,10]=>[8,1,1]=>226800
[1,4,5,7,9,2,3,6,8]=>[8,1]=>45360
[2,3,5,7,9,1,4,6,8,10]=>[7,2,1]=>259200
[8,6,3,2,1,7,5,4]=>[7,1]=>5760
[8,6,4,9,7,5,3,2,1]=>[9]=>40320
[8,6,4,2,9,7,5,3,1]=>[9]=>40320
[6,2,7,3,8,4,9,5,1]=>[6,2,1]=>30240
[4,5,6,7,8,2,9,3,1]=>[5,4]=>18144
[4,5,6,7,1,8,2,9,3]=>[5,4]=>18144
[9,7,10,8,6,5,4,3,2,1]=>[8,2]=>226800
[9,7,5,10,8,6,4,3,2,1]=>[6,3,1]=>201600
[8,5,2,9,6,3,10,7,4,1]=>[4,4,2]=>56700
[7,3,8,4,9,5,1,10,6,2]=>[4,3,2,1]=>151200
[6,1,3,4,2,5,8,7]=>[4,2,1,1]=>2520
[5,1,3,6,2,4,8,7]=>[3,2,2,1]=>1680
[5,7,1,3,8,4,2,6]=>[6,2]=>3360
[2,6,1,4,3,7,8,5]=>[7,1]=>5760
[1,6,2,4,3,5,8,7]=>[4,2,1,1]=>2520
[5,3,7,6,1,8,4,2]=>[6,2]=>3360
[1,5,6,3,7,8,4,2]=>[7,1]=>5760
[1,5,7,6,3,8,4,2]=>[7,1]=>5760
[7,3,5,6,1,8,4,2]=>[8]=>5040
[7,3,6,1,5,8,4,2]=>[4,3,1]=>3360
[1,6,3,7,8,5,4,2]=>[4,2,1,1]=>2520
[1,7,8,6,3,5,4,2]=>[7,1]=>5760
[3,7,5,6,1,8,4,2]=>[5,3]=>2688
[5,6,2,8,4,7,3,1]=>[4,4]=>1260
[7,3,5,4,1,2,6,8]=>[6,1,1]=>3360
[7,5,1,3,8,6,2,4]=>[7,1]=>5760
[5,7,6,1,3,8,2,4]=>[6,2]=>3360
[5,7,6,3,8,1,4,2]=>[8]=>5040
[5,1,3,7,6,2,4,8]=>[4,2,1,1]=>2520
[1,6,3,7,2,4,5,8]=>[5,1,1,1]=>1344
[5,3,2,4,8,1,7,6]=>[4,2,1,1]=>2520
[6,8,5,3,2,7,1,4]=>[5,3]=>2688
[8,3,7,2,6,5,1,4]=>[6,2]=>3360
[4,6,2,7,1,3,8,5]=>[5,3]=>2688
[3,5,1,4,7,2,8,6]=>[5,2,1]=>4032
[5,1,4,8,7,3,2,6]=>[4,4]=>1260
[6,1,3,4,2,7,8,5]=>[6,1,1]=>3360
[6,5,2,3,7,8,1,4]=>[8]=>5040
[1,5,3,8,4,2,7,6]=>[5,1,1,1]=>1344
[5,4,2,1,8,3,7,6]=>[7,1]=>5760
[3,1,7,4,2,6,8,5]=>[6,1,1]=>3360
[7,4,8,2,3,5,1,6]=>[4,2,2]=>1260
[8,4,1,3,2,6,7,5]=>[6,1,1]=>3360
[8,1,7,3,2,5,6,4]=>[8]=>5040
[8,6,5,2,7,3,1,4]=>[8]=>5040
[3,1,6,8,4,2,7,5]=>[4,3,1]=>3360
[2,3,4,5,9,6,7,8,1]=>[6,1,1,1]=>10080
[2,3,4,5,6,7,10,8,9,1]=>[8,1,1]=>226800
[2,3,4,5,6,10,7,8,9,1]=>[7,1,1,1]=>86400
[2,3,4,5,9,7,8,6,1]=>[6,3]=>20160
[5,6,2,3,7,4,1,8]=>[4,3,1]=>3360
[6,2,4,7,3,5,1,8]=>[6,1,1]=>3360
[1,4,8,5,3,6,7,2]=>[5,1,1,1]=>1344
[2,5,6,3,1,8,4,7]=>[5,3]=>2688
[4,5,1,2,7,8,6,3]=>[8]=>5040
[4,8,5,1,2,6,7,3]=>[4,2,1,1]=>2520
[4,6,7,5,1,2,8,3]=>[3,3,2]=>1120
[7,2,8,1,4,5,3,6]=>[7,1]=>5760
[6,1,4,7,3,8,2,5]=>[8]=>5040
[7,1,6,3,4,8,2,5]=>[5,3]=>2688
[2,8,4,6,3,1,5,7]=>[8]=>5040
[8,2,6,3,5,1,4,7]=>[6,1,1]=>3360
[3,7,4,1,5,8,2,6]=>[3,2,2,1]=>1680
[3,8,4,1,7,2,5,6]=>[3,3,2]=>1120
[6,7,5,1,3,8,2,4]=>[4,2,2]=>1260
[8,5,1,3,6,7,2,4]=>[4,4]=>1260
[7,8,6,2,4,1,3,5]=>[4,4]=>1260
[8,2,4,1,3,6,7,5]=>[5,1,1,1]=>1344
[8,1,3,6,2,5,7,4]=>[6,1,1]=>3360
[1,5,6,3,8,4,7,2]=>[3,3,1,1]=>1120
[5,6,1,3,7,2,8,4]=>[6,2]=>3360
[5,6,1,8,2,3,7,4]=>[5,2,1]=>4032
[5,6,1,2,8,4,7,3]=>[4,3,1]=>3360
[3,7,8,1,6,4,2,5]=>[6,2]=>3360
[1,7,8,6,3,4,2,5]=>[3,2,2,1]=>1680
[1,7,3,8,6,4,2,5]=>[4,2,1,1]=>2520
[5,7,1,8,6,4,2,3]=>[6,2]=>3360
[7,8,1,5,6,4,2,3]=>[5,3]=>2688
[7,1,8,5,6,4,2,3]=>[3,3,2]=>1120
[7,1,5,8,6,4,2,3]=>[5,3]=>2688
[8,1,3,5,6,4,2,7]=>[4,3,1]=>3360
[1,3,8,5,6,4,2,7]=>[4,3,1]=>3360
[1,3,5,8,6,4,2,7]=>[7,1]=>5760
[1,5,7,8,6,4,2,3]=>[7,1]=>5760
[2,1,4,3,6,5,9,8,10,7]=>[3,2,2,2,1]=>25200
[2,1,4,3,7,6,8,5,10,9]=>[3,2,2,2,1]=>25200
[2,1,4,3,7,6,9,8,10,5]=>[4,2,2,1,1]=>56700
[2,1,4,3,8,7,9,6,10,5]=>[6,2,2]=>75600
[2,1,5,4,6,3,8,7,10,9]=>[3,2,2,2,1]=>25200
[2,1,5,4,6,3,9,8,10,7]=>[3,3,2,1,1]=>50400
[2,1,5,4,7,6,8,3,10,9]=>[4,2,2,1,1]=>56700
[2,1,5,4,7,6,9,8,10,3]=>[5,2,1,1,1]=>60480
[2,1,5,4,8,7,9,6,10,3]=>[7,2,1]=>259200
[2,1,6,5,7,4,8,3,10,9]=>[6,2,2]=>75600
[2,1,6,5,7,4,9,8,10,3]=>[7,2,1]=>259200
[2,1,6,5,8,7,9,4,10,3]=>[5,3,2]=>120960
[2,1,7,6,8,5,9,4,10,3]=>[4,4,2]=>56700
[3,2,4,1,6,5,8,7,10,9]=>[3,2,2,2,1]=>25200
[3,2,4,1,6,5,9,8,10,7]=>[3,3,2,1,1]=>50400
[3,2,4,1,7,6,8,5,10,9]=>[3,3,2,1,1]=>50400
[3,2,4,1,7,6,9,8,10,5]=>[4,3,1,1,1]=>50400
[3,2,4,1,8,7,9,6,10,5]=>[6,3,1]=>201600
[3,2,5,4,6,1,8,7,10,9]=>[4,2,2,1,1]=>56700
[3,2,5,4,6,1,9,8,10,7]=>[4,3,1,1,1]=>50400
[3,2,5,4,7,6,8,1,10,9]=>[5,2,1,1,1]=>60480
[3,2,5,4,7,6,9,8,10,1]=>[6,1,1,1,1]=>25200
[3,2,5,4,8,7,9,6,10,1]=>[8,1,1]=>226800
[3,2,6,5,7,4,8,1,10,9]=>[7,2,1]=>259200
[3,2,6,5,7,4,9,8,10,1]=>[8,1,1]=>226800
[3,2,6,5,8,7,9,4,10,1]=>[6,3,1]=>201600
[3,2,7,6,8,5,9,4,10,1]=>[5,4,1]=>181440
[4,3,5,2,6,1,8,7,10,9]=>[6,2,2]=>75600
[4,3,5,2,6,1,9,8,10,7]=>[6,3,1]=>201600
[4,3,5,2,7,6,8,1,10,9]=>[7,2,1]=>259200
[4,3,5,2,7,6,9,8,10,1]=>[8,1,1]=>226800
[4,3,5,2,8,7,9,6,10,1]=>[10]=>362880
[4,3,6,5,7,2,8,1,10,9]=>[5,3,2]=>120960
[4,3,6,5,7,2,9,8,10,1]=>[6,3,1]=>201600
[4,3,6,5,8,7,9,2,10,1]=>[10]=>362880
[4,3,7,6,8,5,9,2,10,1]=>[10]=>362880
[5,4,6,3,7,2,8,1,10,9]=>[4,4,2]=>56700
[5,4,6,3,7,2,9,8,10,1]=>[5,4,1]=>181440
[5,4,6,3,8,7,9,2,10,1]=>[10]=>362880
[5,4,7,6,8,3,9,2,10,1]=>[10]=>362880
[2,1,4,3,6,5,8,7,11,10,12,9]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,6,5,9,8,10,7,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,7,6,8,5,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,7,6,8,5,11,10,12,9]=>[3,3,2,2,1,1]=>1663200
[2,1,4,3,7,6,9,8,11,10,12,5]=>[5,2,2,1,1,1]=>1995840
[2,1,4,3,8,7,10,9,11,6,12,5]=>[5,3,2,2]=>3991680
[2,1,4,3,9,8,10,7,11,6,12,5]=>[4,4,2,2]=>1871100
[2,1,5,4,6,3,8,7,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,5,4,6,3,8,7,11,10,12,9]=>[3,3,2,2,1,1]=>1663200
[2,1,5,4,6,3,9,8,10,7,12,11]=>[3,3,2,2,1,1]=>1663200
[2,1,5,4,7,6,9,8,10,3,12,11]=>[5,2,2,1,1,1]=>1995840
[2,1,5,4,9,8,10,7,11,6,12,3]=>[5,4,2,1]=>11975040
[2,1,6,5,8,7,9,4,10,3,12,11]=>[5,3,2,2]=>3991680
[2,1,7,6,8,5,9,4,10,3,12,11]=>[4,4,2,2]=>1871100
[2,1,7,6,8,5,9,4,11,10,12,3]=>[5,4,2,1]=>11975040
[3,2,4,1,6,5,8,7,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[3,2,4,1,6,5,8,7,11,10,12,9]=>[3,3,2,2,1,1]=>1663200
[3,2,4,1,6,5,9,8,10,7,12,11]=>[3,3,2,2,1,1]=>1663200
[3,2,4,1,7,6,8,5,10,9,12,11]=>[3,3,2,2,1,1]=>1663200
[3,2,4,1,8,7,10,9,11,6,12,5]=>[5,3,3,1]=>5322240
[3,2,4,1,9,8,10,7,11,6,12,5]=>[4,4,3,1]=>4989600
[3,2,5,4,7,6,8,1,10,9,12,11]=>[5,2,2,1,1,1]=>1995840
[3,2,6,5,7,4,10,9,11,8,12,1]=>[11,1]=>43545600
[3,2,6,5,8,7,10,9,11,4,12,1]=>[11,1]=>43545600
[3,2,6,5,9,8,10,7,11,4,12,1]=>[11,1]=>43545600
[3,2,7,6,8,5,9,4,10,1,12,11]=>[5,4,2,1]=>11975040
[3,2,7,6,8,5,10,9,11,4,12,1]=>[11,1]=>43545600
[3,2,7,6,9,8,10,5,11,4,12,1]=>[11,1]=>43545600
[4,3,5,2,6,1,10,9,11,8,12,7]=>[6,6]=>6652800
[4,3,5,2,7,6,10,9,11,8,12,1]=>[11,1]=>43545600
[4,3,5,2,8,7,9,6,11,10,12,1]=>[11,1]=>43545600
[4,3,5,2,8,7,10,9,11,6,12,1]=>[9,3]=>17740800
[4,3,6,5,7,2,8,1,10,9,12,11]=>[5,3,2,2]=>3991680
[4,3,6,5,7,2,8,1,11,10,12,9]=>[5,3,3,1]=>5322240
[4,3,6,5,7,2,10,9,11,8,12,1]=>[9,3]=>17740800
[4,3,6,5,8,7,9,2,11,10,12,1]=>[11,1]=>43545600
[4,3,6,5,8,7,10,9,11,2,12,1]=>[7,5]=>13685760
[4,3,6,5,9,8,10,7,11,2,12,1]=>[6,6]=>6652800
[4,3,7,6,8,5,9,2,11,10,12,1]=>[11,1]=>43545600
[4,3,8,7,9,6,10,5,11,2,12,1]=>[11,1]=>43545600
[5,4,6,3,7,2,8,1,10,9,12,11]=>[4,4,2,2]=>1871100
[5,4,6,3,7,2,8,1,11,10,12,9]=>[4,4,3,1]=>4989600
[5,4,6,3,7,2,9,8,10,1,12,11]=>[5,4,2,1]=>11975040
[5,4,6,3,8,7,9,2,11,10,12,1]=>[11,1]=>43545600
[5,4,6,3,8,7,10,9,11,2,12,1]=>[6,6]=>6652800
[5,4,6,3,9,8,10,7,11,2,12,1]=>[7,5]=>13685760
[5,4,7,6,8,3,9,2,11,10,12,1]=>[11,1]=>43545600
[5,4,7,6,8,3,10,9,11,2,12,1]=>[6,6]=>6652800
[5,4,7,6,9,8,10,3,11,2,12,1]=>[7,5]=>13685760
[5,4,8,7,9,6,10,3,11,2,12,1]=>[5,4,2,1]=>11975040
[6,5,7,4,8,3,10,9,11,2,12,1]=>[11,1]=>43545600
[6,5,7,4,9,8,10,3,11,2,12,1]=>[11,1]=>43545600
[1,8,2,6,5,3,4,7]=>[6,1,1]=>3360
[8,6,1,5,2,3,4,7]=>[8]=>5040
[8,5,1,6,2,3,4,7]=>[6,2]=>3360
[7,6,1,2,3,8,4,5]=>[8]=>5040
[2,7,8,4,1,3,5,6]=>[4,3,1]=>3360
[6,8,1,2,3,7,4,5]=>[8]=>5040
[8,1,3,5,6,7,2,4]=>[7,1]=>5760
[8,1,2,5,3,4,7,6]=>[7,1]=>5760
[5,2,7,3,4,8,1,6]=>[5,2,1]=>4032
[2,7,5,4,1,3,6,8]=>[6,1,1]=>3360
[2,7,4,6,5,1,8,3]=>[7,1]=>5760
[6,8,7,5,2,1,4,3]=>[6,2]=>3360
[2,8,6,3,5,1,4,7]=>[7,1]=>5760
[1,2,8,6,4,5,3,7]=>[3,3,1,1]=>1120
[1,5,8,7,6,3,4,2]=>[5,2,1]=>4032
[1,4,7,8,5,6,3,2]=>[3,2,1,1,1]=>1120
[1,6,8,5,2,7,3,4]=>[7,1]=>5760
[1,3,4,8,5,2,7,6]=>[5,1,1,1]=>1344
[2,1,8,3,4,5,6,7,9]=>[6,2,1]=>30240
[3,5,8,7,6,2,4,1]=>[3,3,2]=>1120
[6,5,3,7,4,1,8,2]=>[5,2,1]=>4032
[3,1,5,4,6,8,7,2]=>[6,1,1]=>3360
[3,1,6,4,2,5,8,7]=>[5,2,1]=>4032
[3,6,1,4,5,7,8,2]=>[4,2,1,1]=>2520
[1,8,4,7,2,3,6,5]=>[4,3,1]=>3360
[5,7,8,2,4,6,1,3]=>[5,2,1]=>4032
[5,4,2,3,6,8,1,7]=>[5,3]=>2688
[3,8,1,6,4,2,5,7]=>[6,2]=>3360
[7,3,2,1,8,6,4,5]=>[3,2,2,1]=>1680
[8,7,2,4,1,3,6,5]=>[4,3,1]=>3360
[8,2,6,3,5,7,1,4]=>[6,1,1]=>3360
[1,8,3,7,4,6,5,2]=>[3,2,1,1,1]=>1120
[8,2,3,1,7,4,5,6]=>[4,2,1,1]=>2520
[3,1,7,8,6,2,5,4]=>[6,2]=>3360
[4,8,1,2,6,5,7,3]=>[5,2,1]=>4032
[5,6,1,8,3,7,2,4]=>[3,3,2]=>1120
[2,8,1,6,5,3,7,4]=>[6,1,1]=>3360
[2,1,5,7,6,3,8,4]=>[3,3,2]=>1120
[4,1,2,5,7,6,8,3]=>[7,1]=>5760
[4,3,5,1,7,8,6,2]=>[6,2]=>3360
[1,8,5,2,3,4,7,6]=>[4,2,1,1]=>2520
[1,9,6,2,3,4,5,8,7]=>[7,1,1]=>25920
[1,5,8,2,3,4,7,6]=>[6,1,1]=>3360
[1,2,3,4,5,6,9,7,10,8]=>[4,1,1,1,1,1,1]=>1260
[2,3,4,5,6,9,10,1,7,8]=>[10]=>362880
[4,3,8,7,6,2,5,1]=>[8]=>5040
[5,4,8,2,7,6,3,1]=>[5,2,1]=>4032
[2,3,6,1,7,5,8,4]=>[8]=>5040
[4,6,5,2,1,7,8,3]=>[8]=>5040
[4,6,1,7,5,8,3,2]=>[4,3,1]=>3360
[4,1,5,7,6,8,3,2]=>[8]=>5040
[3,5,6,2,1,4,7,8]=>[6,1,1]=>3360
[4,3,6,5,1,7,8,2]=>[5,3]=>2688
[4,6,5,3,1,7,8,2]=>[4,4]=>1260
[1,2,3,4,5,7,6,8,9,10]=>[2,1,1,1,1,1,1,1,1]=>45
[1,2,3,5,4,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]=>45
[1,2,3,5,4,7,6,9,8,10]=>[2,2,2,1,1,1,1]=>3150
[5,8,1,4,2,3,6,7]=>[7,1]=>5760
[4,5,8,2,3,1,6,7]=>[8]=>5040
[3,5,4,8,1,7,2,6]=>[8]=>5040
[5,3,6,8,1,4,7,2]=>[5,2,1]=>4032
[3,5,1,8,6,4,7,2]=>[5,2,1]=>4032
[4,7,2,8,3,1,6,5]=>[8]=>5040
[1,2,5,6,8,3,7,4]=>[5,1,1,1]=>1344
[5,3,8,4,6,2,7,1]=>[6,1,1]=>3360
[7,4,8,1,5,2,6,3]=>[5,2,1]=>4032
[8,3,2,1,6,5,7,4]=>[3,2,2,1]=>1680
[4,1,5,6,8,7,2,3]=>[5,3]=>2688
[1,2,5,6,8,4,7,3]=>[3,2,1,1,1]=>1120
[1,5,6,8,4,7,2,3]=>[7,1]=>5760
[5,6,8,1,2,4,7,3]=>[5,2,1]=>4032
[6,8,1,4,5,7,2,3]=>[6,1,1]=>3360
[4,3,5,1,8,6,7,2]=>[4,2,1,1]=>2520
[1,3,5,6,8,4,7,2]=>[4,2,1,1]=>2520
[5,6,8,2,3,4,7,1]=>[4,3,1]=>3360
[9,8,7,4,5,6,3,2,1]=>[2,2,2,1,1,1]=>1260
[6,5,1,2,4,8,7,3]=>[4,3,1]=>3360
[5,8,7,2,1,3,6,4]=>[3,3,2]=>1120
[5,1,7,2,8,6,3,4]=>[5,2,1]=>4032
[6,1,5,3,4,8,7,2]=>[4,3,1]=>3360
[5,8,6,3,2,1,4,7]=>[8]=>5040
[8,7,1,6,3,5,4,2]=>[8]=>5040
[3,2,1,7,8,6,4,5]=>[2,2,2,1,1]=>420
[8,6,7,1,2,5,3,4]=>[3,3,2]=>1120
[1,5,6,4,2,8,7,3]=>[3,2,1,1,1]=>1120
[7,5,1,4,8,2,3,6]=>[4,3,1]=>3360
[3,2,8,1,7,5,6,4]=>[4,3,1]=>3360
[8,4,3,1,7,5,6,2]=>[4,3,1]=>3360
[6,1,7,8,4,2,3,5]=>[3,3,2]=>1120
[7,4,3,1,8,5,2,6]=>[4,3,1]=>3360
[7,8,1,6,3,4,5,2]=>[4,2,2]=>1260
[6,8,1,7,3,4,2,5]=>[8]=>5040
[1,5,6,7,8,9,2,3,4]=>[8,1]=>45360
[1,8,9,10,2,3,4,5,6,7]=>[3,3,3,1]=>22400
[1,7,2,8,9,3,4,5,6]=>[8,1]=>45360
[1,6,2,7,8,9,3,4,5]=>[8,1]=>45360
[1,5,2,6,7,8,9,3,4]=>[8,1]=>45360
[1,5,6,7,8,9,10,2,3,4]=>[3,3,3,1]=>22400
[3,4,2,1,5,6,7,8,9]=>[4,1,1,1,1,1]=>756
[4,3,1,2,5,6,7,8,9]=>[4,1,1,1,1,1]=>756
[3,4,2,1,5,6,7,8,9,10]=>[4,1,1,1,1,1,1]=>1260
[4,5,2,1,3,6,7,8,9]=>[3,2,1,1,1,1]=>2520
[3,4,2,5,1,6,7,8,9]=>[5,1,1,1,1]=>3024
[5,3,1,2,4,6,7,8,9]=>[5,1,1,1,1]=>3024
[4,3,5,1,2,6,7,8,9]=>[3,2,1,1,1,1]=>2520
[4,3,1,2,5,6,7,8,9,10]=>[4,1,1,1,1,1,1]=>1260
[4,6,5,3,8,2,7,1]=>[5,2,1]=>4032
[4,5,6,3,8,1,7,2]=>[4,3,1]=>3360
[7,8,3,5,2,1,6,4]=>[4,3,1]=>3360
[6,2,4,5,7,3,1,8]=>[6,1,1]=>3360
[7,8,1,5,6,4,3,2]=>[3,3,2]=>1120
[6,3,7,5,1,4,2,8]=>[4,3,1]=>3360
[1,3,8,2,4,6,7,5]=>[5,1,1,1]=>1344
[6,1,7,3,4,2,5,8]=>[4,3,1]=>3360
[3,1,7,2,5,8,6,4]=>[7,1]=>5760
[2,8,7,6,3,5,1,4]=>[8]=>5040
[2,8,7,1,5,6,4,3]=>[6,1,1]=>3360
[3,5,6,2,8,1,7,4]=>[4,3,1]=>3360
[4,1,5,7,3,8,2,6]=>[4,2,2]=>1260
[7,1,6,8,2,5,3,4]=>[6,2]=>3360
[1,6,5,7,4,2,3,8]=>[4,2,1,1]=>2520
[5,4,3,1,2,6,7,8,9]=>[4,1,1,1,1,1]=>756
[6,5,4,3,1,2,7,8,9]=>[4,2,1,1,1]=>7560
[8,5,4,3,9,1,2,6,7]=>[4,3,2]=>15120
[6,5,4,3,1,2,7,8,9,10]=>[4,2,1,1,1,1]=>18900
[7,6,5,4,3,1,2,8,9,10]=>[4,2,1,1,1,1]=>18900
[9,6,5,4,3,10,1,2,7,8]=>[4,3,2,1]=>151200
[6,8,7,3,2,4,5,1]=>[8]=>5040
[3,8,6,1,4,5,7,2]=>[5,2,1]=>4032
[7,5,8,6,4,1,3,2]=>[8]=>5040
[2,7,6,3,8,5,1,4]=>[5,3]=>2688
[2,3,1,8,4,6,5,7]=>[4,3,1]=>3360
[2,3,1,8,4,6,7,5]=>[3,3,1,1]=>1120
[4,2,3,5,1,8,6,7]=>[3,3,1,1]=>1120
[2,3,4,5,9,7,1,8,6]=>[8,1]=>45360
[2,3,4,9,6,7,1,8,5]=>[8,1]=>45360
[2,3,9,5,6,1,7,8,4]=>[7,1,1]=>25920
[2,3,9,5,1,7,4,8,6]=>[8,1]=>45360
[2,3,4,5,6,7,10,9,1,8]=>[10]=>362880
[2,3,4,5,6,10,8,9,1,7]=>[10]=>362880
[2,3,4,5,6,10,8,1,9,7]=>[9,1]=>403200
[2,3,4,5,6,10,8,1,7,9]=>[10]=>362880
[2,3,4,5,6,10,1,7,8,9]=>[10]=>362880
[2,3,4,5,10,7,8,9,1,6]=>[10]=>362880
[2,3,4,5,10,7,8,1,9,6]=>[9,1]=>403200
[2,3,4,5,10,7,8,1,6,9]=>[10]=>362880
[2,3,4,5,10,7,1,9,6,8]=>[10]=>362880
[2,3,4,5,10,7,1,6,8,9]=>[10]=>362880
[2,3,4,5,10,1,6,7,8,9]=>[10]=>362880
[2,3,4,10,6,7,8,1,9,5]=>[9,1]=>403200
[2,3,4,10,6,7,8,1,5,9]=>[10]=>362880
[2,3,4,10,6,7,1,8,9,5]=>[8,1,1]=>226800
[2,3,4,10,6,7,1,9,5,8]=>[10]=>362880
[2,3,4,10,6,7,1,5,8,9]=>[10]=>362880
[2,3,4,10,6,1,8,5,9,7]=>[9,1]=>403200
[2,3,4,10,6,1,8,5,7,9]=>[10]=>362880
[2,3,4,10,6,1,5,7,8,9]=>[10]=>362880
[2,3,4,10,1,5,6,7,8,9]=>[10]=>362880
[2,3,10,5,6,1,8,9,4,7]=>[10]=>362880
[2,3,10,5,6,1,8,4,9,7]=>[9,1]=>403200
[2,3,10,5,6,1,8,4,7,9]=>[10]=>362880
[2,3,10,5,6,1,4,7,8,9]=>[10]=>362880
[2,3,10,5,1,7,4,9,6,8]=>[10]=>362880
[2,3,10,5,1,7,4,6,8,9]=>[10]=>362880
[2,3,10,5,1,4,6,7,8,9]=>[10]=>362880
[2,10,4,1,6,3,8,5,9,7]=>[9,1]=>403200
[2,10,4,1,6,3,8,5,7,9]=>[10]=>362880
[2,10,4,1,6,3,5,7,8,9]=>[10]=>362880
[2,10,4,1,3,5,6,7,8,9]=>[10]=>362880
[5,8,7,2,6,4,1,3]=>[8]=>5040
[6,8,5,1,7,4,3,2]=>[3,3,2]=>1120
[6,8,5,2,7,4,1,3]=>[8]=>5040
[7,3,8,6,5,2,1,4]=>[5,2,1]=>4032
[7,5,8,1,6,4,3,2]=>[8]=>5040
[7,5,8,2,6,4,1,3]=>[4,2,2]=>1260
[6,3,2,8,1,7,5,4]=>[4,2,2]=>1260
[2,1,3,4,5,6,8,7,9]=>[2,2,1,1,1,1,1]=>378
[2,3,4,5,6,8,7,9,1]=>[8,1]=>45360
[2,6,8,7,1,3,5,4]=>[8]=>5040
[5,3,8,7,6,2,1,4]=>[8]=>5040
[3,7,6,1,4,5,2,8]=>[5,2,1]=>4032
[4,1,6,2,7,5,3,8]=>[4,3,1]=>3360
[7,6,2,5,3,1,4,8]=>[7,1]=>5760
[4,3,1,7,6,2,5,8]=>[7,1]=>5760
[4,5,3,1,2,8,6,7]=>[3,2,2,1]=>1680
[2,4,5,3,1,8,6,7]=>[5,3]=>2688
[5,7,6,2,3,1,4,8]=>[4,3,1]=>3360
[4,1,3,7,5,2,6,8]=>[5,1,1,1]=>1344
[4,1,6,3,2,7,5,8]=>[7,1]=>5760
[7,5,4,1,3,2,6,8]=>[7,1]=>5760
[2,4,8,5,6,3,1,7]=>[8]=>5040
[2,5,7,4,1,3,6,8]=>[3,3,1,1]=>1120
[5,7,4,1,3,2,6,8]=>[4,3,1]=>3360
[2,6,8,4,5,3,1,7]=>[6,1,1]=>3360
[5,2,3,7,4,1,6,8]=>[5,1,1,1]=>1344
[4,5,1,6,3,2,7,8]=>[6,1,1]=>3360
[5,1,6,3,2,4,7,8]=>[3,3,1,1]=>1120
[4,2,5,1,6,3,7,8]=>[3,2,1,1,1]=>1120
[5,1,6,2,4,3,7,8]=>[4,2,1,1]=>2520
[5,3,4,8,7,6,2,1]=>[7,1]=>5760
[8,3,1,6,7,5,4,2]=>[4,4]=>1260
[8,4,6,5,7,2,3,1]=>[6,2]=>3360
[1,8,2,6,7,4,5,3]=>[3,2,2,1]=>1680
[8,5,7,2,4,3,6,1]=>[3,3,2]=>1120
[8,5,3,6,4,7,2,1]=>[5,2,1]=>4032
[8,2,5,3,6,7,4,1]=>[5,2,1]=>4032
[1,2,8,3,4,7,6,5]=>[4,2,1,1]=>2520
[6,8,5,2,7,1,3,4]=>[3,3,2]=>1120
[7,6,4,5,2,1,8,3]=>[8]=>5040
[8,2,4,7,6,3,1,5]=>[7,1]=>5760
[8,7,5,1,4,6,3,2]=>[7,1]=>5760
[7,3,8,5,4,2,1,6]=>[4,2,2]=>1260
[6,3,4,7,2,8,5,1]=>[5,3]=>2688
[8,1,7,3,6,4,2,5]=>[8]=>5040
[7,1,8,5,3,4,2,6]=>[5,3]=>2688
[6,8,4,3,1,5,2,7]=>[3,3,2]=>1120
[1,4,5,8,3,2,6,7]=>[5,2,1]=>4032
[1,5,2,4,7,8,6,3]=>[6,1,1]=>3360
[5,2,7,4,3,8,6,1]=>[6,1,1]=>3360
[2,7,3,4,8,5,6,1]=>[6,1,1]=>3360
[2,7,6,8,3,5,4,1]=>[5,3]=>2688
[2,7,4,5,3,8,6,1]=>[5,3]=>2688
[6,2,3,7,4,5,8,1]=>[6,1,1]=>3360
[1,6,3,2,7,5,8,4]=>[6,1,1]=>3360
[7,3,5,2,6,8,1,4]=>[6,2]=>3360
[6,4,2,7,1,5,8,3]=>[5,3]=>2688
[2,5,3,6,4,7,8,1]=>[7,1]=>5760
[4,2,5,3,6,7,8,1]=>[7,1]=>5760
[1,6,5,2,4,7,3,8]=>[6,1,1]=>3360
[1,8,7,2,4,6,3,5]=>[4,2,1,1]=>2520
[1,8,7,2,5,4,3,6]=>[4,2,1,1]=>2520
[1,5,4,2,7,3,6,8]=>[6,1,1]=>3360
[1,5,4,2,8,7,3,6]=>[7,1]=>5760
[1,6,8,3,5,2,4,7]=>[4,2,1,1]=>2520
[1,7,6,2,3,5,8,4]=>[4,3,1]=>3360
[1,2,8,3,6,5,4,7]=>[4,2,1,1]=>2520
[1,3,8,6,5,2,4,7]=>[6,1,1]=>3360
[1,4,7,3,2,8,6,5]=>[7,1]=>5760
[1,8,6,5,2,4,7,3]=>[6,1,1]=>3360
[1,6,8,4,3,2,5,7]=>[4,2,1,1]=>2520
[1,7,5,3,2,6,4,8]=>[5,1,1,1]=>1344
[1,2,6,5,3,8,4,7]=>[6,1,1]=>3360
[1,7,3,2,8,4,6,5]=>[4,2,1,1]=>2520
[1,6,5,2,8,4,7,3]=>[3,3,1,1]=>1120
[1,8,3,7,2,4,6,5]=>[3,3,1,1]=>1120
[5,4,2,8,7,6,1,3]=>[4,3,1]=>3360
[8,6,3,2,5,7,4,1]=>[4,2,1,1]=>2520
[7,3,2,1,6,5,8,4]=>[4,2,2]=>1260
[7,3,2,6,1,5,8,4]=>[6,2]=>3360
[6,8,5,2,7,1,4,3]=>[6,2]=>3360
[6,8,2,5,1,7,4,3]=>[5,3]=>2688
[6,8,5,7,2,1,4,3]=>[4,2,2]=>1260
[6,5,8,2,7,4,1,3]=>[6,2]=>3360
[6,2,1,7,5,8,4,3]=>[4,2,1,1]=>2520
[1,6,4,8,5,3,7,2]=>[5,1,1,1]=>1344
[4,2,6,7,8,1,3,5]=>[5,2,1]=>4032
[4,6,5,1,3,7,8,2]=>[4,2,2]=>1260
[5,1,7,2,6,4,8,3]=>[5,3]=>2688
[4,1,7,6,5,8,2,3]=>[7,1]=>5760
[4,2,3,6,7,8,1,5]=>[6,1,1]=>3360
[4,7,2,1,6,5,8,3]=>[4,2,2]=>1260
[2,4,3,6,7,8,1,5]=>[7,1]=>5760
[6,8,5,2,7,3,1,4]=>[5,3]=>2688
[6,5,1,3,7,8,2,4]=>[5,3]=>2688
[7,2,1,4,3,5,8,6]=>[6,1,1]=>3360
[6,1,2,4,3,7,8,5]=>[7,1]=>5760
[8,1,5,4,2,3,6,7]=>[7,1]=>5760
[7,1,2,4,6,3,8,5]=>[7,1]=>5760
[7,1,2,6,5,3,8,4]=>[7,1]=>5760
[7,5,6,1,2,4,8,3]=>[6,2]=>3360
[7,1,4,5,2,3,6,8]=>[7,1]=>5760
[6,1,4,8,7,2,3,5]=>[5,3]=>2688
[6,1,8,5,7,2,3,4]=>[5,3]=>2688
[1,6,7,5,8,3,4,2]=>[7,1]=>5760
[6,1,7,5,8,2,3,4]=>[3,3,2]=>1120
[6,1,4,7,8,2,3,5]=>[3,3,2]=>1120
[8,1,2,3,7,5,4,6]=>[8]=>5040
[5,8,6,1,2,4,7,3]=>[7,1]=>5760
[1,6,8,7,5,3,4,2]=>[4,2,1,1]=>2520
[6,1,8,7,5,2,3,4]=>[4,3,1]=>3360
[8,3,1,2,4,6,5,7]=>[7,1]=>5760
[8,3,1,2,4,5,7,6]=>[7,1]=>5760
[6,3,1,2,4,7,5,8]=>[7,1]=>5760
[6,7,1,4,2,3,5,8]=>[3,3,1,1]=>1120
[6,1,7,4,8,2,3,5]=>[3,2,2,1]=>1680
[6,7,8,5,1,2,4,3]=>[6,2]=>3360
[8,6,5,4,3,2,7,9,1]=>[3,2,2,1,1]=>7560
[8,9,5,4,3,2,1,6,7]=>[6,2,1]=>30240
[7,6,5,4,3,8,9,1,2]=>[6,2,1]=>30240
[9,6,5,4,3,2,7,1,8]=>[3,2,2,1,1]=>7560
[8,7,6,5,4,3,2,9,1,10]=>[3,2,2,2,1]=>25200
[9,2,3,4,5,6,1,7,8]=>[4,1,1,1,1,1]=>756
[3,1,5,6,7,8,9,2,4]=>[9]=>40320
[2,1,3,5,6,7,8,9,4]=>[6,2,1]=>30240
[4,3,8,5,6,2,7,1]=>[7,1]=>5760
[4,3,8,6,7,2,5,1]=>[6,2]=>3360
[7,6,8,1,5,3,4,2]=>[4,3,1]=>3360
[7,4,6,1,5,3,8,2]=>[5,2,1]=>4032
[6,3,8,1,7,2,5,4]=>[6,2]=>3360
[6,1,5,4,8,2,7,3]=>[3,3,1,1]=>1120
[6,2,5,4,7,1,8,3]=>[4,2,1,1]=>2520
[8,3,6,7,5,1,2,4]=>[7,1]=>5760
[8,2,1,6,5,7,4,3]=>[3,3,1,1]=>1120
[2,7,1,8,5,6,4,3]=>[6,1,1]=>3360
[4,6,8,2,3,5,1,7]=>[8]=>5040
[6,8,2,1,3,5,4,7]=>[8]=>5040
[3,5,1,6,4,8,2,7]=>[6,2]=>3360
[3,5,8,6,2,1,4,7]=>[6,2]=>3360
[2,4,8,5,6,1,3,7]=>[5,3]=>2688
[4,8,2,5,6,1,3,7]=>[4,4]=>1260
[5,3,8,4,2,7,6,1]=>[5,2,1]=>4032
[2,8,5,3,1,4,7,6]=>[7,1]=>5760
[1,7,8,4,6,3,2,5]=>[4,2,1,1]=>2520
[8,7,2,4,6,3,1,5]=>[7,1]=>5760
[8,7,3,2,1,6,4,5]=>[3,3,1,1]=>1120
[7,8,3,4,6,5,2,1]=>[4,2,1,1]=>2520
[8,7,3,6,5,2,4,1]=>[4,2,1,1]=>2520
[3,1,2,8,6,5,7,4]=>[3,2,2,1]=>1680
[3,8,2,7,5,4,6,1]=>[4,3,1]=>3360
[8,7,1,4,5,3,6,2]=>[6,1,1]=>3360
[2,8,7,4,6,3,5,1]=>[4,3,1]=>3360
[2,8,7,4,6,3,1,5]=>[7,1]=>5760
[8,3,4,1,2,5,7,6]=>[7,1]=>5760
[8,4,1,3,2,5,7,6]=>[7,1]=>5760
[7,3,8,6,2,1,4,5]=>[4,4]=>1260
[7,2,8,4,6,5,1,3]=>[2,2,2,1,1]=>420
[5,8,6,4,7,2,3,1]=>[7,1]=>5760
[4,7,2,6,5,8,3,1]=>[4,3,1]=>3360
[3,6,8,5,7,4,2,1]=>[5,3]=>2688
[6,7,5,2,4,8,3,1]=>[5,3]=>2688
[8,1,2,7,5,6,3,4]=>[6,1,1]=>3360
[8,2,7,3,4,6,1,5]=>[6,1,1]=>3360
[6,7,5,4,8,1,3,2]=>[5,2,1]=>4032
[8,3,5,6,4,7,2,1]=>[6,2]=>3360
[8,5,6,2,4,3,7,1]=>[3,2,2,1]=>1680
[6,5,8,1,3,4,2,7]=>[5,3]=>2688
[6,8,4,5,1,3,2,7]=>[5,3]=>2688
[6,4,8,7,5,3,2,1]=>[4,3,1]=>3360
[6,7,1,4,3,2,8,5]=>[7,1]=>5760
[7,2,5,1,4,8,3,6]=>[5,2,1]=>4032
[5,8,1,3,4,2,7,6]=>[4,3,1]=>3360
[1,5,6,3,2,8,7,4]=>[4,2,1,1]=>2520
[1,3,7,6,8,4,2,5]=>[3,2,2,1]=>1680
[1,6,7,3,2,8,5,4]=>[7,1]=>5760
[3,2,7,6,8,4,5,1]=>[5,2,1]=>4032
[1,3,8,5,2,7,6,4]=>[5,2,1]=>4032
[6,4,1,5,2,8,7,3]=>[4,3,1]=>3360
[7,6,5,3,1,8,2,4]=>[8]=>5040
[2,5,1,4,7,3,6,8]=>[6,1,1]=>3360
[3,1,6,5,7,2,4,8]=>[4,3,1]=>3360
[2,6,1,5,7,4,8,3]=>[8]=>5040
[2,5,7,1,6,3,8,4]=>[8]=>5040
[2,6,1,5,7,4,3,8]=>[7,1]=>5760
[3,1,6,5,2,4,7,8]=>[6,1,1]=>3360
[3,6,5,1,4,2,7,8]=>[4,2,1,1]=>2520
[3,6,5,1,7,2,4,8]=>[5,2,1]=>4032
[3,6,5,2,1,4,7,8]=>[3,3,1,1]=>1120
[5,4,3,6,1,7,2,8]=>[4,2,1,1]=>2520
[4,5,2,7,6,1,3,8]=>[7,1]=>5760
[4,6,5,3,1,2,7,8]=>[4,2,1,1]=>2520
[5,4,1,6,3,7,2,8]=>[4,3,1]=>3360
[5,4,2,6,3,7,8,1]=>[8]=>5040
[3,6,5,7,1,4,2,8]=>[4,3,1]=>3360
[3,6,5,1,4,7,2,8]=>[4,3,1]=>3360
[4,3,6,5,7,1,2,8]=>[7,1]=>5760
[4,2,6,5,1,3,7,8]=>[3,2,1,1,1]=>1120
[4,1,6,5,3,7,8,2]=>[8]=>5040
[4,2,5,7,6,1,3,8]=>[6,1,1]=>3360
[3,4,7,6,1,2,5,8]=>[4,3,1]=>3360
[4,2,5,7,6,3,8,1]=>[4,3,1]=>3360
[4,1,6,5,2,7,3,8]=>[4,3,1]=>3360
[3,6,5,7,2,1,4,8]=>[5,2,1]=>4032
[3,5,7,6,2,4,1,8]=>[3,2,2,1]=>1680
[5,4,2,6,3,7,1,8]=>[7,1]=>5760
[4,6,5,2,7,3,1,8]=>[7,1]=>5760
[4,6,5,2,1,7,3,8]=>[7,1]=>5760
[3,5,8,2,1,4,6,7]=>[8]=>5040
[3,5,8,2,4,6,7,1]=>[3,3,1,1]=>1120
[5,3,8,2,1,4,6,7]=>[6,2]=>3360
[5,3,1,8,2,4,6,7]=>[4,4]=>1260
[5,1,3,8,2,4,6,7]=>[4,3,1]=>3360
[1,5,8,4,2,3,6,7]=>[4,2,1,1]=>2520
[5,8,2,1,4,3,6,7]=>[5,3]=>2688
[5,8,2,4,1,6,7,3]=>[3,2,1,1,1]=>1120
[5,8,2,4,6,3,1,7]=>[7,1]=>5760
[5,8,2,4,3,6,1,7]=>[6,1,1]=>3360
[5,8,1,4,6,2,3,7]=>[7,1]=>5760
[1,5,8,4,6,7,2,3]=>[4,2,1,1]=>2520
[5,1,8,4,6,7,2,3]=>[5,2,1]=>4032
[5,8,2,4,6,3,7,1]=>[6,1,1]=>3360
[3,8,4,6,7,2,1,5]=>[8]=>5040
[3,8,4,6,7,2,5,1]=>[6,2]=>3360
[8,4,3,6,7,2,5,1]=>[3,2,2,1]=>1680
[8,4,3,6,7,2,1,5]=>[4,3,1]=>3360
[8,6,2,4,5,3,7,1]=>[3,2,1,1,1]=>1120
[1,8,6,4,5,7,2,3]=>[5,1,1,1]=>1344
[8,6,2,4,5,3,1,7]=>[3,3,1,1]=>1120
[1,8,6,4,2,3,5,7]=>[4,2,1,1]=>2520
[3,8,1,6,2,4,5,7]=>[4,2,2]=>1260
[3,8,6,2,1,4,5,7]=>[8]=>5040
[3,8,6,2,4,1,5,7]=>[5,3]=>2688
[3,8,6,2,4,5,7,1]=>[7,1]=>5760
[8,3,6,2,4,5,1,7]=>[5,3]=>2688
[8,1,3,6,2,4,5,7]=>[5,2,1]=>4032
[8,3,6,7,2,1,4,5]=>[6,2]=>3360
[3,8,6,7,2,1,4,5]=>[3,3,2]=>1120
[8,2,6,4,5,1,7,3]=>[4,1,1,1,1]=>420
[1,8,4,6,7,5,2,3]=>[7,1]=>5760
[8,4,6,2,3,7,5,1]=>[4,2,2]=>1260
[8,4,7,2,1,3,6,5]=>[3,3,2]=>1120
[2,7,1,6,3,5,8,4]=>[8]=>5040
[8,2,1,4,7,3,6,5]=>[6,1,1]=>3360
[1,6,2,5,8,4,7,3]=>[6,1,1]=>3360
[2,1,5,8,7,3,6,4]=>[4,2,2]=>1260
[3,2,1,6,7,4,8,5]=>[3,2,2,1]=>1680
[4,3,1,7,8,5,2,6]=>[5,3]=>2688
[5,6,8,2,4,3,7,1]=>[7,1]=>5760
[2,8,5,3,6,4,7,1]=>[4,3,1]=>3360
[1,2,8,6,4,7,3,5]=>[6,1,1]=>3360
[5,3,2,7,8,6,4,1]=>[3,2,2,1]=>1680
[4,2,7,8,3,5,6,1]=>[4,3,1]=>3360
[2,8,3,7,1,4,6,5]=>[4,3,1]=>3360
[2,8,7,1,5,3,6,4]=>[4,3,1]=>3360
[7,3,5,6,4,2,8,1]=>[5,3]=>2688
[3,8,4,2,7,6,5,1]=>[5,2,1]=>4032
[4,8,3,2,7,5,6,1]=>[4,3,1]=>3360
[3,2,4,8,7,5,6,1]=>[4,3,1]=>3360
[2,6,8,1,5,3,4,7]=>[7,1]=>5760
[3,2,5,6,8,1,4,7]=>[7,1]=>5760
[3,8,1,6,4,5,2,7]=>[3,3,2]=>1120
[8,1,3,6,5,4,2,7]=>[4,2,1,1]=>2520
[7,4,3,6,2,1,8,5]=>[7,1]=>5760
[1,2,4,8,6,3,7,5]=>[5,1,1,1]=>1344
[7,2,1,5,3,4,8,6]=>[7,1]=>5760
[5,7,2,3,1,4,8,6]=>[6,2]=>3360
[7,1,5,2,4,6,8,3]=>[7,1]=>5760
[8,4,2,7,3,5,6,1]=>[6,2]=>3360
[1,8,6,4,7,5,3,2]=>[4,2,1,1]=>2520
[7,4,1,5,8,6,3,2]=>[4,3,1]=>3360
[4,5,8,7,3,1,2,6]=>[8]=>5040
[1,3,8,7,6,4,2,5]=>[7,1]=>5760
[2,8,5,1,7,4,6,3]=>[8]=>5040
[1,8,6,4,7,5,2,3]=>[6,1,1]=>3360
[2,7,4,6,3,8,5,1]=>[8]=>5040
[1,2,8,6,4,7,5,3]=>[4,2,1,1]=>2520
[3,4,5,6,7,9,1,2,8]=>[5,4]=>18144
[3,4,5,7,8,9,1,2,6]=>[7,2]=>25920
[3,5,6,7,8,9,1,2,4]=>[6,3]=>20160
[3,4,5,6,8,9,10,1,2,7]=>[4,4,2]=>56700
[3,5,6,7,8,9,10,1,2,4]=>[7,3]=>172800
[3,4,5,6,7,8,9,10,1,2,11]=>[5,5,1]=>798336
[3,4,5,6,7,8,1,2,9,10]=>[4,4,1,1]=>56700
[3,4,5,6,9,1,2,7,8]=>[9]=>40320
[3,4,5,6,1,2,7,8,9]=>[3,3,1,1,1]=>3360
[5,1,6,7,8,9,2,3,4]=>[9]=>40320
[3,4,6,7,8,9,10,11,1,2,5]=>[4,4,3]=>415800
[4,1,8,6,3,7,5,2]=>[8]=>5040
[8,4,3,1,6,2,5,7]=>[7,1]=>5760
[7,5,4,3,8,1,6,2]=>[3,3,2]=>1120
[5,3,1,6,2,8,7,4]=>[4,3,1]=>3360
[3,5,4,1,7,8,2,6]=>[3,3,2]=>1120
[6,4,2,1,5,7,3,8]=>[6,1,1]=>3360
[3,1,5,8,7,2,4,6]=>[8]=>5040
[3,2,5,7,8,4,6,1]=>[4,3,1]=>3360
[5,3,7,4,2,6,8,1]=>[6,1,1]=>3360
[5,3,7,4,2,6,1,8]=>[5,1,1,1]=>1344
[5,3,8,4,2,1,6,7]=>[7,1]=>5760
[5,2,8,4,3,1,6,7]=>[6,1,1]=>3360
[5,1,8,4,3,2,6,7]=>[7,1]=>5760
[5,2,7,4,3,6,1,8]=>[4,1,1,1,1]=>420
[5,2,7,4,3,6,8,1]=>[5,1,1,1]=>1344
[5,3,7,4,1,6,8,2]=>[4,2,1,1]=>2520
[3,1,5,7,8,4,6,2]=>[5,3]=>2688
[3,1,5,7,8,4,2,6]=>[8]=>5040
[5,2,7,4,1,3,8,6]=>[4,2,1,1]=>2520
[6,2,3,7,4,8,5,1]=>[3,3,1,1]=>1120
[6,2,3,7,4,8,1,5]=>[6,1,1]=>3360
[6,2,3,7,4,5,1,8]=>[5,1,1,1]=>1344
[6,1,3,7,4,5,8,2]=>[7,1]=>5760
[1,2,8,6,4,3,5,7]=>[6,1,1]=>3360
[6,1,3,7,4,5,2,8]=>[6,1,1]=>3360
[1,8,6,3,5,4,2,7]=>[3,3,1,1]=>1120
[2,6,1,8,5,3,4,7]=>[4,3,1]=>3360
[4,5,7,8,1,6,3,2]=>[5,2,1]=>4032
[2,5,7,8,4,6,3,1]=>[5,2,1]=>4032
[1,8,2,7,5,3,4,6]=>[4,2,1,1]=>2520
[5,6,8,3,4,2,7,1]=>[5,2,1]=>4032
[4,1,5,3,8,6,7,2]=>[6,1,1]=>3360
[7,3,5,1,4,8,6,2]=>[8]=>5040
[7,1,3,2,4,5,6,8]=>[6,1,1]=>3360
[3,8,7,1,4,2,5,6]=>[5,3]=>2688
[5,1,7,8,2,4,3,6]=>[3,3,2]=>1120
[8,5,4,6,1,7,3,2]=>[4,4]=>1260
[5,3,2,1,4,6,8,7]=>[3,2,2,1]=>1680
[5,3,2,4,8,1,6,7]=>[5,2,1]=>4032
[5,3,2,4,7,1,8,6]=>[5,2,1]=>4032
[8,4,5,3,7,1,2,6]=>[5,3]=>2688
[4,8,1,7,3,5,6,2]=>[6,2]=>3360
[5,3,2,4,6,8,1,7]=>[5,2,1]=>4032
[1,2,5,6,7,3,8,9,4]=>[7,1,1]=>25920
[1,2,4,3,5,7,8,9,6]=>[4,2,1,1,1]=>7560
[4,6,8,3,7,1,5,2]=>[6,2]=>3360
[1,7,6,4,2,5,3,8]=>[5,1,1,1]=>1344
[7,6,4,2,8,3,1,5]=>[4,2,2]=>1260
[8,5,2,4,3,7,1,6]=>[4,3,1]=>3360
[8,5,1,4,3,7,6,2]=>[5,2,1]=>4032
[7,5,4,1,3,6,8,2]=>[7,1]=>5760
[3,6,7,2,5,1,8,4]=>[7,1]=>5760
[2,6,5,7,1,4,8,3]=>[8]=>5040
[3,5,1,7,8,4,6,2]=>[3,3,2]=>1120
[1,5,2,4,6,8,7,3]=>[5,1,1,1]=>1344
[8,1,2,4,7,6,5,3]=>[4,2,1,1]=>2520
[3,4,1,8,6,7,5,2]=>[3,3,2]=>1120
[4,3,8,5,1,7,6,2]=>[3,3,2]=>1120
[6,1,3,2,8,5,7,4]=>[6,1,1]=>3360
[3,1,2,4,5,6,7,9,8]=>[3,2,1,1,1,1]=>2520
[8,5,3,2,4,7,1,6]=>[4,3,1]=>3360
[6,7,4,2,5,8,3,1]=>[4,3,1]=>3360
[8,5,4,2,6,3,1,7]=>[5,3]=>2688
[8,5,2,1,6,4,3,7]=>[8]=>5040
[8,4,6,5,1,3,2,7]=>[6,2]=>3360
[1,3,8,4,7,5,2,6]=>[6,1,1]=>3360
[5,3,7,1,4,6,8,2]=>[4,3,1]=>3360
[5,7,2,6,1,4,8,3]=>[4,2,2]=>1260
[3,8,5,7,6,1,2,4]=>[4,4]=>1260
[8,4,7,5,2,1,3,6]=>[3,3,2]=>1120
[3,8,6,4,7,2,1,5]=>[7,1]=>5760
[5,2,7,4,6,8,3,1]=>[4,2,1,1]=>2520
[4,8,6,3,7,2,1,5]=>[8]=>5040
[2,8,3,1,7,6,4,5]=>[6,1,1]=>3360
[2,5,6,4,8,1,7,3]=>[6,1,1]=>3360
[5,7,2,1,6,8,3,4]=>[5,3]=>2688
[4,7,8,5,1,6,2,3]=>[3,2,2,1]=>1680
[4,5,2,1,6,7,8,3]=>[6,2]=>3360
[4,5,6,3,1,7,8,2]=>[8]=>5040
[3,5,6,7,4,1,8,2]=>[5,3]=>2688
[3,5,1,4,2,8,7,6]=>[2,2,2,1,1]=>420
[3,5,1,4,2,6,8,7]=>[2,2,2,1,1]=>420
[3,5,1,4,2,6,7,8]=>[2,2,1,1,1,1]=>210
[1,3,8,4,6,2,5,7]=>[6,1,1]=>3360
[1,8,4,2,3,7,5,6]=>[7,1]=>5760
[1,4,8,3,2,7,6,5]=>[5,2,1]=>4032
[1,3,7,6,5,2,4,8]=>[5,1,1,1]=>1344
[1,2,8,6,7,5,4,3]=>[4,2,1,1]=>2520
[1,7,5,4,3,2,6,8]=>[3,2,1,1,1]=>1120
[8,9,10,1,5,6,7,3,4,2]=>[7,1,1,1]=>86400
[8,9,10,5,6,7,1,3,4,2]=>[10]=>362880
[8,9,10,1,5,6,3,4,7,2]=>[5,3,1,1]=>120960
[8,9,10,5,6,1,3,4,7,2]=>[5,5]=>72576
[8,9,10,5,6,3,4,7,1,2]=>[10]=>362880
[8,9,5,6,10,1,3,4,7,2]=>[6,4]=>151200
[8,9,5,6,10,3,4,7,1,2]=>[10]=>362880
[8,9,10,1,5,6,7,3,2,4]=>[5,2,1,1,1]=>60480
[8,9,10,5,6,7,1,3,2,4]=>[8,2]=>226800
[8,9,10,1,5,6,3,7,2,4]=>[6,2,1,1]=>151200
[8,9,10,5,6,1,3,7,2,4]=>[8,2]=>226800
[8,9,10,5,6,3,7,1,2,4]=>[5,2,2,1]=>90720
[8,9,5,6,10,1,3,7,2,4]=>[8,2]=>226800
[8,9,5,6,10,3,7,1,2,4]=>[5,2,2,1]=>90720
[8,9,10,1,5,6,3,2,4,7]=>[5,3,1,1]=>120960
[8,9,10,5,6,1,3,2,4,7]=>[7,3]=>172800
[8,9,10,5,6,3,1,2,4,7]=>[10]=>362880
[8,9,10,5,6,3,2,4,7,1]=>[7,3]=>172800
[8,9,5,6,10,1,3,2,4,7]=>[6,4]=>151200
[8,9,5,6,10,3,1,2,4,7]=>[10]=>362880
[8,9,5,6,10,3,2,4,7,1]=>[7,3]=>172800
[8,9,10,1,5,3,6,7,2,4]=>[7,2,1]=>259200
[8,9,10,5,1,3,6,7,2,4]=>[8,2]=>226800
[8,9,10,5,3,6,7,1,2,4]=>[4,2,2,1,1]=>56700
[8,9,5,10,1,3,6,7,2,4]=>[6,2,2]=>75600
[8,9,5,10,3,6,7,1,2,4]=>[2,2,2,2,1,1]=>4725
[8,9,10,1,5,3,6,2,4,7]=>[5,4,1]=>181440
[8,9,10,5,1,3,6,2,4,7]=>[6,4]=>151200
[8,9,10,5,3,6,1,2,4,7]=>[9,1]=>403200
[8,9,10,5,3,6,2,4,7,1]=>[6,3,1]=>201600
[8,9,5,10,1,3,6,2,4,7]=>[10]=>362880
[8,9,5,10,3,6,1,2,4,7]=>[7,2,1]=>259200
[8,9,5,10,3,6,2,4,7,1]=>[4,3,2,1]=>151200
[8,9,5,3,6,10,1,2,4,7]=>[10]=>362880
[8,9,5,3,6,10,2,4,7,1]=>[7,3]=>172800
[8,5,9,10,1,3,6,7,2,4]=>[8,2]=>226800
[8,5,9,10,3,6,7,1,2,4]=>[4,2,2,1,1]=>56700
[8,5,9,10,1,3,6,2,4,7]=>[6,4]=>151200
[8,5,9,10,3,6,1,2,4,7]=>[9,1]=>403200
[8,5,9,10,3,6,2,4,7,1]=>[5,4,1]=>181440
[3,8,5,7,4,6,2,1]=>[7,1]=>5760
[7,6,3,2,5,1,8,4]=>[6,1,1]=>3360
[4,2,5,7,8,6,3,1]=>[6,1,1]=>3360
[6,7,2,4,5,1,8,3]=>[4,2,1,1]=>2520
[5,2,7,8,3,6,1,4]=>[4,2,1,1]=>2520
[8,5,1,2,3,7,4,6]=>[8]=>5040
[5,2,8,3,1,4,7,6]=>[4,2,1,1]=>2520
[8,7,2,5,1,4,3,6]=>[5,3]=>2688
[8,4,1,3,2,7,6,5]=>[6,2]=>3360
[8,3,5,1,2,4,7,6]=>[4,3,1]=>3360
[8,7,4,5,1,2,6,3]=>[5,3]=>2688
[3,8,6,2,7,1,5,4]=>[3,3,2]=>1120
[3,8,4,2,1,7,6,5]=>[6,2]=>3360
[8,4,1,7,5,2,6,3]=>[4,3,1]=>3360
[8,5,7,6,4,3,1,2]=>[8]=>5040
[8,3,5,7,6,2,4,1]=>[4,2,2]=>1260
[1,4,6,8,2,5,7,3]=>[6,1,1]=>3360
[7,3,8,2,4,6,1,5]=>[5,2,1]=>4032
[1,5,2,6,8,3,7,4]=>[6,1,1]=>3360
[7,2,8,4,1,3,5,6]=>[3,3,1,1]=>1120
[6,1,7,3,2,8,4,5]=>[5,3]=>2688
[6,2,1,7,3,8,4,5]=>[5,2,1]=>4032
[5,8,2,1,3,4,6,7]=>[8]=>5040
[4,2,5,1,8,3,6,7]=>[5,2,1]=>4032
[7,4,2,8,3,5,1,6]=>[6,2]=>3360
[6,7,8,5,2,1,4,3]=>[4,2,2]=>1260
[1,6,2,7,8,4,3,5]=>[5,2,1]=>4032
[10,1,9,5,6,7,8,2,3,4]=>[8,2]=>226800
[9,1,10,8,6,7,2,3,4,5]=>[10]=>362880
[8,1,9,10,7,2,3,4,5,6]=>[6,4]=>151200
[10,1,8,9,2,3,4,5,6,7]=>[10]=>362880
[3,1,10,9,6,7,8,2,4,5]=>[8,2]=>226800
[10,1,11,9,6,7,8,2,3,4,5]=>[11]=>3628800
[3,1,9,10,8,7,2,4,5,6]=>[10]=>362880
[9,1,10,11,8,7,2,3,4,5,6]=>[7,4]=>1425600
[3,1,8,9,10,2,4,5,6,7]=>[10]=>362880
[8,1,9,10,11,2,3,4,5,6,7]=>[6,5]=>1330560
[11,1,10,9,2,3,4,5,6,7,8]=>[6,5]=>1330560
[7,3,4,1,8,6,2,5]=>[5,2,1]=>4032
[4,7,6,3,5,8,2,1]=>[5,2,1]=>4032
[3,7,6,5,2,4,8,1]=>[8]=>5040
[1,4,7,8,6,2,5,3]=>[7,1]=>5760
[1,6,7,8,3,2,5,4]=>[3,2,2,1]=>1680
[1,3,2,7,8,4,6,5]=>[3,2,2,1]=>1680
[5,7,1,4,6,2,8,3]=>[7,1]=>5760
[6,3,1,4,7,8,2,5]=>[7,1]=>5760
[9,8,7,1,5,6,4,3,2]=>[7,1,1]=>25920
[9,1,7,8,6,5,4,3,2]=>[4,3,2]=>15120
[4,3,8,6,5,2,7,1]=>[6,1,1]=>3360
[5,4,7,3,1,2,6,8]=>[5,2,1]=>4032
[3,1,2,6,5,7,8,4]=>[4,3,1]=>3360
[7,3,2,6,1,4,8,5]=>[4,2,2]=>1260
[3,2,5,6,8,4,1,7]=>[5,2,1]=>4032
[7,2,6,8,5,4,3,1]=>[6,1,1]=>3360
[3,7,5,6,2,4,1,8]=>[5,2,1]=>4032
[1,3,4,5,6,7,2,9,8]=>[6,2,1]=>30240
[3,4,5,6,7,1,9,2,8]=>[9]=>40320
[3,2,4,1,6,5,8,7,9]=>[3,2,2,1,1]=>7560
[4,2,5,1,6,3,8,7,9]=>[3,2,2,1,1]=>7560
[4,2,6,1,7,3,8,5,9]=>[3,2,2,1,1]=>7560
[4,2,6,1,8,3,9,5,7]=>[2,2,2,2,1]=>945
[4,2,6,1,7,3,5,9,8]=>[2,2,2,2,1]=>945
[4,2,5,1,3,7,6,9,8]=>[2,2,2,2,1]=>945
[3,2,5,4,6,1,8,7,9]=>[4,2,1,1,1]=>7560
[4,2,5,1,6,3,8,7,10,9]=>[3,2,2,2,1]=>25200
[4,2,5,1,7,6,8,3,9]=>[4,2,1,1,1]=>7560
[4,2,6,1,7,3,8,5,10,9]=>[3,2,2,2,1]=>25200
[4,2,6,1,7,3,9,8,5]=>[3,2,2,1,1]=>7560
[4,2,6,1,8,3,9,5,10,7]=>[3,2,2,2,1]=>25200
[4,2,5,1,3,6,8,7]=>[2,2,2,1,1]=>420
[4,2,6,1,7,3,5,8,9]=>[2,2,2,1,1,1]=>1260
[4,2,6,1,8,3,9,5,7,10]=>[2,2,2,2,1,1]=>4725
[4,2,5,1,3,8,9,6,7]=>[2,2,2,2,1]=>945
[4,2,6,1,7,3,5,9,8,10]=>[2,2,2,2,1,1]=>4725
[3,2,1,6,7,4,5,9,8]=>[2,2,2,2,1]=>945
[4,2,5,1,3,7,6,9,8,10]=>[2,2,2,2,1,1]=>4725
[1,4,5,2,3,7,6,9,8]=>[2,2,2,2,1]=>945
[5,3,4,2,7,1,8,6]=>[5,3]=>2688
[6,5,2,1,3,8,4,7]=>[5,3]=>2688
[2,4,3,5,6,8,1,7]=>[7,1]=>5760
[6,3,2,4,8,5,1,7]=>[5,2,1]=>4032
[6,3,1,2,7,8,4,5]=>[8]=>5040
[8,4,7,1,2,5,3,6]=>[6,2]=>3360
[7,4,6,1,8,5,2,3]=>[4,4]=>1260
[8,5,6,7,2,1,4,3]=>[4,2,2]=>1260
[2,5,6,3,8,4,7,1]=>[4,3,1]=>3360
[1,7,6,2,8,3,5,4]=>[5,2,1]=>4032
[4,1,3,8,5,2,7,6]=>[5,1,1,1]=>1344
[1,8,5,4,7,2,3,6]=>[3,3,1,1]=>1120
[8,2,5,6,4,3,1,7]=>[4,3,1]=>3360
[2,4,3,8,6,5,1,7]=>[5,2,1]=>4032
[3,1,4,5,8,6,2,7]=>[7,1]=>5760
[1,8,3,2,5,4,6,7]=>[5,1,1,1]=>1344
[5,1,7,3,2,8,4,6]=>[3,3,2]=>1120
[5,7,8,1,3,2,4,6]=>[8]=>5040
[8,2,4,1,6,7,3,5]=>[7,1]=>5760
[8,7,3,6,2,4,1,5]=>[5,2,1]=>4032
[1,7,4,8,3,6,2,5]=>[4,2,1,1]=>2520
[7,8,6,1,3,5,4,2]=>[3,3,2]=>1120
[1,7,5,8,4,3,2,6]=>[5,2,1]=>4032
[6,3,1,2,7,8,5,4]=>[6,2]=>3360
[8,2,7,5,3,4,1,6]=>[7,1]=>5760
[6,3,1,2,8,7,5,4]=>[8]=>5040
[8,4,7,2,6,3,1,5]=>[6,2]=>3360
[1,2,5,7,8,3,6,4]=>[6,1,1]=>3360
[7,6,3,4,2,1,8,5]=>[6,1,1]=>3360
[8,4,6,2,3,7,1,5]=>[6,2]=>3360
[3,4,5,8,1,7,2,6]=>[5,3]=>2688
[6,3,4,2,7,8,1,5]=>[5,3]=>2688
[8,6,3,4,7,2,1,5]=>[4,2,1,1]=>2520
[4,5,6,2,7,8,3,1]=>[8]=>5040
[4,5,6,2,7,1,8,3]=>[8]=>5040
[4,5,6,2,1,7,8,3]=>[4,4]=>1260
[4,5,6,2,1,7,3,8]=>[4,3,1]=>3360
[6,8,7,2,3,1,4,5]=>[6,2]=>3360
[4,5,1,6,7,3,2,8]=>[4,3,1]=>3360
[2,5,1,8,3,7,4,6]=>[4,4]=>1260
[5,7,2,1,3,8,4,6]=>[6,2]=>3360
[7,1,5,4,2,6,3,8]=>[5,1,1,1]=>1344
[9,8,7,6,5,3,2,4,1]=>[6,2,1]=>30240
[9,8,7,6,5,2,4,3,1]=>[6,2,1]=>30240
[10,9,8,7,6,5,4,2,3,1]=>[4,2,2,2]=>18900
[2,7,4,5,6,8,1,3]=>[5,3]=>2688
[2,3,4,6,8,1,7,5]=>[5,2,1]=>4032
[2,3,4,8,6,7,9,5,1]=>[9]=>40320
[2,3,8,5,6,7,9,1,4]=>[5,4]=>18144
[2,8,4,5,6,7,9,3,1]=>[9]=>40320
[8,3,4,5,6,7,9,2,1]=>[9]=>40320
[2,3,4,5,7,9,1,8,6]=>[6,2,1]=>30240
[2,3,4,6,7,1,9,5,8]=>[5,4]=>18144
[2,3,4,5,9,7,8,10,6,1]=>[10]=>362880
[2,3,5,8,1,6,7,4]=>[4,2,1,1]=>2520
[2,3,5,6,1,7,9,4,8]=>[5,4]=>18144
[2,3,4,9,6,7,8,10,1,5]=>[5,5]=>72576
[2,4,5,1,6,7,9,8,3]=>[5,3,1]=>24192
[2,3,9,5,6,7,8,10,4,1]=>[10]=>362880
[2,4,7,5,6,8,1,3]=>[8]=>5040
[3,4,1,5,6,7,9,2,8]=>[7,2]=>25920
[2,9,4,5,6,7,8,10,3,1]=>[10]=>362880
[3,2,4,5,6,7,9,1,8]=>[8,1]=>45360
[9,3,4,5,6,7,8,10,1,2]=>[8,2]=>226800
[2,3,4,5,6,8,10,1,9,7]=>[7,2,1]=>259200
[2,3,4,5,6,7,10,9,11,8,1]=>[11]=>3628800
[2,3,4,7,6,9,8,5,1]=>[9]=>40320
[2,3,4,5,7,8,1,10,6,9]=>[6,4]=>151200
[2,3,4,5,6,10,8,9,11,7,1]=>[11]=>3628800
[2,3,4,6,9,1,7,8,5]=>[5,2,1,1]=>18144
[2,3,4,6,7,1,8,10,5,9]=>[5,5]=>72576
[2,3,4,5,10,7,8,9,11,1,6]=>[6,5]=>1330560
[7,3,4,6,2,8,1,5]=>[6,2]=>3360
[2,5,4,6,8,7,9,1,3]=>[5,4]=>18144
[2,3,5,7,1,6,9,4,8]=>[4,4,1]=>11340
[2,3,5,6,1,7,8,10,9,4]=>[5,4,1]=>181440
[2,3,4,10,6,7,8,9,11,5,1]=>[11]=>3628800
[4,7,6,5,2,8,3,1]=>[8]=>5040
[4,3,5,8,6,7,9,2,1]=>[9]=>40320
[2,5,4,8,6,7,3,1]=>[8]=>5040
[2,4,6,1,5,7,9,3,8]=>[5,3,1]=>24192
[2,4,5,1,6,7,8,10,3,9]=>[7,3]=>172800
[2,3,10,5,6,7,8,9,11,4,1]=>[11]=>3628800
[7,5,4,1,6,8,2,3]=>[8]=>5040
[2,4,8,5,6,7,9,1,3]=>[9]=>40320
[3,5,1,4,6,7,9,8,2]=>[5,2,1,1]=>18144
[3,4,1,5,6,7,8,10,2,9]=>[8,2]=>226800
[2,10,4,5,6,7,8,9,11,1,3]=>[8,3]=>1663200
[4,2,3,5,6,7,9,1,8]=>[7,1,1]=>25920
[3,2,4,5,6,7,8,10,9,1]=>[8,1,1]=>226800
[10,3,4,5,6,7,8,9,11,2,1]=>[11]=>3628800
[2,7,3,6,4,1,8,5]=>[7,1]=>5760
[3,6,5,1,4,8,2,7]=>[4,4]=>1260
[6,3,5,4,8,1,2,7]=>[5,2,1]=>4032
[2,5,1,4,6,3,8,7]=>[5,2,1]=>4032
[3,1,5,6,4,2,8,7]=>[6,2]=>3360
[8,5,6,4,3,1,7,2]=>[6,1,1]=>3360
[8,3,5,6,7,1,2,4]=>[4,4]=>1260
[2,1,4,7,3,6,8,5]=>[5,2,1]=>4032
[5,3,7,6,4,8,2,1]=>[5,3]=>2688
[3,7,6,4,2,8,1,5]=>[7,1]=>5760
[8,6,1,4,3,7,2,5]=>[4,3,1]=>3360
[8,4,7,5,1,6,3,2]=>[5,2,1]=>4032
[2,1,5,3,7,8,6,4]=>[6,2]=>3360
[5,1,4,7,6,8,2,3]=>[8]=>5040
[8,4,1,3,7,6,5,2]=>[5,2,1]=>4032
[8,3,4,1,6,7,5,2]=>[5,3]=>2688
[8,1,4,2,6,5,7,3]=>[5,2,1]=>4032
[5,8,1,4,3,2,6,7]=>[4,3,1]=>3360
[1,6,4,3,8,2,7,5]=>[2,2,2,1,1]=>420
[7,8,1,4,3,2,5,6]=>[4,3,1]=>3360
[7,1,8,4,5,3,6,2]=>[6,1,1]=>3360
[4,3,1,8,6,5,7,2]=>[5,2,1]=>4032
[4,3,2,7,5,1,8,6]=>[5,2,1]=>4032
[5,2,3,7,4,1,8,6]=>[6,1,1]=>3360
[2,1,7,4,3,6,8,5]=>[4,2,1,1]=>2520
[7,1,2,4,5,6,8,3]=>[5,1,1,1]=>1344
[2,8,7,1,4,5,6,3]=>[8]=>5040
[8,7,1,3,4,5,6,2]=>[8]=>5040
[5,8,3,1,4,6,7,2]=>[3,2,1,1,1]=>1120
[1,7,2,5,4,6,8,3]=>[4,2,1,1]=>2520
[2,5,3,8,1,6,7,4]=>[3,2,1,1,1]=>1120
[1,6,4,2,5,7,8,3]=>[6,1,1]=>3360
[6,5,3,4,1,7,8,2]=>[6,1,1]=>3360
[5,6,3,4,1,7,8,2]=>[4,2,1,1]=>2520
[2,5,3,1,4,7,8,6]=>[4,3,1]=>3360
[6,8,2,3,1,5,7,4]=>[4,3,1]=>3360
[4,3,1,5,2,7,8,6]=>[5,3]=>2688
[5,2,3,1,4,7,8,6]=>[3,3,1,1]=>1120
[7,2,1,3,5,6,8,4]=>[5,1,1,1]=>1344
[5,2,4,7,8,6,3,1]=>[3,3,1,1]=>1120
[5,4,8,7,2,3,1,6]=>[5,3]=>2688
[8,1,4,5,3,6,2,7]=>[4,3,1]=>3360
[8,3,5,1,4,6,2,7]=>[7,1]=>5760
[5,8,2,1,7,4,3,6]=>[8]=>5040
[6,5,7,2,1,8,4,3]=>[8]=>5040
[1,5,4,7,3,8,6,2]=>[7,1]=>5760
[7,4,1,3,8,5,6,2]=>[8]=>5040
[3,6,8,4,1,7,2,5]=>[4,3,1]=>3360
[2,1,8,4,7,6,3,5]=>[4,2,1,1]=>2520
[2,7,5,6,8,4,3,1]=>[6,2]=>3360
[3,5,2,4,7,8,6,1]=>[7,1]=>5760
[7,5,6,3,8,2,1,4]=>[6,2]=>3360
[1,6,2,7,4,5,8,3]=>[7,1]=>5760
[7,4,2,6,1,5,8,3]=>[8]=>5040
[8,4,1,6,2,5,7,3]=>[4,3,1]=>3360
[7,3,4,5,1,6,8,2]=>[7,1]=>5760
[1,3,2,5,4,7,6,9,8,11,10]=>[2,2,2,2,2,1]=>10395
[1,4,2,6,3,7,5,9,8]=>[6,2,1]=>30240
[1,3,2,6,4,7,5,9,8]=>[4,2,2,1]=>11340
[2,1,6,3,7,4,8,5,9]=>[3,3,2,1]=>10080
[8,4,2,7,6,1,5,3]=>[8]=>5040
[8,4,7,1,2,6,5,3]=>[7,1]=>5760
[8,4,7,6,1,2,5,3]=>[5,3]=>2688
[8,7,6,2,1,5,3,4]=>[8]=>5040
[5,7,8,1,6,2,4,3]=>[6,2]=>3360
[6,8,7,4,2,5,1,3]=>[7,1]=>5760
[6,8,4,5,7,2,1,3]=>[8]=>5040
[6,5,4,3,2,7,1,8,9]=>[3,2,2,1,1]=>7560
[5,4,3,2,6,1,7,8,9]=>[3,2,1,1,1,1]=>2520
[4,3,2,5,1,6,7,8,9]=>[3,2,1,1,1,1]=>2520
[3,2,4,1,5,6,7,8,9]=>[3,1,1,1,1,1,1]=>168
[3,1,6,5,4,7,2,8]=>[5,2,1]=>4032
[4,1,2,6,5,3,7,8]=>[5,1,1,1]=>1344
[4,6,1,3,5,2,7,8]=>[3,2,1,1,1]=>1120
[4,2,6,3,5,1,7,8]=>[4,1,1,1,1]=>420
[4,6,1,2,5,3,7,8]=>[5,1,1,1]=>1344
[5,8,4,7,1,3,6,2]=>[4,2,2]=>1260
[6,4,7,1,3,5,2,8]=>[7,1]=>5760
[6,8,3,1,5,4,7,2]=>[3,2,1,1,1]=>1120
[5,1,3,6,7,4,2,8]=>[4,2,1,1]=>2520
[4,2,8,6,7,1,3,5]=>[4,3,1]=>3360
[6,1,2,4,7,3,5,8]=>[4,2,1,1]=>2520
[5,3,1,6,4,7,2,8]=>[7,1]=>5760
[4,2,8,1,6,5,7,3]=>[2,2,2,1,1]=>420
[1,3,5,2,7,4,6,9,8]=>[6,2,1]=>30240
[1,2,4,3,6,5,8,7,9]=>[2,2,2,1,1,1]=>1260
[1,3,5,7,2,4,6,9,8]=>[3,3,2,1]=>10080
[1,3,5,7,2,4,6,9,8,10]=>[3,3,2,1,1]=>50400
[1,3,5,7,2,9,4,6,8]=>[3,3,2,1]=>10080
[5,6,1,4,8,3,2,7]=>[7,1]=>5760
[3,6,4,1,7,2,8,5]=>[3,3,2]=>1120
[5,6,2,1,3,7,4,8,9]=>[7,1,1]=>25920
[3,2,5,1,6,4,7,8,9]=>[5,1,1,1,1]=>3024
[6,7,2,1,8,3,4,9,5]=>[6,3]=>20160
[3,6,4,1,7,2,8,5,9]=>[3,3,2,1]=>10080
[3,6,7,2,1,4,8,5,9]=>[5,3,1]=>24192
[4,2,6,1,7,5,3,8,9]=>[4,2,1,1,1]=>7560
[4,3,2,6,1,7,5,8,9]=>[5,2,1,1]=>18144
[4,7,2,5,1,8,3,9,6]=>[3,3,3]=>2240
[4,3,7,8,2,1,5,9,6]=>[5,4]=>18144
[3,5,2,7,1,8,6,4,9]=>[4,4,1]=>11340
[5,4,3,2,7,1,8,6,9]=>[5,2,1,1]=>18144
[6,4,2,8,1,9,7,5,3]=>[8,1]=>45360
[4,3,6,2,8,1,9,7,5]=>[5,4]=>18144
[6,5,4,3,2,8,1,9,7]=>[5,2,2]=>9072
[2,4,1,5,3,6,7,8,9,10]=>[5,1,1,1,1,1]=>6048
[5,6,2,1,3,7,4,8,9,10]=>[7,1,1,1]=>86400
[3,2,5,1,6,4,7,8,9,10]=>[5,1,1,1,1,1]=>6048
[6,7,2,1,8,3,4,9,5,10]=>[6,3,1]=>201600
[3,6,4,1,7,2,8,5,9,10]=>[3,3,2,1,1]=>50400
[3,6,7,2,1,4,8,5,9,10]=>[5,3,1,1]=>120960
[4,2,6,1,7,5,3,8,9,10]=>[4,2,1,1,1,1]=>18900
[4,3,2,6,1,7,5,8,9,10]=>[5,2,1,1,1]=>60480
[3,4,7,1,8,2,9,5,10,6]=>[8,2]=>226800
[7,8,9,3,2,1,4,5,10,6]=>[7,3]=>172800
[4,7,2,5,1,8,3,9,6,10]=>[3,3,3,1]=>22400
[4,3,7,8,2,1,5,9,6,10]=>[5,4,1]=>181440
[3,5,2,7,1,8,6,4,9,10]=>[4,4,1,1]=>56700
[5,4,3,2,7,1,8,6,9,10]=>[5,2,1,1,1]=>60480
[5,8,9,2,1,6,3,10,7,4]=>[4,3,2,1]=>151200
[5,3,8,6,4,1,9,2,10,7]=>[4,3,3]=>50400
[3,5,8,2,6,1,9,4,10,7]=>[7,3]=>172800
[5,4,3,8,9,2,1,6,10,7]=>[5,4,1]=>181440
[6,4,2,8,1,9,7,5,3,10]=>[8,1,1]=>226800
[4,3,6,2,8,1,9,7,5,10]=>[5,4,1]=>181440
[6,5,4,3,2,8,1,9,7,10]=>[5,2,2,1]=>90720
[5,3,7,2,9,1,10,8,6,4]=>[5,4,1]=>181440
[5,4,3,7,2,9,1,10,8,6]=>[5,4,1]=>181440
[7,6,5,4,3,2,9,1,10,8]=>[5,2,2,1]=>90720
[2,4,1,3,7,8,6,5]=>[4,4]=>1260
[8,4,6,3,7,5,1,2]=>[8]=>5040
[4,7,6,8,2,3,5,1]=>[3,3,2]=>1120
[4,8,7,3,5,6,2,1]=>[6,1,1]=>3360
[4,3,8,1,6,5,7,2]=>[3,2,2,1]=>1680
[1,3,6,2,5,8,7,4]=>[5,1,1,1]=>1344
[5,8,7,1,4,6,3,2]=>[3,2,2,1]=>1680
[4,6,5,1,2,7,3,8]=>[5,2,1]=>4032
[5,7,1,4,3,2,6,8]=>[3,3,1,1]=>1120
[7,8,5,3,2,1,6,4]=>[5,3]=>2688
[1,2,6,7,8,4,5,3]=>[6,1,1]=>3360
[6,1,4,8,2,7,5,3]=>[5,3]=>2688
[5,2,3,7,1,8,4,6]=>[2,2,2,1,1]=>420
[7,2,3,1,8,4,6,5]=>[4,2,1,1]=>2520
[7,3,4,5,1,8,6,2]=>[8]=>5040
[1,5,6,7,4,8,2,3]=>[4,3,1]=>3360
[6,3,2,5,7,4,8,1]=>[6,2]=>3360
[4,5,2,7,6,3,1,8]=>[4,3,1]=>3360
[4,5,2,1,7,6,3,8]=>[4,2,1,1]=>2520
[2,6,7,8,3,1,4,5]=>[5,3]=>2688
[6,3,2,5,1,7,8,4]=>[6,2]=>3360
[4,6,3,7,8,2,1,5]=>[3,2,2,1]=>1680
[5,6,7,1,8,4,2,3]=>[8]=>5040
[1,7,8,4,6,5,2,3]=>[2,2,2,1,1]=>420
[1,7,3,2,8,6,5,4]=>[5,1,1,1]=>1344
[3,7,1,2,8,6,5,4]=>[5,2,1]=>4032
[2,7,8,1,6,5,3,4]=>[6,2]=>3360
[8,1,5,7,3,4,6,2]=>[3,3,2]=>1120
[2,8,4,7,6,3,1,5]=>[8]=>5040
[1,8,2,4,7,6,3,5]=>[5,1,1,1]=>1344
[4,5,8,7,1,6,2,3]=>[5,2,1]=>4032
[1,8,2,4,6,7,5,3]=>[3,3,1,1]=>1120
[3,4,2,8,1,7,6,5]=>[6,2]=>3360
[2,4,5,8,1,7,6,3]=>[6,2]=>3360
[3,1,8,2,6,7,5,4]=>[5,3]=>2688
[2,6,8,1,4,3,7,5]=>[7,1]=>5760
[1,6,5,2,8,7,3,4]=>[7,1]=>5760
[2,6,1,5,8,7,3,4]=>[5,3]=>2688
[8,1,7,3,5,2,4,6]=>[4,3,1]=>3360
[8,1,3,2,7,6,4,5]=>[6,1,1]=>3360
[7,3,4,8,6,2,5,1]=>[8]=>5040
[7,5,8,1,6,2,3,4]=>[5,3]=>2688
[6,8,4,5,3,1,7,2]=>[3,2,2,1]=>1680
[6,7,5,3,2,8,4,1]=>[5,3]=>2688
[6,2,5,3,8,1,4,7]=>[5,2,1]=>4032
[7,6,1,3,5,2,4,8]=>[4,2,1,1]=>2520
[6,2,4,5,3,8,1,7]=>[4,3,1]=>3360
[6,1,5,4,7,2,3,8]=>[3,3,1,1]=>1120
[6,8,5,4,7,1,3,2]=>[3,2,2,1]=>1680
[1,6,8,4,2,5,7,3]=>[3,2,1,1,1]=>1120
[1,4,2,8,3,5,7,6]=>[6,1,1]=>3360
[1,3,5,4,8,7,2,6]=>[6,1,1]=>3360
[1,6,2,4,8,3,7,5]=>[3,2,1,1,1]=>1120
[1,7,8,5,4,2,6,3]=>[3,2,2,1]=>1680
[1,5,2,8,6,4,7,3]=>[6,1,1]=>3360
[1,6,5,2,7,4,8,3]=>[4,3,1]=>3360
[5,1,6,7,4,2,8,3]=>[8]=>5040
[1,7,5,4,6,2,8,3]=>[6,1,1]=>3360
[5,8,4,1,6,2,7,3]=>[7,1]=>5760
[6,4,5,1,7,2,8,3]=>[4,4]=>1260
[4,5,3,1,2,8,7,6]=>[2,2,2,1,1]=>420
[5,7,8,1,2,4,3,6]=>[8]=>5040
[7,1,6,8,2,5,4,3]=>[8]=>5040
[1,7,8,6,4,5,3,2]=>[4,3,1]=>3360
[1,6,8,7,4,3,5,2]=>[4,3,1]=>3360
[3,1,2,6,8,7,5,4]=>[5,3]=>2688
[5,7,4,2,1,8,6,3]=>[6,2]=>3360
[8,6,5,7,2,4,3,1]=>[6,2]=>3360
[7,4,6,1,8,5,3,2]=>[8]=>5040
[7,4,6,3,8,1,5,2]=>[8]=>5040
[7,4,8,1,6,3,2,5]=>[4,4]=>1260
[7,4,8,3,6,2,1,5]=>[6,2]=>3360
[6,4,8,2,3,5,7,1]=>[5,2,1]=>4032
[4,6,8,2,5,7,1,3]=>[5,2,1]=>4032
[6,4,8,2,5,7,1,3]=>[3,2,2,1]=>1680
[6,2,4,5,8,3,7,1]=>[6,1,1]=>3360
[6,8,2,4,7,3,5,1]=>[5,2,1]=>4032
[8,4,6,2,7,1,3,5]=>[6,2]=>3360
[6,8,4,2,7,1,3,5]=>[6,2]=>3360
[6,8,2,4,1,7,3,5]=>[7,1]=>5760
[7,5,1,6,2,4,8,3]=>[4,2,2]=>1260
[4,2,5,7,1,6,8,3]=>[6,1,1]=>3360
[2,5,4,7,6,1,3,8]=>[4,3,1]=>3360
[5,2,3,7,6,1,4,8]=>[3,2,1,1,1]=>1120
[4,2,3,7,6,1,5,8]=>[5,1,1,1]=>1344
[4,2,7,3,5,1,6,8]=>[5,1,1,1]=>1344
[5,6,2,3,8,4,7,1]=>[4,3,1]=>3360
[5,6,2,3,1,7,8,4]=>[6,2]=>3360
[5,7,2,3,4,1,6,8]=>[7,1]=>5760
[6,2,7,3,5,1,4,8]=>[3,2,1,1,1]=>1120
[7,2,6,3,5,1,4,8]=>[5,1,1,1]=>1344
[6,5,2,3,1,7,8,4]=>[8]=>5040
[6,5,2,3,8,4,7,1]=>[7,1]=>5760
[7,5,2,1,4,6,8,3]=>[7,1]=>5760
[8,5,2,3,1,6,4,7]=>[7,1]=>5760
[8,6,2,3,1,5,4,7]=>[8]=>5040
[8,2,6,3,1,7,4,5]=>[4,3,1]=>3360
[1,6,3,4,2,7,5,8]=>[4,1,1,1,1]=>420
[8,5,2,7,3,4,6,1]=>[3,3,2]=>1120
[1,7,2,4,5,6,8,3]=>[4,1,1,1,1]=>420
[1,8,3,2,5,6,4,7]=>[4,1,1,1,1]=>420
[7,2,8,1,4,6,3,5]=>[6,1,1]=>3360
[2,7,8,1,5,6,3,4]=>[6,1,1]=>3360
[6,8,2,3,1,5,4,7]=>[5,3]=>2688
[5,8,2,3,1,6,4,7]=>[5,2,1]=>4032
[5,7,2,1,4,6,8,3]=>[4,3,1]=>3360
[4,2,7,1,5,6,8,3]=>[3,2,1,1,1]=>1120
[4,2,3,8,1,7,5,6]=>[6,1,1]=>3360
[4,2,1,5,3,7,6,8]=>[4,2,1,1]=>2520
[5,1,3,8,4,6,7,2]=>[5,1,1,1]=>1344
[5,1,3,2,6,7,8,4]=>[7,1]=>5760
[5,1,3,4,2,7,6,8]=>[3,2,1,1,1]=>1120
[6,1,3,4,2,7,5,8]=>[5,1,1,1]=>1344
[7,2,1,3,5,8,4,6]=>[4,2,1,1]=>2520
[6,8,7,2,3,4,5,1]=>[5,3]=>2688
[1,9,8,10,7,6,5,4,3,2]=>[6,2,1,1]=>151200
[2,8,7,9,6,5,4,3,1]=>[7,2]=>25920
[3,7,2,8,1,4,5,6]=>[5,3]=>2688
[5,2,3,7,4,6,1,8]=>[4,1,1,1,1]=>420
[2,5,3,7,4,6,1,8]=>[5,1,1,1]=>1344
[2,6,7,3,4,5,1,8]=>[7,1]=>5760
[6,2,7,3,4,5,1,8]=>[6,1,1]=>3360
[3,8,4,5,2,1,6,7]=>[8]=>5040
[2,7,6,3,4,5,1,8]=>[4,3,1]=>3360
[2,8,7,5,1,3,4,6]=>[8]=>5040
[3,1,2,9,4,5,6,7,8]=>[6,3]=>20160
[4,1,2,3,9,5,6,7,8]=>[5,4]=>18144
[5,1,2,3,4,9,6,7,8]=>[5,4]=>18144
[6,1,2,3,4,5,9,7,8]=>[6,3]=>20160
[2,1,10,3,4,5,6,7,8,9]=>[8,2]=>226800
[3,1,2,10,4,5,6,7,8,9]=>[7,3]=>172800
[3,4,1,2,9,5,6,7,8]=>[5,2,2]=>9072
[4,1,2,3,10,5,6,7,8,9]=>[6,4]=>151200
[4,5,1,2,3,9,6,7,8]=>[5,4]=>18144
[5,1,2,3,4,10,6,7,8,9]=>[5,5]=>72576
[5,6,1,2,3,4,9,7,8]=>[3,3,3]=>2240
[6,1,2,3,4,5,10,7,8,9]=>[6,4]=>151200
[6,7,1,2,3,4,5,9,8]=>[7,2]=>25920
[7,1,2,3,4,5,6,10,8,9]=>[7,3]=>172800
[4,5,7,2,8,3,6,1]=>[5,3]=>2688
[9,7,5,3,1,8,6,4,2]=>[9]=>40320
[9,6,3,8,5,2,7,4,1]=>[2,2,2,1,1,1]=>1260
[8,5,2,9,6,3,7,4,1]=>[4,4,1]=>11340
[9,5,1,6,2,7,3,8,4]=>[6,2,1]=>30240
[9,5,1,8,4,7,3,6,2]=>[9]=>40320
[8,4,7,3,6,2,9,5,1]=>[9]=>40320
[7,3,8,4,6,2,9,5,1]=>[5,3,1]=>24192
[9,4,7,2,5,8,3,6,1]=>[2,2,2,2,1]=>945
[9,4,6,1,8,3,5,7,2]=>[4,3,2]=>15120
[8,3,5,7,2,9,4,6,1]=>[4,3,2]=>15120
[7,2,8,3,9,4,5,6,1]=>[4,4,1]=>11340
[8,3,7,2,9,4,5,6,1]=>[9]=>40320
[5,8,3,7,2,9,4,6,1]=>[6,2,1]=>30240
[4,5,6,9,3,8,2,7,1]=>[6,3]=>20160
[4,5,6,8,2,9,3,7,1]=>[7,2]=>25920
[9,3,6,5,4,7,1,8,2]=>[6,2,1]=>30240
[8,2,9,3,6,5,4,7,1]=>[6,2,1]=>30240
[6,5,4,8,2,9,3,7,1]=>[4,3,2]=>15120
[5,6,4,8,2,9,3,7,1]=>[5,4]=>18144
[9,2,7,4,5,6,3,8,1]=>[2,2,1,1,1,1,1]=>378
[7,4,5,6,3,9,2,8,1]=>[6,2,1]=>30240
[5,7,4,6,3,9,2,8,1]=>[6,2,1]=>30240
[10,8,6,4,2,9,7,5,3,1]=>[3,3,2,1,1]=>50400
[10,7,4,1,8,5,2,9,6,3]=>[4,4,2]=>56700
[9,6,3,8,5,2,10,7,4,1]=>[6,2,1,1]=>151200
[9,5,1,7,3,10,6,2,8,4]=>[6,4]=>151200
[10,6,2,7,3,8,4,9,5,1]=>[6,2,2]=>75600
[7,3,8,4,10,6,2,9,5,1]=>[8,1,1]=>226800
[8,4,7,3,10,6,2,9,5,1]=>[5,4,1]=>181440
[10,5,8,3,6,1,9,4,7,2]=>[5,3,2]=>120960
[9,4,7,2,10,5,8,3,6,1]=>[5,3,2]=>120960
[10,5,7,2,8,3,9,4,6,1]=>[4,4,2]=>56700
[8,3,10,5,7,2,9,4,6,1]=>[10]=>362880
[8,3,9,4,7,2,10,5,6,1]=>[5,4,1]=>181440
[9,3,5,7,1,10,4,6,8,2]=>[8,2]=>226800
[10,4,6,8,2,9,3,5,7,1]=>[4,4,2]=>56700
[10,4,5,6,7,1,8,2,9,3]=>[9,1]=>403200
[8,2,9,3,10,4,5,6,7,1]=>[9,1]=>403200
[9,3,8,2,10,4,5,6,7,1]=>[5,5]=>72576
[5,6,9,3,7,1,10,4,8,2]=>[6,4]=>151200
[5,6,10,4,8,2,9,3,7,1]=>[5,2,2,1]=>90720
[5,6,9,3,8,2,10,4,7,1]=>[8,2]=>226800
[6,5,9,3,8,2,10,4,7,1]=>[10]=>362880
[9,2,7,6,5,4,10,3,8,1]=>[6,2,1,1]=>151200
[10,3,7,6,5,4,8,1,9,2]=>[6,2,1,1]=>151200
[9,2,10,3,7,6,5,4,8,1]=>[6,2,1,1]=>151200
[7,6,5,4,9,2,10,3,8,1]=>[4,3,2,1]=>151200
[6,4,7,5,10,3,9,2,8,1]=>[10]=>362880
[6,4,7,5,9,2,10,3,8,1]=>[10]=>362880
[7,5,6,4,9,2,10,3,8,1]=>[6,3,1]=>201600
[6,5,7,4,9,2,10,3,8,1]=>[9,1]=>403200
[5,6,7,3,8,4,9,1,10,2]=>[7,3]=>172800
[5,6,7,3,8,4,10,2,9,1]=>[9,1]=>403200
[5,6,8,4,7,3,10,2,9,1]=>[4,4,1,1]=>56700
[6,5,8,4,7,3,10,2,9,1]=>[8,1,1]=>226800
[5,2,1,3,6,7,8,4]=>[7,1]=>5760
[7,5,2,6,1,8,4,3]=>[8]=>5040
[6,1,5,2,7,8,4,3]=>[8]=>5040
[7,5,6,8,4,1,3,2]=>[4,4]=>1260
[8,1,5,7,3,6,2,4]=>[5,2,1]=>4032
[8,3,2,6,4,5,1,7]=>[3,3,2]=>1120
[8,5,3,7,4,1,2,6]=>[4,3,1]=>3360
[8,5,6,2,7,1,3,4]=>[8]=>5040
[8,4,7,2,6,5,1,3]=>[4,2,2]=>1260
[8,5,7,3,2,6,1,4]=>[5,2,1]=>4032
[8,1,2,3,6,4,7,5]=>[7,1]=>5760
[7,6,2,3,5,8,1,4]=>[5,2,1]=>4032
[4,5,3,7,8,1,6,2]=>[4,3,1]=>3360
[3,4,2,8,1,6,7,5]=>[6,1,1]=>3360
[8,3,4,1,5,7,6,2]=>[5,2,1]=>4032
[4,3,7,5,1,6,2,8]=>[3,3,1,1]=>1120
[5,2,6,1,4,3,7,8]=>[3,2,1,1,1]=>1120
[3,5,2,8,6,7,4,1]=>[8]=>5040
[5,3,7,4,2,8,6,1]=>[7,1]=>5760
[7,4,8,2,3,5,6,1]=>[6,2]=>3360
[5,6,2,8,7,1,4,3]=>[8]=>5040
[4,6,3,5,2,7,8,1]=>[7,1]=>5760
[4,1,6,3,5,7,2,8]=>[6,1,1]=>3360
[3,1,5,7,4,6,8,2]=>[7,1]=>5760
[7,2,5,8,6,1,4,3]=>[7,1]=>5760
[4,3,6,1,5,7,8,2]=>[5,2,1]=>4032
[3,5,4,1,2,6,7,8]=>[3,2,1,1,1]=>1120
[5,3,1,4,6,7,8,2]=>[7,1]=>5760
[4,6,7,1,3,5,8,2]=>[6,2]=>3360
[5,6,1,3,4,7,2,8]=>[4,3,1]=>3360
[2,5,3,7,8,4,6,1]=>[4,3,1]=>3360
[4,6,2,1,3,7,8,5]=>[6,2]=>3360
[3,6,2,4,1,7,5,8]=>[6,1,1]=>3360
[3,2,6,7,4,8,5,1]=>[4,3,1]=>3360
[7,1,3,8,4,5,2,6]=>[4,3,1]=>3360
[7,1,8,3,4,6,2,5]=>[4,3,1]=>3360
[6,3,2,7,5,8,4,1]=>[3,2,2,1]=>1680
[6,2,7,1,4,5,3,8]=>[4,2,1,1]=>2520
[4,2,6,1,5,7,3,8]=>[3,2,1,1,1]=>1120
[2,5,4,1,3,6,7,8]=>[5,1,1,1]=>1344
[5,4,1,2,6,7,3,8]=>[5,2,1]=>4032
[6,5,2,7,4,1,3,8]=>[5,2,1]=>4032
[6,5,7,3,1,4,2,8]=>[7,1]=>5760
[6,7,4,3,1,5,8,2]=>[3,3,2]=>1120
[4,2,5,6,7,8,9,1,3]=>[4,4,1]=>11340
[3,1,6,7,8,4,5,2]=>[8]=>5040
[7,4,5,6,2,1,8,3]=>[8]=>5040
[4,2,5,6,7,8,9,10,1,3]=>[9,1]=>403200
[6,4,5,2,7,1,8,3]=>[4,2,2]=>1260
[3,7,5,6,2,1,8,4]=>[8]=>5040
[1,7,6,3,8,4,5,2]=>[4,3,1]=>3360
[6,4,1,2,7,8,3,5]=>[6,2]=>3360
[6,4,1,3,5,2,7,8]=>[5,1,1,1]=>1344
[5,1,8,3,4,6,2,7]=>[7,1]=>5760
[4,5,8,2,3,7,1,6]=>[8]=>5040
[7,3,4,8,2,5,1,6]=>[6,2]=>3360
[4,7,2,5,1,6,8,3]=>[4,3,1]=>3360
[6,5,4,7,2,8,3,1]=>[3,3,2]=>1120
[3,2,4,6,5,8,1,7]=>[6,1,1]=>3360
[3,5,4,8,7,1,6,2]=>[8]=>5040
[7,5,2,1,6,3,4,8]=>[4,3,1]=>3360
[6,3,1,7,4,2,5,8]=>[4,3,1]=>3360
[8,7,2,1,5,3,6,4]=>[4,3,1]=>3360
[6,8,5,3,7,4,2,1]=>[8]=>5040
[7,2,8,1,5,6,4,3]=>[3,2,1,1,1]=>1120
[8,3,6,4,1,5,7,2]=>[6,1,1]=>3360
[7,5,6,1,4,8,2,3]=>[5,3]=>2688
[5,7,2,6,3,8,4,1]=>[8]=>5040
[8,4,1,2,3,6,7,5]=>[4,2,1,1]=>2520
[5,6,4,2,1,8,3,7]=>[6,2]=>3360
[6,8,1,3,2,7,5,4]=>[8]=>5040
[5,7,3,6,4,1,2,8]=>[4,2,1,1]=>2520
[7,2,4,3,8,1,5,6]=>[5,2,1]=>4032
[2,5,4,6,1,3,8,7]=>[3,3,2]=>1120
[2,4,3,5,8,1,6,7]=>[7,1]=>5760
[2,6,5,3,8,1,4,7]=>[5,3]=>2688
[6,1,2,4,3,5,7,8]=>[5,1,1,1]=>1344
[6,5,8,2,7,3,4,1]=>[4,4]=>1260
[1,7,6,8,4,3,2,5]=>[3,2,2,1]=>1680
[1,7,6,5,3,8,2,4]=>[5,2,1]=>4032
[6,1,2,4,3,5,8,7]=>[5,2,1]=>4032
[4,6,1,3,7,8,5,2]=>[3,3,2]=>1120
[1,5,6,3,8,7,2,4]=>[7,1]=>5760
[5,3,2,6,8,7,1,4]=>[6,2]=>3360
[6,3,5,2,7,1,4,8]=>[5,2,1]=>4032
[8,5,2,6,7,1,4,3]=>[8]=>5040
[5,3,8,7,1,4,2,6]=>[6,2]=>3360
[6,4,5,3,1,8,7,2]=>[7,1]=>5760
[8,5,1,2,3,6,7,4]=>[6,1,1]=>3360
[2,8,6,1,5,4,7,3]=>[6,1,1]=>3360
[8,3,2,6,1,5,7,4]=>[5,2,1]=>4032
[3,8,6,4,7,1,2,5]=>[4,3,1]=>3360
[1,8,7,5,4,3,2,6]=>[5,2,1]=>4032
[8,6,4,7,1,3,2,5]=>[5,3]=>2688
[3,1,4,7,6,2,5,8]=>[7,1]=>5760
[5,3,4,1,6,2,7,8]=>[6,1,1]=>3360
[2,7,1,4,6,3,5,8]=>[6,1,1]=>3360
[7,3,1,6,5,2,4,8]=>[6,1,1]=>3360
[7,1,5,2,4,6,3,8]=>[6,1,1]=>3360
[6,1,4,5,2,7,3,8]=>[7,1]=>5760
[6,1,5,8,2,7,4,3]=>[8]=>5040
[7,1,2,3,6,4,5,8]=>[7,1]=>5760
[2,8,4,6,5,1,7,3]=>[6,1,1]=>3360
[7,4,1,3,6,5,2,8]=>[5,2,1]=>4032
[5,7,2,8,1,3,6,4]=>[4,2,2]=>1260
[5,4,1,2,6,3,8,7]=>[4,2,2]=>1260
[6,5,1,4,7,3,2,8]=>[3,3,1,1]=>1120
[2,7,8,4,1,3,6,5]=>[7,1]=>5760
[2,4,6,5,7,8,1,3]=>[5,3]=>2688
[2,4,6,7,5,8,1,3]=>[4,3,1]=>3360
[2,4,6,3,7,8,1,5]=>[8]=>5040
[2,4,5,6,8,7,1,3]=>[5,3]=>2688
[2,4,5,6,8,3,7,1]=>[7,1]=>5760
[2,4,5,6,3,8,1,7]=>[6,2]=>3360
[2,3,4,6,8,5,1,7]=>[8]=>5040
[5,2,8,3,4,1,6,7]=>[7,1]=>5760
[3,6,4,1,2,7,8,5]=>[5,3]=>2688
[4,1,7,3,8,6,2,5]=>[5,2,1]=>4032
[8,4,1,2,5,3,7,6]=>[4,2,1,1]=>2520
[1,5,2,7,6,8,4,3]=>[5,2,1]=>4032
[4,7,6,8,3,1,2,5]=>[6,2]=>3360
[4,8,2,7,6,5,1,3]=>[3,3,2]=>1120
[7,4,2,8,6,5,1,3]=>[4,2,2]=>1260
[8,6,5,2,7,1,4,3]=>[8]=>5040
[6,5,8,2,7,1,4,3]=>[4,2,2]=>1260
[7,5,8,2,1,6,4,3]=>[5,2,1]=>4032
[3,2,1,6,5,8,4,7]=>[4,2,1,1]=>2520
[2,6,4,8,5,7,3,1]=>[7,1]=>5760
[6,3,1,4,5,8,2,7]=>[6,1,1]=>3360
[3,4,8,5,2,1,7,6]=>[4,3,1]=>3360
[4,8,7,1,3,2,6,5]=>[6,2]=>3360
[5,8,7,4,6,1,3,2]=>[3,2,2,1]=>1680
[3,4,1,8,7,6,2,5]=>[5,2,1]=>4032
[1,3,5,6,8,7,2,4]=>[7,1]=>5760
[2,8,7,5,4,1,6,3]=>[6,2]=>3360
[8,1,5,7,4,2,6,3]=>[8]=>5040
[5,8,7,3,4,1,6,2]=>[6,2]=>3360
[4,6,1,3,2,8,5,7]=>[5,3]=>2688
[2,6,5,8,3,1,4,7]=>[3,3,2]=>1120
[6,7,8,2,4,5,3,1]=>[8]=>5040
[3,2,8,4,5,7,1,6]=>[5,1,1,1]=>1344
[6,1,8,2,4,5,3,7]=>[5,3]=>2688
[8,3,6,4,2,7,1,5]=>[7,1]=>5760
[1,3,8,4,7,6,2,5]=>[5,1,1,1]=>1344
[8,3,7,5,4,1,2,6]=>[3,3,2]=>1120
[2,6,4,7,8,5,1,3]=>[8]=>5040
[5,4,3,7,6,1,8,2]=>[4,3,1]=>3360
[8,6,3,7,1,4,2,5]=>[4,3,1]=>3360
[3,1,2,8,7,6,4,5]=>[4,3,1]=>3360
[8,5,4,1,2,3,7,6]=>[5,2,1]=>4032
[8,3,2,1,6,4,7,5]=>[5,2,1]=>4032
[2,3,8,4,1,7,5,6]=>[7,1]=>5760
[4,6,1,3,2,7,8,5]=>[5,3]=>2688
[6,7,2,5,8,4,1,3]=>[8]=>5040
[4,1,7,8,2,5,6,3]=>[8]=>5040
[3,4,6,7,1,5,8,2]=>[4,4]=>1260
[3,4,5,7,8,1,6,2]=>[8]=>5040
[1,8,7,4,3,5,2,6]=>[6,1,1]=>3360
[2,4,5,8,1,3,7,6]=>[7,1]=>5760
[2,7,8,6,5,3,1,4]=>[4,3,1]=>3360
[6,3,1,5,8,4,2,7]=>[8]=>5040
[2,8,3,5,6,1,4,7]=>[7,1]=>5760
[1,3,6,4,2,7,5,8]=>[5,1,1,1]=>1344
[2,3,7,5,8,1,4,6]=>[8]=>5040
[3,2,8,5,6,1,4,7]=>[7,1]=>5760
[7,2,5,8,1,4,6,3]=>[7,1]=>5760
[4,7,5,8,1,2,6,3]=>[5,3]=>2688
[4,7,5,8,1,2,3,6]=>[8]=>5040
[3,4,7,5,2,8,1,6]=>[3,3,2]=>1120
[4,3,2,5,7,8,1,6]=>[4,2,2]=>1260
[2,4,7,5,8,3,1,6]=>[8]=>5040
[2,5,4,7,3,8,1,6]=>[6,2]=>3360
[3,7,8,4,2,1,6,5]=>[7,1]=>5760
[5,6,7,9,1,2,3,4,8]=>[3,2,2,2]=>2520
[4,5,6,7,9,1,2,3,8]=>[9]=>40320
[7,8,10,1,2,3,4,5,6,9]=>[4,3,3]=>50400
[4,5,6,7,8,10,1,2,3,9]=>[4,3,3]=>50400
[8,5,4,7,6,3,1,2]=>[8]=>5040
[3,2,4,5,8,1,6,7]=>[7,1]=>5760
[3,6,8,4,2,7,1,5]=>[7,1]=>5760
[3,6,5,1,7,2,8,4]=>[6,2]=>3360
[7,4,1,6,2,8,5,3]=>[8]=>5040
[1,3,6,8,2,4,7,5]=>[6,1,1]=>3360
[1,6,7,4,3,8,2,5]=>[6,1,1]=>3360
[8,5,4,1,6,2,7,3]=>[4,3,1]=>3360
[4,7,2,8,5,1,6,3]=>[7,1]=>5760
[7,8,6,2,1,5,4,3]=>[8]=>5040
[2,1,3,8,7,5,6,4]=>[3,2,2,1]=>1680
[1,6,5,7,4,8,3,9,2]=>[4,4,1]=>11340
[5,4,6,3,8,2,7,1,9]=>[4,3,1,1]=>15120
[1,6,7,5,8,4,9,3,10,2]=>[9,1]=>403200
[1,6,4,7,3,8,5,2]=>[4,3,1]=>3360
[1,2,3,4,5,6,8,10,7,9]=>[4,1,1,1,1,1,1]=>1260
[3,4,5,6,7,8,2,1,9]=>[8,1]=>45360
[3,4,5,6,7,2,1,8,9]=>[4,3,1,1]=>15120
[4,5,6,7,8,1,2,3,9]=>[8,1]=>45360
[4,8,1,6,3,7,2,5]=>[8]=>5040
[8,5,4,1,6,3,7,2]=>[7,1]=>5760
[1,7,6,2,4,8,5,3]=>[4,3,1]=>3360
[5,7,3,2,4,8,6,1]=>[7,1]=>5760
[2,6,8,5,4,3,1,7]=>[6,2]=>3360
[2,8,4,6,3,5,1,7]=>[4,4]=>1260
[3,8,1,4,6,5,2,7]=>[3,2,2,1]=>1680
[2,7,5,4,1,8,3,6]=>[5,2,1]=>4032
[4,6,1,8,5,3,2,7]=>[7,1]=>5760
[3,8,5,2,1,6,4,7]=>[4,3,1]=>3360
[5,1,4,8,2,6,3,7]=>[4,3,1]=>3360
[4,5,8,1,3,7,6,2]=>[4,2,2]=>1260
[8,6,7,1,4,3,2,5]=>[4,4]=>1260
[1,4,7,8,6,3,5,2]=>[4,3,1]=>3360
[8,5,2,6,3,4,7,1]=>[3,2,2,1]=>1680
[8,3,6,1,2,7,4,5]=>[8]=>5040
[3,8,6,1,2,5,7,4]=>[7,1]=>5760
[3,7,6,2,1,8,5,4]=>[8]=>5040
[4,3,7,6,1,8,5,2]=>[8]=>5040
[8,6,3,2,7,1,5,4]=>[5,2,1]=>4032
[6,8,1,5,4,7,2,3]=>[6,2]=>3360
[6,7,2,5,4,8,1,3]=>[6,2]=>3360
[7,6,2,4,8,5,1,3]=>[5,2,1]=>4032
[4,6,8,7,3,1,2,5]=>[5,3]=>2688
[4,7,5,2,6,3,8,1]=>[5,3]=>2688
[3,5,6,2,8,1,4,7]=>[5,3]=>2688
[6,1,8,2,4,3,5,7]=>[8]=>5040
[1,6,8,2,5,3,4,7]=>[6,1,1]=>3360
[5,4,8,7,1,2,6,3]=>[4,2,2]=>1260
[2,5,6,4,3,8,1,7]=>[7,1]=>5760
[8,7,3,5,1,4,6,2]=>[7,1]=>5760
[8,6,3,5,2,1,4,7]=>[7,1]=>5760
[8,7,3,5,2,4,6,1]=>[5,2,1]=>4032
[4,6,3,8,5,2,7,1]=>[3,2,1,1,1]=>1120
[4,1,3,8,5,6,2,7]=>[5,1,1,1]=>1344
[1,7,8,6,3,2,5,4]=>[7,1]=>5760
[3,2,8,1,5,7,4,6]=>[6,1,1]=>3360
[3,4,6,7,2,1,5,8]=>[4,3,1]=>3360
[2,6,7,1,4,3,8,5]=>[8]=>5040
[4,2,5,3,8,6,7,1]=>[5,1,1,1]=>1344
[3,2,7,4,8,5,6,1]=>[6,1,1]=>3360
[7,2,5,1,6,3,8,4]=>[4,3,1]=>3360
[5,8,2,7,4,6,3,1]=>[7,1]=>5760
[4,5,2,8,3,7,1,6]=>[5,3]=>2688
[7,8,5,1,6,4,3,2]=>[6,2]=>3360
[8,7,5,1,6,4,3,2]=>[8]=>5040
[4,5,8,3,1,2,7,6]=>[7,1]=>5760
[1,4,6,3,7,5,2,8]=>[6,1,1]=>3360
[1,7,6,3,8,5,2,4]=>[5,2,1]=>4032
[1,3,8,7,4,5,6,2]=>[4,3,1]=>3360
[7,3,1,8,4,5,6,2]=>[8]=>5040
[6,2,4,3,7,5,8,1]=>[5,2,1]=>4032
[3,8,2,1,5,7,6,4]=>[5,2,1]=>4032
[1,3,2,8,7,4,6,5]=>[5,2,1]=>4032
[7,5,2,8,3,1,6,4]=>[3,3,2]=>1120
[4,6,3,7,8,1,2,5]=>[5,2,1]=>4032
[6,2,5,4,1,7,8,3]=>[6,1,1]=>3360
[4,1,5,6,3,8,7,2]=>[5,2,1]=>4032
[8,5,1,6,3,2,4,7]=>[8]=>5040
[6,8,7,4,3,2,5,1]=>[4,3,1]=>3360
[2,8,5,1,3,7,6,4]=>[4,2,2]=>1260
[2,4,5,8,3,7,6,1]=>[4,2,2]=>1260
[5,6,4,1,8,2,7,3]=>[5,2,1]=>4032
[6,1,3,5,4,8,2,7]=>[5,2,1]=>4032
[1,3,8,7,2,5,6,4]=>[7,1]=>5760
[2,5,4,1,8,3,7,6]=>[7,1]=>5760
[5,1,4,8,3,7,6,2]=>[6,2]=>3360
[8,4,1,2,7,6,5,3]=>[3,2,2,1]=>1680
[4,8,3,2,7,6,5,1]=>[4,2,1,1]=>2520
[1,8,7,3,4,6,5,2]=>[4,2,1,1]=>2520
[4,3,1,2,6,5,8,7,9]=>[4,2,2,1]=>11340
[6,5,3,1,2,4,8,7,9]=>[3,2,2,1,1]=>7560
[8,7,5,3,1,2,4,6,9]=>[8,1]=>45360
[7,5,3,1,2,4,6,9,8]=>[4,2,2,1]=>11340
[5,3,1,2,4,7,6,9,8]=>[5,2,2]=>9072
[4,1,2,6,5,3,8,7,9]=>[5,2,1,1]=>18144
[6,5,3,1,2,4,8,7,10,9]=>[3,2,2,2,1]=>25200
[6,3,1,2,4,8,7,5,9]=>[7,1,1]=>25920
[8,7,5,3,1,2,4,6,10,9]=>[8,2]=>226800
[8,5,3,1,2,4,6,9,7]=>[6,2,1]=>30240
[10,9,7,5,3,1,2,4,6,8]=>[10]=>362880
[5,3,1,2,4,6,8,7]=>[5,2,1]=>4032
[8,5,7,3,1,2,4,6]=>[5,3]=>2688
[7,5,3,1,2,4,6,8,9]=>[4,2,1,1,1]=>7560
[3,1,2,8,7,5,4,6]=>[5,3]=>2688
[5,3,1,2,4,9,7,6,8]=>[5,3,1]=>24192
[7,5,3,1,2,4,6,9,8,10]=>[4,2,2,1,1]=>56700
[3,1,2,7,5,4,6,9,8]=>[3,3,2,1]=>10080
[5,3,1,2,4,7,6,9,8,10]=>[5,2,2,1]=>90720
[1,5,3,2,4,7,6,9,8]=>[3,2,2,1,1]=>7560
[1,4,3,8,5,7,2,6]=>[5,1,1,1]=>1344
[6,7,1,5,2,8,4,3]=>[4,4]=>1260
[1,5,3,7,6,4,8,2]=>[6,1,1]=>3360
[4,8,1,3,6,2,7,5]=>[4,3,1]=>3360
[2,7,3,4,8,6,5,1]=>[5,1,1,1]=>1344
[1,8,2,4,7,3,6,5]=>[6,1,1]=>3360
[2,7,1,6,5,8,3,4]=>[4,3,1]=>3360
[6,2,3,8,1,5,7,4]=>[3,2,1,1,1]=>1120
[2,5,7,4,8,3,6,1]=>[4,3,1]=>3360
[8,5,6,2,4,7,1,3]=>[5,3]=>2688
[8,1,5,7,3,6,4,2]=>[3,2,2,1]=>1680
[4,3,7,1,2,8,5,6]=>[4,2,2]=>1260
[3,8,6,2,7,5,4,1]=>[8]=>5040
[4,8,1,6,2,5,3,7]=>[8]=>5040
[1,8,4,2,5,7,3,6]=>[6,1,1]=>3360
[5,8,3,1,2,4,6,7]=>[7,1]=>5760
[1,4,8,5,2,3,6,7]=>[4,3,1]=>3360
[1,4,8,5,2,3,7,6]=>[3,3,1,1]=>1120
[7,1,4,2,6,8,3,5]=>[5,3]=>2688
[1,5,8,7,2,4,3,6]=>[5,2,1]=>4032
[1,5,4,2,8,3,7,6]=>[6,1,1]=>3360
[1,2,8,7,3,5,4,6]=>[4,2,1,1]=>2520
[8,7,1,3,2,5,4,6]=>[8]=>5040
[6,7,4,2,8,1,3,5]=>[4,2,2]=>1260
[4,1,6,8,7,2,3,5]=>[8]=>5040
[4,7,5,6,2,8,3,1]=>[4,4]=>1260
[8,4,3,6,7,5,2,1]=>[5,2,1]=>4032
[6,7,5,2,8,4,3,1]=>[8]=>5040
[6,8,4,3,2,7,5,1]=>[6,2]=>3360
[2,1,4,3,6,5,9,7,10,8]=>[4,2,2,2]=>18900
[2,1,4,3,7,5,8,6,10,9]=>[4,2,2,2]=>18900
[2,1,4,3,7,5,9,6,10,8]=>[6,2,2]=>75600
[2,1,4,3,8,5,9,6,10,7]=>[3,3,2,2]=>25200
[2,1,5,3,6,4,8,7,10,9]=>[4,2,2,2]=>18900
[2,1,5,3,6,4,9,7,10,8]=>[4,4,2]=>56700
[2,1,5,3,7,4,8,6,10,9]=>[6,2,2]=>75600
[2,1,5,3,7,4,9,6,10,8]=>[8,2]=>226800
[2,1,5,3,8,4,9,6,10,7]=>[5,3,2]=>120960
[2,1,6,3,7,4,8,5,10,9]=>[3,3,2,2]=>25200
[2,1,6,3,7,4,9,5,10,8]=>[5,3,2]=>120960
[2,1,6,3,8,4,9,5,10,7]=>[3,3,2,2]=>25200
[2,1,7,3,8,4,9,5,10,6]=>[6,2,2]=>75600
[3,1,4,2,6,5,9,7,10,8]=>[4,4,2]=>56700
[3,1,4,2,7,5,8,6,10,9]=>[4,4,2]=>56700
[3,1,4,2,7,5,9,6,10,8]=>[6,4]=>151200
[3,1,4,2,8,5,9,6,10,7]=>[4,3,3]=>50400
[3,1,5,2,6,4,9,7,10,8]=>[6,4]=>151200
[3,1,5,2,8,4,9,6,10,7]=>[7,3]=>172800
[3,1,6,2,7,4,8,5,10,9]=>[5,3,2]=>120960
[3,1,6,2,7,4,9,5,10,8]=>[5,5]=>72576
[3,1,6,2,8,4,9,5,10,7]=>[5,3,2]=>120960
[3,1,7,2,8,4,9,5,10,6]=>[8,2]=>226800
[4,1,5,2,6,3,9,7,10,8]=>[4,3,3]=>50400
[4,1,5,2,7,3,8,6,10,9]=>[5,3,2]=>120960
[4,1,5,2,7,3,9,6,10,8]=>[7,3]=>172800
[4,1,5,2,8,3,9,6,10,7]=>[4,3,3]=>50400
[4,1,6,2,7,3,8,5,10,9]=>[3,3,2,2]=>25200
[4,1,6,2,7,3,9,5,10,8]=>[5,3,2]=>120960
[4,1,6,2,8,3,9,5,10,7]=>[3,3,2,2]=>25200
[4,1,7,2,8,3,9,5,10,6]=>[5,3,2]=>120960
[5,1,6,2,7,3,9,4,10,8]=>[8,2]=>226800
[5,1,6,2,8,3,9,4,10,7]=>[5,3,2]=>120960
[5,1,7,2,8,3,9,4,10,6]=>[5,5]=>72576
[2,1,4,3,6,5,10,7,11,8,12,9]=>[3,3,2,2,2]=>554400
[2,1,4,3,7,5,8,6,11,9,12,10]=>[4,4,2,2]=>1871100
[2,1,4,3,7,5,10,6,11,8,12,9]=>[5,3,2,2]=>3991680
[2,1,4,3,8,5,9,6,10,7,12,11]=>[3,3,2,2,2]=>554400
[2,1,4,3,8,5,9,6,11,7,12,10]=>[5,3,2,2]=>3991680
[2,1,4,3,8,5,10,6,11,7,12,9]=>[3,3,2,2,2]=>554400
[2,1,5,3,6,4,8,7,11,9,12,10]=>[4,4,2,2]=>1871100
[2,1,5,3,6,4,9,7,10,8,12,11]=>[4,4,2,2]=>1871100
[2,1,5,3,6,4,9,7,11,8,12,10]=>[6,4,2]=>9979200
[2,1,5,3,6,4,10,7,11,8,12,9]=>[4,3,3,2]=>3326400
[2,1,5,3,7,4,8,6,11,9,12,10]=>[6,4,2]=>9979200
[2,1,5,3,8,4,9,6,10,7,12,11]=>[5,3,2,2]=>3991680
[2,1,5,3,8,4,9,6,11,7,12,10]=>[5,5,2]=>4790016
[2,1,5,3,8,4,10,6,11,7,12,9]=>[5,3,2,2]=>3991680
[2,1,6,3,7,4,8,5,10,9,12,11]=>[3,3,2,2,2]=>554400
[2,1,6,3,7,4,8,5,11,9,12,10]=>[4,3,3,2]=>3326400
[2,1,6,3,7,4,9,5,10,8,12,11]=>[5,3,2,2]=>3991680
[2,1,6,3,7,4,10,5,11,8,12,9]=>[4,3,3,2]=>3326400
[2,1,6,3,8,4,9,5,10,7,12,11]=>[3,3,2,2,2]=>554400
[2,1,6,3,8,4,9,5,11,7,12,10]=>[5,3,2,2]=>3991680
[2,1,6,3,8,4,10,5,11,7,12,9]=>[3,3,2,2,2]=>554400
[2,1,6,3,9,4,10,5,11,7,12,8]=>[5,3,2,2]=>3991680
[2,1,7,3,8,4,10,5,11,6,12,9]=>[5,3,2,2]=>3991680
[2,1,7,3,9,4,10,5,11,6,12,8]=>[5,5,2]=>4790016
[3,1,4,2,6,5,8,7,11,9,12,10]=>[4,4,2,2]=>1871100
[3,1,4,2,6,5,9,7,10,8,12,11]=>[4,4,2,2]=>1871100
[3,1,4,2,6,5,9,7,11,8,12,10]=>[6,4,2]=>9979200
[3,1,4,2,6,5,10,7,11,8,12,9]=>[4,3,3,2]=>3326400
[3,1,4,2,7,5,8,6,10,9,12,11]=>[4,4,2,2]=>1871100
[3,1,4,2,7,5,8,6,11,9,12,10]=>[4,4,4]=>1247400
[3,1,4,2,7,5,9,6,10,8,12,11]=>[6,4,2]=>9979200
[3,1,4,2,7,5,10,6,11,8,12,9]=>[5,4,3]=>7983360
[3,1,4,2,8,5,9,6,10,7,12,11]=>[4,3,3,2]=>3326400
[3,1,4,2,8,5,9,6,11,7,12,10]=>[5,4,3]=>7983360
[3,1,4,2,8,5,10,6,11,7,12,9]=>[4,3,3,2]=>3326400
[3,1,4,2,9,5,10,6,11,7,12,8]=>[6,4,2]=>9979200
[3,1,5,2,6,4,8,7,11,9,12,10]=>[6,4,2]=>9979200
[3,1,5,2,6,4,9,7,10,8,12,11]=>[6,4,2]=>9979200
[3,1,5,2,6,4,9,7,11,8,12,10]=>[6,6]=>6652800
[3,1,5,2,7,4,9,6,11,8,12,10]=>[12]=>39916800
[3,1,5,2,7,4,10,6,11,8,12,9]=>[9,3]=>17740800
[3,1,5,2,8,4,9,6,11,7,12,10]=>[7,5]=>13685760
[3,1,6,2,7,4,8,5,10,9,12,11]=>[5,3,2,2]=>3991680
[3,1,6,2,7,4,8,5,11,9,12,10]=>[5,4,3]=>7983360
[3,1,6,2,7,4,9,5,10,8,12,11]=>[5,5,2]=>4790016
[3,1,6,2,7,4,9,5,11,8,12,10]=>[7,5]=>13685760
[3,1,6,2,7,4,10,5,11,8,12,9]=>[5,4,3]=>7983360
[3,1,6,2,8,4,9,5,10,7,12,11]=>[5,3,2,2]=>3991680
[3,1,6,2,8,4,9,5,11,7,12,10]=>[5,5,2]=>4790016
[3,1,6,2,8,4,10,5,11,7,12,9]=>[5,3,2,2]=>3991680
[3,1,6,2,9,4,10,5,11,7,12,8]=>[5,5,2]=>4790016
[3,1,7,2,9,4,10,5,11,6,12,8]=>[7,5]=>13685760
[3,1,8,2,9,4,10,5,11,6,12,7]=>[12]=>39916800
[4,1,5,2,6,3,8,7,10,9,12,11]=>[3,3,2,2,2]=>554400
[4,1,5,2,6,3,8,7,11,9,12,10]=>[4,3,3,2]=>3326400
[4,1,5,2,6,3,9,7,10,8,12,11]=>[4,3,3,2]=>3326400
[4,1,5,2,6,3,10,7,11,8,12,9]=>[3,3,3,3]=>246400
[4,1,5,2,7,3,8,6,10,9,12,11]=>[5,3,2,2]=>3991680
[4,1,5,2,7,3,8,6,11,9,12,10]=>[5,4,3]=>7983360
[4,1,5,2,7,3,9,6,11,8,12,10]=>[9,3]=>17740800
[4,1,5,2,8,3,9,6,10,7,12,11]=>[4,3,3,2]=>3326400
[4,1,5,2,8,3,9,6,11,7,12,10]=>[5,4,3]=>7983360
[4,1,5,2,8,3,10,6,11,7,12,9]=>[4,3,3,2]=>3326400
[4,1,6,2,7,3,8,5,10,9,12,11]=>[3,3,2,2,2]=>554400
[4,1,6,2,7,3,8,5,11,9,12,10]=>[4,3,3,2]=>3326400
[4,1,6,2,7,3,9,5,10,8,12,11]=>[5,3,2,2]=>3991680
[4,1,6,2,7,3,10,5,11,8,12,9]=>[4,3,3,2]=>3326400
[4,1,6,2,8,3,9,5,10,7,12,11]=>[3,3,2,2,2]=>554400
[4,1,6,2,8,3,9,5,11,7,12,10]=>[5,3,2,2]=>3991680
[4,1,6,2,8,3,10,5,11,7,12,9]=>[3,3,2,2,2]=>554400
[4,1,6,2,9,3,10,5,11,7,12,8]=>[5,3,2,2]=>3991680
[4,1,7,2,8,3,9,5,10,6,12,11]=>[5,3,2,2]=>3991680
[4,1,7,2,8,3,10,5,11,6,12,9]=>[4,3,3,2]=>3326400
[4,1,7,2,9,3,10,5,11,6,12,8]=>[5,4,3]=>7983360
[4,1,8,2,9,3,10,5,11,6,12,7]=>[9,3]=>17740800
[5,1,6,2,7,3,8,4,11,9,12,10]=>[6,4,2]=>9979200
[5,1,6,2,8,3,9,4,10,7,12,11]=>[5,3,2,2]=>3991680
[5,1,6,2,8,3,9,4,11,7,12,10]=>[5,5,2]=>4790016
[5,1,6,2,8,3,10,4,11,7,12,9]=>[5,3,2,2]=>3991680
[5,1,7,2,8,3,9,4,10,6,12,11]=>[5,5,2]=>4790016
[5,1,7,2,8,3,9,4,11,6,12,10]=>[7,5]=>13685760
[5,1,7,2,8,3,10,4,11,6,12,9]=>[5,4,3]=>7983360
[5,1,8,2,9,3,10,4,11,6,12,7]=>[12]=>39916800
[6,1,7,2,8,3,9,4,11,5,12,10]=>[12]=>39916800
[6,1,7,2,8,3,10,4,11,5,12,9]=>[9,3]=>17740800
[6,1,7,2,9,3,10,4,11,5,12,8]=>[12]=>39916800
[6,1,8,2,9,3,10,4,11,5,12,7]=>[6,6]=>6652800
[6,1,7,3,5,8,2,4]=>[7,1]=>5760
[1,3,7,6,4,8,2,5]=>[4,3,1]=>3360
[2,6,4,8,7,3,1,5]=>[8]=>5040
[2,1,8,7,3,5,4,6]=>[4,2,2]=>1260
[6,1,8,5,7,4,3,2]=>[8]=>5040
[8,5,1,4,7,6,3,2]=>[6,1,1]=>3360
[8,1,3,7,2,4,6,5]=>[4,3,1]=>3360
[5,3,1,6,4,8,2,7]=>[8]=>5040
[2,5,6,7,1,4,8,3]=>[5,3]=>2688
[4,7,5,3,2,8,1,6]=>[6,2]=>3360
[4,7,5,2,8,6,1,3]=>[4,3,1]=>3360
[3,8,6,7,2,5,4,1]=>[6,2]=>3360
[5,8,1,2,7,4,3,6]=>[4,4]=>1260
[4,6,3,7,8,1,5,2]=>[7,1]=>5760
[6,3,1,8,4,5,2,7]=>[8]=>5040
[7,6,2,4,8,3,1,5]=>[3,2,2,1]=>1680
[6,5,8,1,4,3,7,2]=>[7,1]=>5760
[8,1,4,2,7,5,6,3]=>[5,3]=>2688
[9,3,4,5,6,7,1,2,10,8]=>[10]=>362880
[8,9,10,11,12,1,2,3,4,5,6,7]=>[12]=>39916800
[7,2,4,3,8,6,1,5]=>[2,2,2,1,1]=>420
[1,7,6,5,4,3,2,9,8]=>[2,2,2,2,1]=>945
[6,8,4,3,5,1,7,2]=>[2,2,2,1,1]=>420
[1,4,7,3,6,8,2,5]=>[4,3,1]=>3360
[2,4,7,3,6,8,1,5]=>[5,3]=>2688
[2,7,5,6,1,8,4,3]=>[8]=>5040
[1,2,6,7,4,5,8,3]=>[6,1,1]=>3360
[6,5,2,8,7,1,4,3]=>[6,2]=>3360
[7,2,3,6,8,1,4,5]=>[4,2,1,1]=>2520
[2,6,1,3,8,5,4,7]=>[8]=>5040
[6,4,1,8,3,2,5,7]=>[8]=>5040
[5,8,1,4,2,7,3,6]=>[7,1]=>5760
[6,4,8,2,1,7,3,5]=>[6,2]=>3360
[2,3,1,8,7,5,6,4]=>[3,3,2]=>1120
[1,5,6,7,2,4,3,8]=>[4,2,1,1]=>2520
[2,8,6,4,1,5,3,7]=>[7,1]=>5760
[6,7,4,5,1,3,8,2]=>[5,3]=>2688
[1,6,5,3,8,2,4,7]=>[5,2,1]=>4032
[5,6,1,2,4,8,3,7]=>[8]=>5040
[8,7,4,5,1,3,2,6]=>[6,2]=>3360
[8,5,1,2,7,4,3,6]=>[8]=>5040
[4,1,8,7,2,5,3,6]=>[8]=>5040
[3,2,4,6,1,8,7,5]=>[6,1,1]=>3360
[3,6,7,4,1,2,5,8]=>[4,2,1,1]=>2520
[1,4,7,5,8,2,3,6]=>[5,2,1]=>4032
[1,6,8,4,7,3,2,5]=>[6,1,1]=>3360
[3,6,7,5,4,8,1,2]=>[3,3,2]=>1120
[4,5,7,2,6,3,8,1]=>[8]=>5040
[2,1,5,7,4,6,8,3]=>[5,2,1]=>4032
[2,3,5,7,8,1,6,4]=>[8]=>5040
[1,5,7,4,2,3,6,8]=>[3,2,1,1,1]=>1120
[2,4,7,5,3,6,8,1]=>[7,1]=>5760
[8,1,7,2,4,6,3,5]=>[5,2,1]=>4032
[1,2,4,7,8,6,3,5]=>[3,2,1,1,1]=>1120
[2,4,7,8,3,5,1,6]=>[8]=>5040
[1,3,6,2,5,8,4,7]=>[6,1,1]=>3360
[1,5,3,6,8,2,4,7]=>[6,1,1]=>3360
[4,8,1,2,6,3,7,5]=>[7,1]=>5760
[5,8,1,2,6,3,7,4]=>[4,3,1]=>3360
[1,6,2,3,7,5,8,4]=>[7,1]=>5760
[4,1,2,6,5,7,8,3]=>[7,1]=>5760
[1,8,4,2,7,3,6,5]=>[7,1]=>5760
[1,7,5,2,3,8,6,4]=>[5,2,1]=>4032
[8,1,4,7,3,5,2,6]=>[8]=>5040
[8,4,3,6,1,7,2,5]=>[4,3,1]=>3360
[2,6,1,8,3,7,4,5]=>[8]=>5040
[8,4,2,1,3,7,5,6]=>[8]=>5040
[2,5,1,7,6,8,3,4]=>[8]=>5040
[5,3,1,8,2,4,7,6]=>[4,3,1]=>3360
[1,2,6,3,7,5,8,4]=>[6,1,1]=>3360
[5,1,8,3,2,4,7,6]=>[4,3,1]=>3360
[3,1,5,4,6,7,8,2]=>[7,1]=>5760
[2,8,5,7,3,1,4,6]=>[4,2,2]=>1260
[2,6,8,7,3,1,4,5]=>[3,3,2]=>1120
[7,4,2,1,3,8,5,6]=>[6,2]=>3360
[7,2,1,3,8,5,4,6]=>[4,3,1]=>3360
[2,1,7,3,8,6,4,5]=>[3,2,2,1]=>1680
[1,7,5,3,2,4,8,6]=>[7,1]=>5760
[1,4,2,7,6,5,8,3]=>[5,2,1]=>4032
[3,4,1,6,5,7,8,2]=>[5,2,1]=>4032
[2,8,7,3,4,1,5,6]=>[4,4]=>1260
[5,7,6,2,3,8,1,4]=>[8]=>5040
[4,5,7,6,2,8,1,3]=>[6,2]=>3360
[3,1,8,7,5,2,6,4]=>[7,1]=>5760
[4,5,6,8,7,2,1,3]=>[8]=>5040
[2,8,3,1,5,4,7,6]=>[5,1,1,1]=>1344
[3,8,4,1,5,2,7,6]=>[3,3,1,1]=>1120
[4,8,3,1,6,2,7,5]=>[4,2,1,1]=>2520
[2,8,3,1,6,4,7,5]=>[6,1,1]=>3360
[6,2,7,1,5,8,4,3]=>[6,1,1]=>3360
[1,7,8,9,6,5,4,3,2]=>[4,2,2,1]=>11340
[1,6,7,8,9,5,4,3,2]=>[4,4,1]=>11340
[1,5,6,7,8,9,4,3,2]=>[6,2,1]=>30240
[1,4,5,6,7,8,9,3,2]=>[8,1]=>45360
[1,8,9,10,7,6,5,4,3,2]=>[4,2,2,1,1]=>56700
[1,7,6,8,9,5,4,3,2]=>[8,1]=>45360
[1,7,8,9,10,6,5,4,3,2]=>[4,4,1,1]=>56700
[1,6,5,7,8,9,4,3,2]=>[3,3,2,1]=>10080
[1,6,7,8,9,10,5,4,3,2]=>[4,3,2,1]=>151200
[1,5,4,6,7,8,9,3,2]=>[4,4,1]=>11340
[1,5,6,7,8,9,10,4,3,2]=>[6,3,1]=>201600
[1,4,5,6,7,8,9,10,3,2]=>[5,4,1]=>181440
[4,8,5,1,3,2,6,7]=>[4,2,2]=>1260
[5,4,3,1,2,7,6,8]=>[4,2,1,1]=>2520
[4,1,6,5,2,3,7,8]=>[4,2,1,1]=>2520
[7,1,5,2,3,6,4,8]=>[4,2,1,1]=>2520
[4,1,6,3,7,2,5,8]=>[5,2,1]=>4032
[4,6,1,2,8,3,7,5]=>[5,2,1]=>4032
[4,1,3,6,7,2,5,8]=>[4,2,1,1]=>2520
[2,6,5,1,3,4,7,8]=>[4,2,1,1]=>2520
[2,6,7,4,3,1,5,8]=>[3,3,1,1]=>1120
[2,6,3,1,7,4,5,8]=>[4,2,1,1]=>2520
[6,5,3,7,2,4,1,8]=>[4,2,1,1]=>2520
[2,3,6,7,1,5,4,8]=>[5,2,1]=>4032
[2,7,5,8,1,3,6,4]=>[6,2]=>3360
[5,1,6,7,3,2,4,8]=>[5,2,1]=>4032
[5,6,1,4,7,2,3,8]=>[4,2,1,1]=>2520
[1,2,5,7,8,6,3,4]=>[5,1,1,1]=>1344
[1,2,6,7,4,5,3,8]=>[5,1,1,1]=>1344
[8,6,5,2,1,7,4,3]=>[4,4]=>1260
[7,3,2,8,6,1,5,4]=>[4,2,2]=>1260
[7,5,8,2,6,1,4,3]=>[6,2]=>3360
[5,6,8,2,7,4,1,3]=>[3,3,2]=>1120
[7,4,1,2,6,5,8,3]=>[4,2,2]=>1260
[5,4,8,6,3,2,1,7]=>[5,3]=>2688
[4,1,3,6,8,5,2,7]=>[7,1]=>5760
[6,3,5,7,1,2,8,4]=>[5,3]=>2688
[1,8,5,3,2,4,6,7]=>[7,1]=>5760
[1,6,7,3,4,2,5,8]=>[4,2,1,1]=>2520
[1,6,8,3,4,2,5,7]=>[5,2,1]=>4032
[1,8,7,5,3,4,2,6]=>[7,1]=>5760
[1,7,8,5,3,4,2,6]=>[5,2,1]=>4032
[1,7,6,8,4,2,3,5]=>[4,3,1]=>3360
[1,7,8,6,4,3,2,5]=>[5,2,1]=>4032
[9,8,7,6,5,2,1,3,4]=>[8,1]=>45360
[7,2,8,9,10,1,3,4,5,6]=>[9,1]=>403200
[9,7,8,6,5,4,3,2,1]=>[4,2,2,1]=>11340
[5,1,7,8,4,2,3,6]=>[6,2]=>3360
[3,8,2,1,6,7,5,4]=>[5,3]=>2688
[2,8,3,1,7,5,6,4]=>[4,3,1]=>3360
[9,10,6,4,2,1,3,5,8,7]=>[9,1]=>403200
[10,7,8,4,2,1,3,6,5,9]=>[9,1]=>403200
[9,7,10,4,2,1,3,6,8,5]=>[5,4,1]=>181440
[8,9,10,4,2,1,3,7,6,5]=>[9,1]=>403200
[10,8,5,6,2,1,4,3,7,9]=>[6,4]=>151200
[9,10,5,6,2,1,4,3,8,7]=>[10]=>362880
[10,7,5,8,2,1,4,6,3,9]=>[10]=>362880
[9,7,5,10,2,1,4,6,8,3]=>[6,4]=>151200
[8,9,5,10,2,1,4,7,6,3]=>[10]=>362880
[10,6,7,8,2,1,5,4,3,9]=>[8,2]=>226800
[9,6,7,10,2,1,5,4,8,3]=>[10]=>362880
[8,6,9,10,2,1,5,7,4,3]=>[6,4]=>151200
[7,8,9,10,2,1,6,5,4,3]=>[4,3,3]=>50400
[10,8,6,3,4,2,1,5,7,9]=>[6,4]=>151200
[9,10,6,3,4,2,1,5,8,7]=>[10]=>362880
[10,7,8,3,4,2,1,6,5,9]=>[10]=>362880
[9,7,10,3,4,2,1,6,8,5]=>[6,4]=>151200
[8,9,10,3,4,2,1,7,6,5]=>[4,3,3]=>50400
[10,8,5,3,6,2,4,1,7,9]=>[10]=>362880
[9,10,5,3,6,2,4,1,8,7]=>[7,3]=>172800
[10,7,5,3,8,2,4,6,1,9]=>[7,3]=>172800
[9,7,5,3,10,2,4,6,8,1]=>[10]=>362880
[8,9,5,3,10,2,4,7,6,1]=>[7,3]=>172800
[10,6,7,3,8,2,5,4,1,9]=>[5,3,2]=>120960
[9,6,7,3,10,2,5,4,8,1]=>[8,2]=>226800
[8,6,9,3,10,2,5,7,4,1]=>[5,3,2]=>120960
[7,8,9,3,10,2,6,5,4,1]=>[7,3]=>172800
[10,8,4,5,6,3,2,1,7,9]=>[6,4]=>151200
[9,10,4,5,6,3,2,1,8,7]=>[4,3,3]=>50400
[10,7,4,5,8,3,2,6,1,9]=>[5,3,2]=>120960
[9,7,4,5,10,3,2,6,8,1]=>[8,2]=>226800
[8,9,4,5,10,3,2,7,6,1]=>[10]=>362880
[10,6,4,7,8,3,5,2,1,9]=>[7,3]=>172800
[9,6,4,7,10,3,5,2,8,1]=>[10]=>362880
[8,6,4,9,10,3,5,7,2,1]=>[5,5]=>72576
[7,8,4,9,10,3,6,5,2,1]=>[10]=>362880
[10,5,6,7,8,4,3,2,1,9]=>[4,3,3]=>50400
[9,5,6,7,10,4,3,2,8,1]=>[6,4]=>151200
[8,5,6,9,10,4,3,7,2,1]=>[10]=>362880
[7,5,8,9,10,4,6,3,2,1]=>[8,2]=>226800
[11,12,8,6,4,2,1,3,5,7,10,9]=>[6,4,2]=>9979200
[12,9,10,6,4,2,1,3,5,8,7,11]=>[5,4,3]=>7983360
[11,9,12,6,4,2,1,3,5,8,10,7]=>[7,5]=>13685760
[10,11,12,6,4,2,1,3,5,9,8,7]=>[12]=>39916800
[12,10,7,8,4,2,1,3,6,5,9,11]=>[12]=>39916800
[12,9,7,10,4,2,1,3,6,8,5,11]=>[9,3]=>17740800
[10,11,7,12,4,2,1,3,6,9,8,5]=>[9,3]=>17740800
[12,8,9,10,4,2,1,3,7,6,5,11]=>[12]=>39916800
[11,8,9,12,4,2,1,3,7,6,10,5]=>[9,3]=>17740800
[10,8,11,12,4,2,1,3,7,9,6,5]=>[5,4,3]=>7983360
[9,10,11,12,4,2,1,3,8,7,6,5]=>[9,3]=>17740800
[12,10,8,5,6,2,1,4,3,7,9,11]=>[12]=>39916800
[11,9,12,5,6,2,1,4,3,8,10,7]=>[12]=>39916800
[10,11,12,5,6,2,1,4,3,9,8,7]=>[6,6]=>6652800
[12,10,7,5,8,2,1,4,6,3,9,11]=>[9,3]=>17740800
[11,12,7,5,8,2,1,4,6,3,10,9]=>[5,4,3]=>7983360
[12,9,7,5,10,2,1,4,6,8,3,11]=>[5,4,3]=>7983360
[11,9,7,5,12,2,1,4,6,8,10,3]=>[9,3]=>17740800
[10,11,7,5,12,2,1,4,6,9,8,3]=>[12]=>39916800
[12,8,9,5,10,2,1,4,7,6,3,11]=>[6,6]=>6652800
[11,8,9,5,12,2,1,4,7,6,10,3]=>[12]=>39916800
[9,10,11,5,12,2,1,4,8,7,6,3]=>[12]=>39916800
[12,10,6,7,8,2,1,5,4,3,9,11]=>[6,4,2]=>9979200
[12,9,6,7,10,2,1,5,4,8,3,11]=>[9,3]=>17740800
[11,9,6,7,12,2,1,5,4,8,10,3]=>[12]=>39916800
[10,11,6,7,12,2,1,5,4,9,8,3]=>[7,5]=>13685760
[12,8,6,9,10,2,1,5,7,4,3,11]=>[12]=>39916800
[11,8,6,9,12,2,1,5,7,4,10,3]=>[6,6]=>6652800
[10,8,6,11,12,2,1,5,7,9,4,3]=>[6,4,2]=>9979200
[11,7,8,9,12,2,1,6,5,4,10,3]=>[12]=>39916800
[9,7,10,11,12,2,1,6,8,5,4,3]=>[6,4,2]=>9979200
[8,9,10,11,12,2,1,7,6,5,4,3]=>[4,3,3,2]=>3326400
[11,9,12,6,3,4,2,1,5,8,10,7]=>[6,4,2]=>9979200
[12,10,7,8,3,4,2,1,6,5,9,11]=>[7,5]=>13685760
[11,12,7,8,3,4,2,1,6,5,10,9]=>[12]=>39916800
[12,9,7,10,3,4,2,1,6,8,5,11]=>[12]=>39916800
[10,11,7,12,3,4,2,1,6,9,8,5]=>[12]=>39916800
[12,8,9,10,3,4,2,1,7,6,5,11]=>[9,3]=>17740800
[11,8,9,12,3,4,2,1,7,6,10,5]=>[12]=>39916800
[10,8,11,12,3,4,2,1,7,9,6,5]=>[6,6]=>6652800
[12,10,8,5,3,6,2,4,1,7,9,11]=>[4,4,3,1]=>4989600
[11,12,8,5,3,6,2,4,1,7,10,9]=>[7,4,1]=>17107200
[11,9,12,5,3,6,2,4,1,8,10,7]=>[11,1]=>43545600
[12,10,7,5,3,8,2,4,6,1,9,11]=>[12]=>39916800
[11,12,7,5,3,8,2,4,6,1,10,9]=>[9,3]=>17740800
[12,9,7,5,3,10,2,4,6,8,1,11]=>[9,3]=>17740800
[11,9,7,5,3,12,2,4,6,8,10,1]=>[12]=>39916800
[10,11,7,5,3,12,2,4,6,9,8,1]=>[7,5]=>13685760
[11,8,9,5,3,12,2,4,7,6,10,1]=>[7,5]=>13685760
[10,8,11,5,3,12,2,4,7,9,6,1]=>[12]=>39916800
[9,10,11,5,3,12,2,4,8,7,6,1]=>[9,3]=>17740800
[11,12,6,7,3,8,2,5,4,1,10,9]=>[5,4,3]=>7983360
[12,9,6,7,3,10,2,5,4,8,1,11]=>[5,4,3]=>7983360
[10,11,6,7,3,12,2,5,4,9,8,1]=>[12]=>39916800
[12,8,6,9,3,10,2,5,7,4,1,11]=>[9,3]=>17740800
[11,8,6,9,3,12,2,5,7,4,10,1]=>[12]=>39916800
[9,7,10,11,3,12,2,6,8,5,4,1]=>[5,3,2,2]=>3991680
[12,10,8,4,5,6,3,2,1,7,9,11]=>[5,4,1,1,1]=>3991680
[11,12,7,4,5,8,3,2,6,1,10,9]=>[5,3,2,1,1]=>7983360
[12,9,7,4,5,10,3,2,6,8,1,11]=>[5,3,2,1,1]=>7983360
[10,11,7,4,5,12,3,2,6,9,8,1]=>[5,3,2,1,1]=>7983360
[12,8,9,4,5,10,3,2,7,6,1,11]=>[3,3,2,2,1,1]=>1663200
[11,8,9,4,5,12,3,2,7,6,10,1]=>[5,3,2,1,1]=>7983360
[9,10,11,4,5,12,3,2,8,7,6,1]=>[10,1,1]=>23950080
[11,12,6,4,7,8,3,5,2,1,10,9]=>[5,3,3,1]=>5322240
[10,11,6,4,7,12,3,5,2,9,8,1]=>[11,1]=>43545600
[11,8,6,4,9,12,3,5,7,2,10,1]=>[11,1]=>43545600
[10,8,6,4,11,12,3,5,7,9,2,1]=>[7,4,1]=>17107200
[9,10,6,4,11,12,3,5,8,7,2,1]=>[11,1]=>43545600
[10,7,8,4,11,12,3,6,5,9,2,1]=>[11,1]=>43545600
[8,9,10,4,11,12,3,7,6,5,2,1]=>[11,1]=>43545600
[12,10,5,6,7,8,4,3,2,1,9,11]=>[6,6]=>6652800
[10,11,5,6,7,12,4,3,2,9,8,1]=>[12]=>39916800
[12,8,5,6,9,10,4,3,7,2,1,11]=>[9,3]=>17740800
[11,8,5,6,9,12,4,3,7,2,10,1]=>[12]=>39916800
[10,8,5,6,11,12,4,3,7,9,2,1]=>[7,5]=>13685760
[9,10,5,6,11,12,4,3,8,7,2,1]=>[12]=>39916800
[11,7,5,8,9,12,4,6,3,2,10,1]=>[9,3]=>17740800
[10,7,5,8,11,12,4,6,3,9,2,1]=>[12]=>39916800
[9,7,5,10,11,12,4,6,8,3,2,1]=>[7,5]=>13685760
[8,9,5,10,11,12,4,7,6,3,2,1]=>[12]=>39916800
[12,6,7,8,9,10,5,4,3,2,1,11]=>[4,3,3,2]=>3326400
[11,6,7,8,9,12,5,4,3,2,10,1]=>[6,4,2]=>9979200
[9,6,7,10,11,12,5,4,8,3,2,1]=>[12]=>39916800
[2,3,4,5,6,7,8,11,10,1,9]=>[11]=>3628800
[2,3,4,5,6,7,8,9,12,11,1,10]=>[12]=>39916800
[11,3,4,5,6,7,8,10,1,2,9]=>[8,3]=>1663200
[2,10,4,5,6,7,9,1,3,8]=>[6,4]=>151200
[10,3,4,5,6,7,1,9,2,8]=>[10]=>362880
[2,7,4,1,5,8,3,6]=>[5,2,1]=>4032
[2,1,6,4,7,8,3,5]=>[5,2,1]=>4032
[5,7,8,3,4,2,1,6]=>[8]=>5040
[4,7,5,3,8,2,6,1]=>[5,3]=>2688
[7,8,4,5,6,1,3,2]=>[6,2]=>3360
[2,5,1,8,4,6,7,3]=>[6,1,1]=>3360
[6,5,8,3,4,2,1,7]=>[8]=>5040
[8,2,7,6,3,4,5,1]=>[3,2,2,1]=>1680
[6,8,7,3,2,1,4,5]=>[3,3,2]=>1120
[3,4,8,2,7,1,5,6]=>[4,2,2]=>1260
[7,2,6,1,4,8,3,5]=>[7,1]=>5760
[7,8,1,2,4,6,3,5]=>[4,3,1]=>3360
[7,2,8,3,4,5,1,6]=>[5,2,1]=>4032
[6,1,8,3,4,2,5,7]=>[5,3]=>2688
[7,5,1,2,4,3,8,6]=>[5,3]=>2688
[7,6,8,1,4,2,3,5]=>[6,2]=>3360
[2,4,3,7,8,5,6,1]=>[7,1]=>5760
[2,1,7,6,3,4,5,8]=>[3,2,2,1]=>1680
[6,1,5,3,8,2,4,7]=>[5,3]=>2688
[2,3,6,8,5,1,7,4]=>[4,2,1,1]=>2520
[3,2,4,8,6,1,7,5]=>[6,1,1]=>3360
[2,1,3,8,4,5,7,6]=>[4,2,1,1]=>2520
[3,1,2,8,5,4,7,6]=>[3,3,1,1]=>1120
[2,1,3,7,8,4,6,5]=>[3,2,2,1]=>1680
[2,1,3,8,4,7,6,5]=>[3,2,2,1]=>1680
[3,1,2,8,4,5,7,6]=>[4,3,1]=>3360
[1,2,8,7,5,4,6,3]=>[3,2,1,1,1]=>1120
[4,6,7,2,3,8,1,5]=>[8]=>5040
[3,2,6,5,7,8,1,4]=>[7,1]=>5760
[2,1,8,7,4,6,5,3]=>[3,2,2,1]=>1680
[6,1,5,8,4,7,3,2]=>[8]=>5040
[1,4,6,8,5,7,2,3]=>[6,1,1]=>3360
[2,4,7,1,8,3,6,5]=>[3,3,2]=>1120
[6,1,5,4,2,3,8,7]=>[5,2,1]=>4032
[6,4,5,1,2,8,3,7]=>[8]=>5040
[8,4,1,5,7,6,3,2]=>[7,1]=>5760
[8,1,6,3,5,2,4,7]=>[7,1]=>5760
[4,6,2,5,3,8,1,7]=>[8]=>5040
[4,6,5,2,1,8,3,7]=>[8]=>5040
[5,8,4,3,6,7,2,1]=>[6,2]=>3360
[6,8,2,1,5,3,4,7]=>[7,1]=>5760
[2,5,3,8,6,7,4,1]=>[7,1]=>5760
[3,2,6,5,1,8,4,7]=>[7,1]=>5760
[7,4,5,8,1,6,2,3]=>[7,1]=>5760
[4,5,8,1,6,7,3,2]=>[6,2]=>3360
[5,1,8,4,6,7,3,2]=>[7,1]=>5760
[6,5,3,8,1,7,2,4]=>[5,2,1]=>4032
[8,3,7,1,6,2,4,5]=>[8]=>5040
[8,1,4,6,5,7,2,3]=>[7,1]=>5760
[8,1,7,5,6,4,2,3]=>[5,3]=>2688
[8,6,1,5,3,7,2,4]=>[5,3]=>2688
[7,2,3,6,8,1,5,4]=>[6,1,1]=>3360
[2,6,3,7,8,1,4,5]=>[3,2,2,1]=>1680
[6,3,8,7,2,1,5,4]=>[6,2]=>3360
[7,2,5,6,3,4,8,1]=>[3,2,2,1]=>1680
[7,2,8,6,3,1,5,4]=>[7,1]=>5760
[7,2,4,5,8,6,3,1]=>[6,1,1]=>3360
[6,3,8,4,7,2,5,1]=>[5,2,1]=>4032
[7,2,3,6,8,5,4,1]=>[6,1,1]=>3360
[7,2,8,5,4,1,3,6]=>[5,2,1]=>4032
[7,4,5,2,8,1,6,3]=>[3,3,2]=>1120
[7,5,4,2,8,1,6,3]=>[5,3]=>2688
[7,6,3,2,8,4,5,1]=>[4,3,1]=>3360
[7,2,3,6,8,4,5,1]=>[4,2,1,1]=>2520
[7,2,5,4,8,3,6,1]=>[6,1,1]=>3360
[7,2,8,3,6,1,4,5]=>[7,1]=>5760
[7,4,5,2,8,3,6,1]=>[6,2]=>3360
[5,1,3,2,4,6,8,7]=>[4,2,1,1]=>2520
[6,4,5,3,8,1,2,7]=>[6,2]=>3360
[7,2,4,6,3,8,5,1]=>[7,1]=>5760
[2,8,3,7,6,1,5,4]=>[7,1]=>5760
[5,4,2,6,8,7,3,1]=>[5,3]=>2688
[3,7,2,5,8,6,4,1]=>[7,1]=>5760
[4,6,5,3,8,1,7,2]=>[7,1]=>5760
[2,4,8,7,6,1,5,3]=>[6,2]=>3360
[3,2,8,7,4,6,5,1]=>[3,3,1,1]=>1120
[8,2,6,5,1,4,3,7]=>[7,1]=>5760
[4,8,5,2,7,6,3,1]=>[4,3,1]=>3360
[2,8,6,5,7,1,3,4]=>[8]=>5040
[3,8,4,7,2,1,6,5]=>[5,3]=>2688
[5,8,1,7,6,2,3,4]=>[8]=>5040
[3,4,6,2,5,7,1,8]=>[4,2,1,1]=>2520
[1,7,5,2,6,8,3,4]=>[7,1]=>5760
[7,4,8,3,6,5,1,2]=>[4,2,2]=>1260
[1,5,4,3,8,7,2,6]=>[5,2,1]=>4032
[1,5,8,2,6,4,3,7]=>[4,3,1]=>3360
[10,9,8,6,4,2,1,3,5,7]=>[5,3,2]=>120960
[10,8,7,6,4,2,1,3,5,9]=>[10]=>362880
[10,7,9,6,4,2,1,3,8,5]=>[7,3]=>172800
[10,9,8,7,6,4,2,1,3,5]=>[10]=>362880
[10,8,6,5,4,2,1,3,7,9]=>[4,4,2]=>56700
[10,9,8,6,5,4,2,1,3,7]=>[7,2,1]=>259200
[10,8,5,7,4,2,1,6,3,9]=>[7,3]=>172800
[10,5,9,7,4,2,1,6,8,3]=>[10]=>362880
[10,9,8,5,7,4,2,1,6,3]=>[6,4]=>151200
[10,8,7,6,5,4,2,1,3,9]=>[7,2,1]=>259200
[10,7,9,6,5,4,2,1,8,3]=>[5,2,2,1]=>90720
[10,6,9,8,5,7,2,1,4,3]=>[6,3,1]=>201600
[10,8,6,4,3,2,1,5,7,9]=>[5,4,1]=>181440
[10,9,8,6,4,3,2,1,5,7]=>[10]=>362880
[10,8,7,6,4,3,2,1,5,9]=>[10]=>362880
[10,7,9,6,4,3,2,1,8,5]=>[8,2]=>226800
[10,8,6,3,5,2,4,1,7,9]=>[9,1]=>403200
[10,9,8,6,3,5,2,4,1,7]=>[5,5]=>72576
[10,8,3,7,5,2,4,6,1,9]=>[3,3,2,1,1]=>50400
[10,3,9,7,5,2,4,6,8,1]=>[5,2,2,1]=>90720
[10,9,8,3,7,5,2,4,6,1]=>[5,3,2]=>120960
[10,8,7,6,3,5,2,4,1,9]=>[7,3]=>172800
[10,7,9,6,3,5,2,4,8,1]=>[6,2,2]=>75600
[10,9,3,8,6,5,2,7,4,1]=>[5,2,2,1]=>90720
[10,9,8,7,6,3,5,2,4,1]=>[8,2]=>226800
[10,8,6,5,4,3,2,1,7,9]=>[6,2,2]=>75600
[10,8,5,7,4,3,2,6,1,9]=>[7,3]=>172800
[10,5,9,7,4,3,2,6,8,1]=>[4,4,2]=>56700
[10,9,8,5,7,4,3,2,6,1]=>[8,2]=>226800
[10,8,4,7,6,3,5,2,1,9]=>[5,3,2]=>120960
[10,4,9,7,6,3,5,2,8,1]=>[8,2]=>226800
[10,4,9,6,8,3,5,7,2,1]=>[5,3,2]=>120960
[10,9,8,4,7,6,3,5,2,1]=>[4,2,2,1,1]=>56700
[10,7,9,6,5,4,3,2,8,1]=>[5,2,2,1]=>90720
[10,6,9,8,5,4,3,7,2,1]=>[7,2,1]=>259200
[10,5,9,8,7,4,6,3,2,1]=>[8,2]=>226800
[12,11,10,8,6,4,2,1,3,5,7,9]=>[9,3]=>17740800
[12,9,11,8,6,4,2,1,3,5,10,7]=>[12]=>39916800
[12,11,10,9,8,6,4,2,1,3,5,7]=>[5,4,2,1]=>11975040
[12,10,8,7,6,4,2,1,3,5,9,11]=>[6,6]=>6652800
[12,10,7,9,6,4,2,1,3,8,5,11]=>[12]=>39916800
[12,11,10,7,9,6,4,2,1,3,8,5]=>[4,3,2,2,1]=>4989600
[12,10,9,8,7,6,4,2,1,3,5,11]=>[11,1]=>43545600
[12,11,10,8,6,5,4,2,1,3,7,9]=>[5,3,2,2]=>3991680
[12,11,10,9,8,6,5,4,2,1,3,7]=>[11,1]=>43545600
[12,10,8,5,7,4,2,1,6,3,9,11]=>[12]=>39916800
[12,10,5,9,7,4,2,1,6,8,3,11]=>[9,3]=>17740800
[12,11,10,5,9,7,4,2,1,6,8,3]=>[9,3]=>17740800
[12,9,11,8,5,7,4,2,1,6,10,3]=>[11,1]=>43545600
[12,11,5,10,8,7,4,2,1,9,6,3]=>[12]=>39916800
[12,11,10,9,8,5,7,4,2,1,6,3]=>[7,4,1]=>17107200
[12,10,8,7,6,5,4,2,1,3,9,11]=>[4,4,2,2]=>1871100
[12,11,10,7,9,6,5,4,2,1,8,3]=>[7,4,1]=>17107200
[12,10,6,9,8,5,7,2,1,4,3,11]=>[11,1]=>43545600
[12,6,11,9,8,5,7,2,1,4,10,3]=>[7,4,1]=>17107200
[12,6,11,8,10,5,7,2,1,9,4,3]=>[11,1]=>43545600
[12,9,11,8,7,6,5,4,2,1,10,3]=>[5,2,2,2,1]=>1995840
[12,10,8,6,4,3,2,1,5,7,9,11]=>[9,3]=>17740800
[12,11,10,8,6,4,3,2,1,5,7,9]=>[9,3]=>17740800
[12,10,9,8,6,4,3,2,1,5,7,11]=>[6,6]=>6652800
[12,9,11,8,6,4,3,2,1,5,10,7]=>[12]=>39916800
[12,11,10,9,8,6,4,3,2,1,5,7]=>[11,1]=>43545600
[12,11,10,8,7,6,4,3,2,1,5,9]=>[11,1]=>43545600
[12,7,11,9,6,4,3,2,1,8,10,5]=>[6,6]=>6652800
[12,10,9,8,7,6,4,3,2,1,5,11]=>[11,1]=>43545600
[12,8,11,10,7,9,4,3,2,1,6,5]=>[6,6]=>6652800
[12,10,8,6,3,5,2,4,1,7,9,11]=>[5,4,3]=>7983360
[12,11,10,8,6,3,5,2,4,1,7,9]=>[12]=>39916800
[12,10,9,8,6,3,5,2,4,1,7,11]=>[12]=>39916800
[12,10,8,3,7,5,2,4,6,1,9,11]=>[9,3]=>17740800
[12,11,10,8,3,7,5,2,4,6,1,9]=>[7,5]=>13685760
[12,10,9,8,3,7,5,2,4,6,1,11]=>[9,3]=>17740800
[12,9,11,8,3,7,5,2,4,6,10,1]=>[6,4,2]=>9979200
[12,10,8,7,6,3,5,2,4,1,9,11]=>[12]=>39916800
[12,10,7,9,6,3,5,2,4,8,1,11]=>[4,3,3,2]=>3326400
[12,11,10,7,9,6,3,5,2,4,8,1]=>[5,4,2,1]=>11975040
[12,9,11,3,8,6,5,2,7,4,10,1]=>[5,4,2,1]=>11975040
[12,11,3,8,10,6,5,2,7,9,4,1]=>[4,4,2,1,1]=>3742200
[12,11,10,9,3,8,6,5,2,7,4,1]=>[6,4,2]=>9979200
[12,10,8,6,5,4,3,2,1,7,9,11]=>[5,4,2,1]=>11975040
[12,11,10,9,8,6,5,4,3,2,1,7]=>[11,1]=>43545600
[12,10,8,5,7,4,3,2,6,1,9,11]=>[12]=>39916800
[12,10,5,9,7,4,3,2,6,8,1,11]=>[3,3,3,3]=>246400
[12,11,10,4,9,7,6,3,5,2,8,1]=>[5,2,2,2,1]=>1995840
[12,10,4,9,6,8,3,5,7,2,1,11]=>[4,3,3,2]=>3326400
[12,10,9,8,4,7,6,3,5,2,1,11]=>[5,3,2,2]=>3991680
[12,8,11,10,4,7,6,3,5,9,2,1]=>[4,4,2,2]=>1871100
[12,7,11,9,6,5,4,3,2,8,10,1]=>[4,4,2,2]=>1871100
[12,10,6,9,8,5,4,3,7,2,1,11]=>[4,3,3,2]=>3326400
[12,11,10,6,9,8,5,4,3,7,2,1]=>[5,3,2,2]=>3991680
[12,5,11,8,10,7,4,6,3,9,2,1]=>[6,4,2]=>9979200
[12,5,11,7,10,9,4,6,8,3,2,1]=>[5,3,2,2]=>3991680
[12,11,10,5,9,8,7,4,6,3,2,1]=>[5,2,2,2,1]=>1995840
[12,9,11,8,7,6,5,4,3,2,10,1]=>[5,2,2,2,1]=>1995840
[3,5,4,7,8,2,6,1]=>[8]=>5040
[3,2,5,6,7,8,9,1,4]=>[8,1]=>45360
[4,2,5,6,7,3,8,1]=>[7,1]=>5760
[4,2,5,6,7,8,9,3,1]=>[8,1]=>45360
[3,2,4,5,6,7,8,9,10,11,1]=>[10,1]=>3991680
[8,6,1,4,3,5,2,7]=>[7,1]=>5760
[6,1,8,4,3,5,2,7]=>[7,1]=>5760
[5,1,6,4,8,2,3,7]=>[7,1]=>5760
[8,1,4,2,5,3,6,7]=>[7,1]=>5760
[2,8,4,1,5,3,6,7]=>[7,1]=>5760
[8,4,1,3,5,2,6,7]=>[7,1]=>5760
[4,1,8,3,5,2,6,7]=>[7,1]=>5760
[8,3,1,2,5,4,6,7]=>[7,1]=>5760
[3,1,8,2,5,4,6,7]=>[7,1]=>5760
[1,4,8,6,7,2,5,3]=>[3,2,2,1]=>1680
[1,2,5,6,7,4,8,9,3]=>[5,2,1,1]=>18144
[4,6,8,1,2,5,3,7]=>[3,3,2]=>1120
[3,5,6,8,2,1,4,7]=>[3,3,2]=>1120
[8,2,5,4,1,3,7,6]=>[5,1,1,1]=>1344
[2,4,5,8,6,3,1,7]=>[5,3]=>2688
[5,4,8,2,3,1,7,6]=>[5,2,1]=>4032
[4,7,5,8,2,3,1,6]=>[8]=>5040
[4,6,7,5,1,8,3,2]=>[3,3,2]=>1120
[1,7,3,6,5,8,2,4]=>[3,2,1,1,1]=>1120
[8,3,4,2,6,7,1,5]=>[5,3]=>2688
[7,5,3,8,6,2,1,4]=>[3,2,2,1]=>1680
[7,3,1,8,2,6,5,4]=>[5,2,1]=>4032
[4,6,7,5,2,8,3,1]=>[6,2]=>3360
[5,8,7,2,4,3,1,6]=>[8]=>5040
[5,1,2,8,6,7,3,4]=>[6,2]=>3360
[2,5,7,8,6,1,4,3]=>[4,4]=>1260
[7,2,6,8,4,5,1,3]=>[5,2,1]=>4032
[5,1,7,6,8,2,3,4]=>[6,2]=>3360
[1,7,6,2,4,3,8,5]=>[5,2,1]=>4032
[7,1,6,2,4,5,3,8]=>[7,1]=>5760
[5,7,1,6,2,3,4,8]=>[7,1]=>5760
[6,2,5,8,3,4,1,7]=>[5,2,1]=>4032
[1,5,3,4,8,2,6,7]=>[5,1,1,1]=>1344
[2,1,3,6,5,8,4,7]=>[4,2,1,1]=>2520
[5,1,2,8,6,3,7,4]=>[5,2,1]=>4032
[6,1,5,7,8,4,2,3]=>[5,3]=>2688
[4,6,1,5,7,2,8,3]=>[6,2]=>3360
[2,5,8,4,6,3,7,1]=>[6,1,1]=>3360
[4,3,7,1,2,6,8,5]=>[5,2,1]=>4032
[8,1,6,5,2,7,4,3]=>[8]=>5040
[6,8,1,5,2,7,4,3]=>[8]=>5040
[4,5,8,2,3,7,6,1]=>[6,2]=>3360
[1,7,3,2,4,8,6,5]=>[6,1,1]=>3360
[4,3,1,8,2,6,7,5]=>[6,1,1]=>3360
[4,8,1,3,2,5,7,6]=>[4,3,1]=>3360
[1,7,5,3,8,6,2,4]=>[4,2,1,1]=>2520
[2,5,3,8,1,4,7,6]=>[3,3,1,1]=>1120
[4,2,5,8,1,3,7,6]=>[6,1,1]=>3360
[8,1,2,4,3,5,7,6]=>[6,1,1]=>3360
[2,4,3,8,1,5,7,6]=>[6,1,1]=>3360
[3,1,7,4,8,6,5,2]=>[6,1,1]=>3360
[6,4,5,3,2,8,7,1]=>[4,3,1]=>3360
[2,7,3,8,5,1,6,4]=>[4,2,1,1]=>2520
[8,7,3,2,5,6,4,1]=>[3,2,1,1,1]=>1120
[3,1,8,2,6,5,4,7]=>[6,2]=>3360
[7,6,2,8,1,4,5,3]=>[5,3]=>2688
[2,3,8,4,1,5,7,6]=>[6,1,1]=>3360
[8,4,2,3,1,5,7,6]=>[4,3,1]=>3360
[8,2,3,4,1,5,7,6]=>[4,1,1,1,1]=>420
[7,1,6,2,4,8,3,5]=>[8]=>5040
[2,7,8,1,4,3,6,5]=>[8]=>5040
[6,5,8,1,3,2,4,7]=>[8]=>5040
[2,1,8,5,3,4,6,7]=>[6,2]=>3360
[8,4,1,3,2,5,6,7]=>[8]=>5040
[8,6,1,2,3,5,4,7]=>[8]=>5040
[7,8,1,5,2,4,6,3]=>[8]=>5040
[2,8,6,3,1,5,4,7]=>[8]=>5040
[5,7,2,8,4,1,6,3]=>[8]=>5040
[2,5,6,3,8,1,4,7]=>[8]=>5040
[1,3,4,5,6,7,2,8,9]=>[6,1,1,1]=>10080
[7,4,5,6,8,1,3,2]=>[8]=>5040
[7,6,8,1,4,5,3,2]=>[8]=>5040
[7,5,1,8,4,6,3,2]=>[4,3,1]=>3360
[1,7,8,5,6,4,3,2]=>[4,3,1]=>3360
[7,3,6,2,5,4,8,1]=>[4,3,1]=>3360
[1,6,2,3,5,8,4,7]=>[6,1,1]=>3360
[1,8,5,6,4,3,7,2]=>[4,2,1,1]=>2520
[2,6,8,4,5,1,7,3]=>[3,2,1,1,1]=>1120
[5,3,2,1,7,8,4,6]=>[4,2,2]=>1260
[8,4,1,3,6,7,2,5]=>[8]=>5040
[1,6,5,3,8,4,7,2]=>[6,1,1]=>3360
[7,6,2,3,5,1,4,8]=>[6,1,1]=>3360
[6,2,5,3,4,8,1,7]=>[4,3,1]=>3360
[6,2,5,3,4,8,7,1]=>[3,3,1,1]=>1120
[2,6,5,3,4,8,1,7]=>[5,3]=>2688
[5,3,4,8,1,7,2,6]=>[6,2]=>3360
[5,1,3,4,8,7,2,6]=>[6,1,1]=>3360
[1,5,3,4,8,7,2,6]=>[5,1,1,1]=>1344
[5,1,3,8,4,7,6,2]=>[5,2,1]=>4032
[5,3,8,1,4,7,6,2]=>[3,3,2]=>1120
[4,3,5,8,1,7,6,2]=>[6,2]=>3360
[3,6,5,4,8,1,2,7]=>[7,1]=>5760
[3,6,5,4,8,2,7,1]=>[4,2,1,1]=>2520
[3,5,2,4,8,7,6,1]=>[5,2,1]=>4032
[2,5,3,6,8,4,1,7]=>[5,2,1]=>4032
[4,6,2,5,1,7,8,3]=>[5,3]=>2688
[2,3,6,5,8,4,1,7]=>[8]=>5040
[2,3,1,7,4,8,6,5]=>[5,3]=>2688
[1,8,3,6,4,2,7,5]=>[5,1,1,1]=>1344
[2,1,7,4,8,5,3,6]=>[3,2,2,1]=>1680
[8,1,7,3,2,5,4,6]=>[5,3]=>2688
[7,8,5,2,6,4,3,1]=>[8]=>5040
[8,1,2,5,7,4,6,3]=>[4,4]=>1260
[8,2,5,3,6,1,4,7]=>[7,1]=>5760
[6,8,7,4,1,5,2,3]=>[4,3,1]=>3360
[8,6,4,7,5,1,3,2]=>[4,3,1]=>3360
[6,1,2,4,7,8,3,5]=>[7,1]=>5760
[2,4,6,5,7,1,8,3]=>[8]=>5040
[3,5,2,1,7,8,6,4]=>[8]=>5040
[4,2,7,8,6,5,1,3]=>[5,2,1]=>4032
[4,8,1,2,6,5,3,7]=>[6,2]=>3360
[6,4,8,1,2,3,7,5]=>[7,1]=>5760
[7,4,1,3,6,8,5,2]=>[8]=>5040
[7,1,8,3,2,6,5,4]=>[4,3,1]=>3360
[5,2,7,1,4,6,3,8]=>[3,2,1,1,1]=>1120
[6,3,8,5,7,1,4,2]=>[3,3,2]=>1120
[2,8,3,1,4,6,5,7]=>[6,1,1]=>3360
[4,5,7,6,1,3,8,2]=>[8]=>5040
[3,2,8,5,1,4,6,7]=>[7,1]=>5760
[3,5,4,1,2,8,6,7]=>[3,3,2]=>1120
[5,3,8,1,4,2,6,7]=>[5,3]=>2688
[5,3,8,1,4,2,7,6]=>[4,3,1]=>3360
[1,4,7,5,8,6,2,3]=>[6,1,1]=>3360
[8,5,7,6,3,4,1,2]=>[6,2]=>3360
[7,5,2,6,1,4,8,3]=>[6,2]=>3360
[2,4,5,1,8,3,7,6]=>[4,3,1]=>3360
[7,2,8,5,3,4,1,6]=>[5,2,1]=>4032
[6,4,5,3,1,7,8,2]=>[8]=>5040
[7,3,5,6,4,1,8,2]=>[8]=>5040
[2,3,4,7,8,9,1,5,6]=>[5,2,2]=>9072
[2,3,6,7,8,9,1,4,5]=>[9]=>40320
[2,5,6,7,8,9,1,3,4]=>[9]=>40320
[2,3,4,5,1,9,6,7,8]=>[5,4]=>18144
[2,3,4,1,8,9,5,6,7]=>[5,4]=>18144
[2,3,4,5,8,9,10,1,6,7]=>[6,2,2]=>75600
[2,3,1,7,8,9,4,5,6]=>[3,2,2,2]=>2520
[2,3,4,7,8,9,10,1,5,6]=>[10]=>362880
[2,1,6,7,8,9,3,4,5]=>[7,2]=>25920
[2,3,6,7,8,9,10,1,4,5]=>[10]=>362880
[2,5,6,7,8,9,10,1,3,4]=>[4,3,3]=>50400
[2,5,6,3,4,1,8,7]=>[6,2]=>3360
[4,6,2,1,5,8,3,7]=>[5,2,1]=>4032
[4,6,7,2,3,8,5,1]=>[5,3]=>2688
[2,3,5,8,7,4,1,6]=>[5,3]=>2688
[2,3,5,8,7,4,6,1]=>[8]=>5040
[4,5,3,7,8,1,2,6]=>[7,1]=>5760
[2,3,5,8,1,6,4,7]=>[4,3,1]=>3360
[8,6,1,5,4,2,7,3]=>[3,2,2,1]=>1680
[2,8,5,6,3,1,4,7]=>[6,2]=>3360
[4,8,2,6,1,5,7,3]=>[4,3,1]=>3360
[2,3,7,8,1,5,4,6]=>[8]=>5040
[5,6,2,7,8,3,1,4]=>[5,3]=>2688
[2,3,7,5,8,4,6,1]=>[8]=>5040
[3,7,8,5,1,4,6,2]=>[8]=>5040
[2,5,6,7,1,8,4,3]=>[3,3,2]=>1120
[2,3,7,8,5,4,6,1]=>[7,1]=>5760
[7,5,8,1,2,3,6,4]=>[6,2]=>3360
[1,2,8,7,4,6,5,3]=>[3,2,1,1,1]=>1120
[5,1,4,8,7,3,6,2]=>[8]=>5040
[4,3,1,8,7,5,6,2]=>[5,3]=>2688
[4,3,2,7,6,1,5,8]=>[5,2,1]=>4032
[7,2,6,5,3,1,4,8]=>[6,1,1]=>3360
[1,3,7,6,2,4,8,5]=>[5,2,1]=>4032
[1,3,8,2,7,4,6,5]=>[7,1]=>5760
[8,2,7,1,6,4,3,5]=>[5,2,1]=>4032
[4,3,2,8,1,7,5,6]=>[6,2]=>3360
[7,5,4,1,6,3,8,2]=>[8]=>5040
[1,6,5,3,2,4,8,7]=>[5,2,1]=>4032
[1,7,3,5,2,4,8,6]=>[6,1,1]=>3360
[4,3,7,2,5,1,6,8]=>[6,1,1]=>3360
[5,1,4,3,2,6,8,7]=>[3,2,2,1]=>1680
[7,2,1,3,5,4,6,8]=>[5,1,1,1]=>1344
[8,3,7,5,4,2,6,1]=>[4,2,2]=>1260
[1,6,8,7,5,2,3,4]=>[4,2,1,1]=>2520
[1,3,6,2,5,4,8,7]=>[4,2,1,1]=>2520
[1,2,7,3,8,4,9,5,10,6]=>[6,2,1,1]=>151200
[4,5,7,6,3,1,8,2]=>[5,3]=>2688
[4,6,7,5,1,3,8,2]=>[5,3]=>2688
[3,6,5,1,4,7,8,2]=>[4,4]=>1260
[4,6,7,3,1,5,8,2]=>[8]=>5040
[6,2,5,1,8,7,3,4]=>[7,1]=>5760
[3,2,6,1,5,8,7,4]=>[5,1,1,1]=>1344
[4,2,3,6,7,5,1,8]=>[5,1,1,1]=>1344
[6,2,3,5,7,4,1,8]=>[5,1,1,1]=>1344
[1,6,3,8,4,7,2,5]=>[3,3,1,1]=>1120
[8,1,5,2,4,7,3,6]=>[8]=>5040
[7,5,8,1,4,2,3,6]=>[8]=>5040
[4,1,2,3,6,5,8,7,9]=>[4,2,2,1]=>11340
[4,1,2,3,6,5,8,7,10,9]=>[4,2,2,2]=>18900
[4,1,6,2,3,5,8,7,9]=>[3,3,2,1]=>10080
[3,2,7,1,8,6,5,4]=>[6,1,1]=>3360
[6,2,4,1,5,7,8,3]=>[6,1,1]=>3360
[5,8,4,1,3,6,7,2]=>[4,2,1,1]=>2520
[6,7,2,3,8,1,4,5]=>[4,2,2]=>1260
[5,2,8,1,7,4,6,3]=>[5,2,1]=>4032
[2,5,4,7,3,1,8,6]=>[8]=>5040
[4,6,3,1,2,5,7,8]=>[3,2,1,1,1]=>1120
[7,4,6,8,3,1,2,5]=>[8]=>5040
[8,5,4,7,3,1,2,6]=>[5,3]=>2688
[7,3,2,1,5,4,8,6]=>[5,2,1]=>4032
[2,5,6,4,8,1,3,7]=>[7,1]=>5760
[5,4,1,6,2,3,7,8]=>[6,1,1]=>3360
[1,3,6,5,2,4,7,8]=>[5,1,1,1]=>1344
[5,4,1,2,7,6,3,8]=>[4,2,1,1]=>2520
[5,8,7,3,1,2,4,6]=>[3,3,2]=>1120
[2,7,8,1,4,5,3,6]=>[8]=>5040
[4,1,2,8,7,3,6,5]=>[8]=>5040
[6,1,2,4,3,8,7,5]=>[6,1,1]=>3360
[3,7,8,1,2,4,6,5]=>[8]=>5040
[7,3,4,1,2,6,8,5]=>[7,1]=>5760
[8,4,3,1,2,6,5,7]=>[6,1,1]=>3360
[3,8,2,7,4,5,1,6]=>[8]=>5040
[8,6,2,3,5,4,1,7]=>[4,3,1]=>3360
[8,2,6,1,3,5,4,7]=>[4,3,1]=>3360
[8,4,3,7,2,5,6,1]=>[5,2,1]=>4032
[8,3,1,7,4,5,2,6]=>[8]=>5040
[8,2,4,5,1,7,3,6]=>[7,1]=>5760
[6,8,2,4,5,1,7,3]=>[3,2,1,1,1]=>1120
[4,3,8,1,7,5,6,2]=>[3,3,2]=>1120
[8,4,3,7,1,5,6,2]=>[7,1]=>5760
[8,3,4,7,2,6,5,1]=>[5,2,1]=>4032
[8,1,3,7,6,4,5,2]=>[4,3,1]=>3360
[8,3,7,1,4,5,6,2]=>[8]=>5040
[8,7,3,6,1,2,5,4]=>[7,1]=>5760
[8,3,7,6,2,4,5,1]=>[4,2,2]=>1260
[8,7,2,3,6,1,5,4]=>[8]=>5040
[8,2,7,1,3,4,6,5]=>[7,1]=>5760
[5,1,8,4,2,3,7,6]=>[3,3,1,1]=>1120
[8,2,4,7,3,1,6,5]=>[7,1]=>5760
[8,2,7,6,3,1,4,5]=>[7,1]=>5760
[6,8,1,4,7,3,2,5]=>[4,3,1]=>3360
[8,5,7,2,6,3,1,4]=>[8]=>5040
[5,8,2,7,3,1,6,4]=>[8]=>5040
[8,1,2,6,7,5,4,3]=>[4,4]=>1260
[8,4,1,7,5,6,2,3]=>[3,3,1,1]=>1120
[8,2,4,7,6,5,1,3]=>[5,2,1]=>4032
[8,2,7,6,4,5,1,3]=>[4,3,1]=>3360
[8,4,7,2,3,6,5,1]=>[3,2,2,1]=>1680
[8,2,4,7,3,6,5,1]=>[4,2,1,1]=>2520
[8,1,7,6,4,5,2,3]=>[5,3]=>2688
[8,1,2,7,6,4,5,3]=>[4,4]=>1260
[8,1,4,7,3,6,5,2]=>[4,3,1]=>3360
[2,3,1,9,8,7,6,5,4]=>[3,2,2,2]=>2520
[3,4,2,1,9,8,7,6,5]=>[4,2,2,1]=>11340
[4,5,3,2,1,9,8,7,6]=>[4,2,2,1]=>11340
[5,6,4,3,2,1,9,8,7]=>[4,2,2,1]=>11340
[6,7,5,4,3,2,1,9,8]=>[4,2,2,1]=>11340
[2,8,1,5,3,7,6,4]=>[6,2]=>3360
[1,8,2,4,7,5,6,3]=>[3,3,1,1]=>1120
[2,3,8,4,7,1,6,5]=>[7,1]=>5760
[1,8,2,3,5,6,4,7]=>[5,1,1,1]=>1344
[1,4,7,6,2,3,5,8]=>[6,1,1]=>3360
[1,7,6,2,3,8,4,5]=>[4,3,1]=>3360
[1,8,2,3,7,6,4,5]=>[6,1,1]=>3360
[1,7,3,8,6,2,5,4]=>[4,2,1,1]=>2520
[5,8,2,3,7,4,1,6]=>[5,3]=>2688
[1,3,5,6,4,8,2,7]=>[7,1]=>5760
[7,1,2,3,4,5,9,6,10,8]=>[10]=>362880
[4,6,1,8,2,7,5,3]=>[4,4]=>1260
[3,4,8,5,6,1,2,7]=>[8]=>5040
[1,7,6,2,5,4,8,3]=>[6,1,1]=>3360
[5,6,1,7,4,3,8,2]=>[8]=>5040
[3,1,5,6,4,2,7,8]=>[6,1,1]=>3360
[8,1,6,4,3,5,2,7]=>[4,3,1]=>3360
[3,7,5,6,4,2,1,8]=>[7,1]=>5760
[6,1,4,3,7,5,8,2]=>[6,2]=>3360
[3,8,6,4,5,2,7,1]=>[5,1,1,1]=>1344
[4,5,8,6,2,3,7,1]=>[5,2,1]=>4032
[4,6,8,5,3,7,2,1]=>[5,3]=>2688
[4,5,7,2,8,6,3,1]=>[5,2,1]=>4032
[3,7,4,5,1,6,8,2]=>[4,3,1]=>3360
[4,6,8,1,2,5,7,3]=>[3,2,2,1]=>1680
[4,6,8,5,1,3,7,2]=>[4,3,1]=>3360
[3,7,4,5,2,8,6,1]=>[8]=>5040
[3,7,8,4,6,1,5,2]=>[7,1]=>5760
[4,5,7,2,1,6,8,3]=>[4,3,1]=>3360
[4,5,1,6,8,3,7,2]=>[4,3,1]=>3360
[3,4,5,6,1,7,2,9,8]=>[4,3,2]=>15120
[1,7,4,5,2,6,8,3]=>[6,1,1]=>3360
[1,4,5,9,6,7,2,8,3]=>[7,1,1]=>25920
[3,4,5,6,7,1,8,2,10,9]=>[8,2]=>226800
[2,4,5,9,6,1,7,3,8]=>[8,1]=>45360
[3,4,5,7,6,1,9,2,8]=>[5,4]=>18144
[1,4,2,6,5,3,8,7]=>[4,2,1,1]=>2520
[3,1,5,8,4,6,2,7]=>[7,1]=>5760
[3,5,6,9,7,1,8,2,4]=>[4,3,2]=>15120
[1,4,8,5,6,2,7,9,3]=>[4,3,1,1]=>15120
[1,4,5,6,10,7,8,2,9,3]=>[5,3,1,1]=>120960
[3,4,5,6,7,8,1,9,2,11,10]=>[5,4,2]=>997920
[2,4,5,6,10,7,1,8,3,9]=>[5,4,1]=>181440
[3,4,5,6,8,7,1,10,2,9]=>[10]=>362880
[2,5,9,6,7,3,1,4,8]=>[5,4]=>18144
[4,1,5,2,7,6,3,9,8]=>[3,3,2,1]=>10080
[3,4,1,6,9,5,7,2,8]=>[6,2,1]=>30240
[8,2,6,3,4,1,5,7]=>[7,1]=>5760
[4,6,5,8,2,1,3,7]=>[8]=>5040
[1,4,8,3,5,6,2,7]=>[5,1,1,1]=>1344
[1,8,7,4,2,3,6,5]=>[3,3,1,1]=>1120
[6,7,9,8,1,3,4,2,5]=>[5,4]=>18144
[9,1,5,2,8,6,3,7,4]=>[4,4,1]=>11340
[3,5,6,7,10,8,1,9,2,4]=>[10]=>362880
[1,7,4,5,2,6,8,9,3]=>[7,1,1]=>25920
[1,4,5,9,6,7,2,8,10,3]=>[8,1,1]=>226800
[1,4,5,6,7,11,8,9,2,10,3]=>[9,1,1]=>2217600
[7,4,6,2,1,3,8,5]=>[4,2,2]=>1260
[8,4,7,2,3,5,6,1]=>[4,2,2]=>1260
[3,8,6,7,1,5,4,2]=>[4,2,2]=>1260
[4,3,2,8,6,1,5,7]=>[6,2]=>3360
[4,1,6,3,2,5,7,8]=>[6,1,1]=>3360
[5,7,1,8,4,3,6,2]=>[8]=>5040
[5,4,8,7,6,2,3,1]=>[8]=>5040
[8,4,6,3,1,5,2,7]=>[8]=>5040
[3,6,1,5,2,4,7,8]=>[4,2,1,1]=>2520
[3,7,6,2,5,4,1,8]=>[6,1,1]=>3360
[2,7,1,5,3,4,6,8]=>[7,1]=>5760
[8,4,5,1,2,7,6,3]=>[6,2]=>3360
[5,2,3,8,7,1,6,4]=>[4,2,1,1]=>2520
[7,5,2,4,1,3,8,6]=>[7,1]=>5760
[7,2,6,8,5,1,3,4]=>[4,2,1,1]=>2520
[8,6,5,4,1,3,7,2]=>[6,1,1]=>3360
[8,2,3,4,1,6,7,5]=>[3,1,1,1,1,1]=>112
[7,4,3,8,1,6,5,2]=>[3,3,1,1]=>1120
[6,5,1,4,3,8,7,2]=>[6,1,1]=>3360
[4,7,6,2,5,8,1,3]=>[4,3,1]=>3360
[6,3,2,4,5,8,1,7]=>[4,2,1,1]=>2520
[2,6,4,5,8,3,1,7]=>[8]=>5040
[7,3,5,2,8,1,4,6]=>[8]=>5040
[1,5,8,7,4,2,3,6]=>[7,1]=>5760
[1,7,2,4,5,8,6,3]=>[5,1,1,1]=>1344
[1,4,6,8,7,2,5,3]=>[5,2,1]=>4032
[1,6,2,7,5,3,4,8]=>[3,2,1,1,1]=>1120
[1,3,7,2,6,4,5,8]=>[6,1,1]=>3360
[1,7,3,2,8,5,6,4]=>[6,1,1]=>3360
[1,6,5,2,4,8,3,7]=>[7,1]=>5760
[1,7,3,8,4,2,5,6]=>[6,1,1]=>3360
[1,6,2,4,7,5,8,3]=>[6,1,1]=>3360
[1,6,2,7,4,3,8,5]=>[4,3,1]=>3360
[1,5,8,2,3,6,4,7]=>[6,1,1]=>3360
[6,8,9,1,2,3,4,5,7]=>[6,3]=>20160
[5,8,9,1,2,3,4,6,7]=>[9]=>40320
[2,5,3,6,7,1,4,8]=>[6,1,1]=>3360
[6,4,1,5,7,2,3,8]=>[7,1]=>5760
[6,4,1,5,7,3,8,2]=>[5,3]=>2688
[1,2,7,3,8,5,6,4]=>[6,1,1]=>3360
[7,4,1,6,3,8,2,5]=>[8]=>5040
[1,5,7,4,3,8,6,2]=>[6,1,1]=>3360
[2,7,3,1,4,5,8,6]=>[7,1]=>5760
[2,3,4,5,1,7,6,9,8]=>[5,2,2]=>9072
[2,3,4,1,6,5,8,7,9]=>[4,2,2,1]=>11340
[2,3,4,5,6,7,1,9,8,10]=>[7,2,1]=>259200
[2,3,4,5,1,8,6,9,7]=>[5,4]=>18144
[2,3,4,1,7,5,8,6,9]=>[4,4,1]=>11340
[2,3,4,5,1,7,6,9,8,10]=>[5,2,2,1]=>90720
[6,5,8,3,2,7,1,4]=>[3,3,2]=>1120
[8,4,3,1,7,6,5,2]=>[4,2,1,1]=>2520
[3,4,5,6,7,9,1,8,2]=>[4,4,1]=>11340
[3,4,5,6,7,8,10,1,9,2]=>[9,1]=>403200
[7,2,1,4,5,6,3,8]=>[3,1,1,1,1,1]=>112
[1,5,6,7,3,4,2,8]=>[6,1,1]=>3360
[4,6,8,5,2,1,7,3]=>[5,2,1]=>4032
[1,6,7,8,2,4,5,3]=>[7,1]=>5760
[5,7,8,3,2,4,6,1]=>[8]=>5040
[5,7,8,2,3,1,6,4]=>[8]=>5040
[5,3,4,2,1,9,8,7,6]=>[3,2,2,2]=>2520
[6,5,3,4,2,1,9,8,7]=>[2,2,2,1,1,1]=>1260
[7,6,4,5,3,2,1,9,8]=>[3,2,2,2]=>2520
[4,5,2,7,8,6,1,3]=>[4,3,1]=>3360
[1,3,5,8,7,2,6,4]=>[5,2,1]=>4032
[6,4,1,8,5,7,3,2]=>[4,3,1]=>3360
[4,1,3,8,7,5,2,6]=>[7,1]=>5760
[8,5,1,6,7,2,4,3]=>[5,3]=>2688
[3,6,7,2,1,5,8,4]=>[8]=>5040
[2,5,6,1,3,8,7,4]=>[7,1]=>5760
[7,2,5,6,1,3,8,4]=>[7,1]=>5760
[6,4,1,2,5,8,3,7]=>[5,2,1]=>4032
[4,7,3,5,2,6,8,1]=>[6,1,1]=>3360
[6,8,4,1,5,7,3,2]=>[5,2,1]=>4032
[8,1,6,2,3,7,5,4]=>[4,4]=>1260
[7,8,9,6,1,2,3,4,10,5]=>[6,4]=>151200
[2,8,9,10,7,1,3,4,5,6]=>[6,4]=>151200
[8,9,10,7,6,1,2,3,4,11,5]=>[7,4]=>1425600
[8,9,7,5,6,1,2,3,10,4]=>[10]=>362880
[2,9,10,8,6,7,1,3,4,5]=>[10]=>362880
[2,9,10,11,8,7,1,3,4,5,6]=>[7,4]=>1425600
[8,9,10,11,7,1,2,3,4,5,12,6]=>[12]=>39916800
[7,8,9,10,1,2,3,4,5,11,6]=>[6,5]=>1330560
[7,8,9,5,1,2,3,4,10,6]=>[10]=>362880
[7,8,9,1,6,2,3,4,10,5]=>[10]=>362880
[2,8,9,10,6,1,3,4,5,7]=>[10]=>362880
[2,8,9,10,1,7,3,4,5,6]=>[10]=>362880
[2,8,9,10,11,1,3,4,5,6,7]=>[6,5]=>1330560
[2,9,10,11,12,8,1,3,4,5,6,7]=>[12]=>39916800
[2,8,3,6,4,1,7,5]=>[6,1,1]=>3360
[6,5,3,4,8,2,1,7]=>[6,1,1]=>3360
[5,4,8,7,3,6,2,1]=>[4,3,1]=>3360
[3,4,5,1,2,6,7,8,9]=>[5,1,1,1,1]=>3024
[5,2,7,6,8,3,4,1]=>[4,3,1]=>3360
[8,4,5,2,7,3,6,1]=>[4,2,2]=>1260
[6,3,7,4,5,2,8,1]=>[6,1,1]=>3360
[7,3,4,2,8,5,6,1]=>[5,3]=>2688
[4,3,6,5,8,2,7,1]=>[4,3,1]=>3360
[8,2,7,4,5,3,6,1]=>[3,2,1,1,1]=>1120
[7,2,8,4,5,3,6,1]=>[5,1,1,1]=>1344
[6,3,8,2,7,4,5,1]=>[6,2]=>3360
[3,2,8,4,7,5,6,1]=>[3,3,1,1]=>1120
[8,3,6,2,7,4,5,1]=>[4,2,2]=>1260
[4,2,3,5,6,7,8,9,10,1]=>[8,1,1]=>226800
[2,3,4,5,6,7,8,11,1,9,10]=>[11]=>3628800
[2,3,4,5,6,7,11,1,8,9,10]=>[11]=>3628800
[2,3,4,5,6,11,1,7,8,9,10]=>[11]=>3628800
[2,3,4,5,11,1,6,7,8,9,10]=>[11]=>3628800
[2,3,4,11,1,5,6,7,8,9,10]=>[11]=>3628800
[2,3,11,1,4,5,6,7,8,9,10]=>[11]=>3628800
[1,7,8,4,3,6,5,2]=>[5,1,1,1]=>1344
[1,7,8,3,6,5,4,2]=>[5,2,1]=>4032
[5,8,1,7,2,4,3,6]=>[8]=>5040
[2,5,7,3,8,1,4,6]=>[5,3]=>2688
[8,3,5,2,1,6,7,4]=>[6,1,1]=>3360
[2,6,4,7,1,8,5,3]=>[8]=>5040
[1,6,5,7,3,8,2,4]=>[5,2,1]=>4032
[1,8,5,3,7,6,2,4]=>[6,1,1]=>3360
[6,4,2,3,8,7,5,1]=>[5,3]=>2688
[6,5,1,3,8,4,2,7]=>[4,4]=>1260
[6,1,4,2,7,8,3,5]=>[8]=>5040
[5,6,8,2,4,7,1,3]=>[6,2]=>3360
[6,7,4,2,3,8,5,1]=>[5,3]=>2688
[5,8,7,3,2,4,6,1]=>[4,4]=>1260
[5,7,1,4,6,8,2,3]=>[5,2,1]=>4032
[2,4,1,7,5,6,3,8]=>[5,1,1,1]=>1344
[1,4,3,7,6,2,8,5]=>[6,1,1]=>3360
[1,6,2,5,7,3,8,4]=>[4,3,1]=>3360
[1,4,3,8,2,5,7,6]=>[5,1,1,1]=>1344
[1,5,7,3,6,4,2,8]=>[6,1,1]=>3360
[1,6,7,2,4,8,3,5]=>[5,2,1]=>4032
[3,7,2,8,4,1,5,6]=>[8]=>5040
[2,4,1,5,3,6,8,7,9]=>[5,2,1,1]=>18144
[2,4,1,7,3,8,5,6,9]=>[6,2,1]=>30240
[5,3,4,1,7,8,6,2]=>[8]=>5040
[4,7,6,5,8,2,3,1]=>[4,4]=>1260
[1,2,6,8,4,3,5,7]=>[4,2,1,1]=>2520
[7,2,6,3,1,8,4,5]=>[7,1]=>5760
[5,8,4,1,3,7,2,6]=>[4,4]=>1260
[3,4,2,1,6,8,5,7]=>[4,4]=>1260
[8,1,3,5,6,4,7,2]=>[3,3,1,1]=>1120
[3,4,7,1,5,6,2,8]=>[5,1,1,1]=>1344
[4,8,2,6,5,3,7,1]=>[6,1,1]=>3360
[4,8,7,2,5,6,1,3]=>[6,1,1]=>3360
[5,8,6,4,7,3,2,1]=>[5,2,1]=>4032
[8,5,2,3,1,6,7,4]=>[6,1,1]=>3360
[2,8,6,3,5,1,7,4]=>[6,1,1]=>3360
[8,3,2,6,4,1,7,5]=>[5,2,1]=>4032
[8,4,1,5,3,6,7,2]=>[6,1,1]=>3360
[8,3,5,1,4,6,7,2]=>[6,1,1]=>3360
[8,5,1,3,4,6,7,2]=>[6,1,1]=>3360
[3,8,6,2,5,4,7,1]=>[6,1,1]=>3360
[3,8,4,6,5,2,7,1]=>[6,1,1]=>3360
[8,1,7,4,2,5,3,6]=>[5,2,1]=>4032
[8,3,2,5,1,4,7,6]=>[5,2,1]=>4032
[8,4,5,1,2,6,7,3]=>[6,1,1]=>3360
[8,1,5,3,2,6,7,4]=>[6,1,1]=>3360
[8,1,5,2,4,6,7,3]=>[6,1,1]=>3360
[5,2,6,4,1,3,8,7]=>[2,2,2,1,1]=>420
[8,6,4,7,1,3,5,2]=>[8]=>5040
[2,1,8,5,4,3,7,6]=>[3,2,2,1]=>1680
[6,4,8,5,3,2,7,1]=>[7,1]=>5760
[8,5,4,6,2,7,1,3]=>[6,2]=>3360
[6,8,5,4,7,2,3,1]=>[4,3,1]=>3360
[2,5,7,3,4,8,1,6]=>[6,2]=>3360
[5,2,4,7,8,1,3,6]=>[4,3,1]=>3360
[8,5,9,3,6,1,2,4,7]=>[9]=>40320
[9,7,1,5,8,3,6,2,4]=>[9]=>40320
[9,7,5,4,1,3,8,2,6]=>[5,3,1]=>24192
[8,9,4,5,10,1,2,3,6,7]=>[10]=>362880
[8,4,3,9,10,1,2,5,6,7]=>[9,1]=>403200
[9,6,10,1,3,7,8,2,4,5]=>[4,3,3]=>50400
[9,10,6,7,4,5,1,2,3,8]=>[7,3]=>172800
[9,6,4,10,3,7,1,2,5,8]=>[10]=>362880
[10,1,8,9,6,7,4,5,2,3]=>[10]=>362880
[10,8,6,1,4,9,3,7,2,5]=>[6,4]=>151200
[10,8,6,5,4,1,3,9,2,7]=>[5,3,2]=>120960
[10,8,7,6,5,4,3,1,2,9]=>[5,2,2,1]=>90720
[2,5,6,8,7,1,4,3]=>[8]=>5040
[1,7,8,5,4,6,2,3]=>[2,2,2,1,1]=>420
[4,6,8,1,5,2,7,3]=>[2,2,2,1,1]=>420
[8,2,3,6,4,1,7,5]=>[5,1,1,1]=>1344
[2,3,7,5,8,6,1,4]=>[4,3,1]=>3360
[1,3,6,4,8,2,7,5]=>[3,2,1,1,1]=>1120
[1,2,3,4,6,5,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]=>45
[1,2,3,4,5,6,8,7,9,10]=>[2,1,1,1,1,1,1,1,1]=>45
[1,7,6,2,8,5,3,4]=>[7,1]=>5760
[1,5,8,6,4,7,2,3]=>[5,2,1]=>4032
[5,6,2,8,1,7,3,4]=>[4,2,2]=>1260
[6,8,4,5,1,3,7,2]=>[5,2,1]=>4032
[5,2,3,8,1,4,6,7]=>[4,2,1,1]=>2520
[1,6,8,3,2,4,5,7]=>[7,1]=>5760
[9,6,5,4,3,2,1,7,8]=>[4,2,2,1]=>11340
[10,7,6,5,4,3,2,1,8,9]=>[4,2,2,2]=>18900
[9,8,5,4,3,2,1,6,7]=>[3,3,2,1]=>10080
[8,6,5,2,4,3,7,1]=>[5,2,1]=>4032
[6,2,5,3,7,4,8,1]=>[7,1]=>5760
[8,5,4,2,6,3,7,1]=>[5,2,1]=>4032
[8,5,3,2,6,4,7,1]=>[4,2,1,1]=>2520
[7,4,6,5,8,2,3,1]=>[8]=>5040
[7,3,6,5,8,2,4,1]=>[5,3]=>2688
[7,3,6,4,8,2,5,1]=>[4,3,1]=>3360
[7,3,5,4,8,2,6,1]=>[7,1]=>5760
[7,3,6,8,4,5,1,2]=>[6,2]=>3360
[1,6,5,7,4,2,8,3]=>[5,2,1]=>4032
[1,2,7,4,8,5,6,3]=>[5,1,1,1]=>1344
[2,6,7,4,8,5,1,3]=>[7,1]=>5760
[2,5,8,6,4,3,7,1]=>[7,1]=>5760
[6,4,2,5,7,1,8,3]=>[6,2]=>3360
[9,1,2,3,4,5,8,7,6]=>[7,2]=>25920
[9,1,2,3,4,8,6,7,5]=>[6,3]=>20160
[8,1,4,7,3,5,6,2]=>[5,3]=>2688
[9,1,2,8,4,5,6,7,3]=>[5,4]=>18144
[8,3,7,2,4,5,6,1]=>[6,2]=>3360
[9,1,8,3,4,5,6,7,2]=>[6,3]=>20160
[10,1,2,3,4,5,6,9,8,7]=>[8,2]=>226800
[9,1,2,3,4,7,8,6,5]=>[6,3]=>20160
[10,1,2,3,4,5,9,7,8,6]=>[7,3]=>172800
[9,1,2,3,6,8,5,7,4]=>[5,4]=>18144
[9,1,2,5,8,4,6,7,3]=>[5,4]=>18144
[10,1,2,3,9,5,6,7,8,4]=>[5,5]=>72576
[8,1,4,5,7,3,6,2]=>[5,3]=>2688
[9,1,4,8,3,5,6,7,2]=>[6,3]=>20160
[10,1,2,9,4,5,6,7,8,3]=>[6,4]=>151200
[9,3,8,2,4,5,6,7,1]=>[7,2]=>25920
[5,6,3,4,2,8,7,1]=>[5,1,1,1]=>1344
[2,5,7,4,6,8,1,3]=>[7,1]=>5760
[2,5,6,4,1,3,8,7]=>[3,2,2,1]=>1680
[4,6,1,3,5,7,2,8]=>[3,3,1,1]=>1120
[3,2,7,5,8,1,6,4]=>[4,3,1]=>3360
[4,3,6,8,5,2,1,7]=>[4,3,1]=>3360
[4,5,3,2,1,8,6,7]=>[4,3,1]=>3360
[3,6,5,8,1,7,4,2]=>[5,3]=>2688
[4,1,6,8,5,2,3,7]=>[7,1]=>5760
[4,5,2,8,6,7,1,3]=>[8]=>5040
[4,5,2,8,6,7,3,1]=>[5,3]=>2688
[3,5,8,6,2,4,7,1]=>[3,2,2,1]=>1680
[2,5,1,6,4,8,3,7]=>[8]=>5040
[3,2,4,5,8,6,1,7]=>[6,1,1]=>3360
[4,5,2,1,3,8,6,7]=>[3,3,2]=>1120
[4,2,3,6,8,5,1,7]=>[6,1,1]=>3360
[4,5,1,3,2,8,6,7]=>[3,3,2]=>1120
[3,4,5,8,6,1,7,2]=>[4,3,1]=>3360
[3,4,5,8,6,1,2,7]=>[4,4]=>1260
[6,4,1,3,7,8,2,5]=>[8]=>5040
[6,3,1,2,5,4,8,7]=>[5,2,1]=>4032
[1,5,8,2,4,3,7,6]=>[3,3,1,1]=>1120
[4,3,7,8,2,6,5,1]=>[4,3,1]=>3360
[3,8,5,1,2,6,7,4]=>[6,1,1]=>3360
[2,4,7,8,3,6,5,1]=>[4,3,1]=>3360
[5,4,7,8,3,6,1,2]=>[4,3,1]=>3360
[6,8,1,3,2,5,7,4]=>[7,1]=>5760
[1,4,8,5,7,2,3,6]=>[7,1]=>5760
[1,8,7,3,2,4,5,6]=>[7,1]=>5760
[8,6,2,7,3,4,1,5]=>[8]=>5040
[8,6,2,7,3,4,5,1]=>[6,2]=>3360
[5,6,3,2,8,7,1,4]=>[7,1]=>5760
[5,1,6,7,8,3,2,4]=>[6,2]=>3360
[1,5,6,3,7,2,4,8]=>[6,1,1]=>3360
[1,5,6,7,4,2,3,8]=>[6,1,1]=>3360
[5,1,6,7,3,4,2,8]=>[7,1]=>5760
[8,6,1,7,3,4,5,2]=>[8]=>5040
[6,8,5,1,7,4,2,3]=>[5,3]=>2688
[8,4,2,3,5,7,6,1]=>[3,2,2,1]=>1680
[4,8,5,2,3,1,6,7]=>[6,2]=>3360
[5,4,8,3,1,2,6,7]=>[6,2]=>3360
[8,4,7,3,2,5,6,1]=>[6,2]=>3360
[6,8,5,1,7,3,4,2]=>[6,2]=>3360
[6,2,7,3,8,1,4,5]=>[3,2,2,1]=>1680
[8,4,2,6,7,1,5,3]=>[6,2]=>3360
[1,7,8,3,6,5,2,4]=>[3,2,2,1]=>1680
[4,6,7,5,1,8,2,3]=>[5,3]=>2688
[3,5,2,6,8,7,4,1]=>[5,3]=>2688
[7,3,6,8,4,1,2,5]=>[5,3]=>2688
[6,4,2,3,7,5,8,1]=>[5,3]=>2688
[6,3,7,5,1,2,8,4]=>[8]=>5040
[7,2,5,4,8,6,3,1]=>[5,1,1,1]=>1344
[6,2,3,8,7,4,5,1]=>[4,2,1,1]=>2520
[7,1,2,8,4,6,5,3]=>[7,1]=>5760
[3,5,8,1,2,7,6,4]=>[4,2,2]=>1260
[1,4,3,6,8,5,2,7]=>[6,1,1]=>3360
[7,6,2,8,5,3,4,1]=>[4,3,1]=>3360
[6,8,3,5,4,7,2,1]=>[5,2,1]=>4032
[8,2,7,6,4,1,3,5]=>[5,2,1]=>4032
[8,3,7,5,1,6,2,4]=>[4,3,1]=>3360
[8,5,7,1,4,2,6,3]=>[8]=>5040
[4,7,1,5,6,3,2,8]=>[5,2,1]=>4032
[4,5,7,1,6,3,8,2]=>[6,2]=>3360
[4,6,5,7,2,3,8,1]=>[4,4]=>1260
[3,6,7,2,5,8,4,1]=>[7,1]=>5760
[5,3,6,7,4,8,1,2]=>[4,4]=>1260
[4,2,7,8,3,6,5,1]=>[3,3,1,1]=>1120
[4,2,7,8,5,6,1,3]=>[5,1,1,1]=>1344
[5,4,3,7,8,1,6,2]=>[7,1]=>5760
[3,5,7,8,4,2,1,6]=>[5,3]=>2688
[4,6,7,3,2,8,1,5]=>[4,4]=>1260
[4,6,5,3,7,8,1,2]=>[5,3]=>2688
[5,6,2,4,7,8,3,1]=>[7,1]=>5760
[5,6,3,2,8,4,7,1]=>[3,3,1,1]=>1120
[5,6,2,8,3,4,7,1]=>[7,1]=>5760
[3,7,4,8,1,6,5,2]=>[7,1]=>5760
[5,2,4,8,6,7,3,1]=>[7,1]=>5760
[5,2,6,4,8,7,3,1]=>[3,3,1,1]=>1120
[2,4,7,8,6,5,1,3]=>[6,2]=>3360
[3,4,5,6,8,9,1,7,2]=>[5,4]=>18144
[3,4,6,7,8,9,1,5,2]=>[7,2]=>25920
[3,5,6,7,8,9,1,4,2]=>[9]=>40320
[4,5,6,7,8,9,1,3,2]=>[6,3]=>20160
[3,4,5,6,7,9,10,1,8,2]=>[10]=>362880
[3,4,5,7,8,9,10,1,6,2]=>[4,4,2]=>56700
[5,2,6,7,8,1,4,3]=>[5,2,1]=>4032
[3,4,6,7,8,9,10,1,5,2]=>[6,4]=>151200
[4,5,6,7,8,9,10,1,3,2]=>[7,3]=>172800
[3,1,4,5,6,7,8,9,11,2,10]=>[11]=>3628800
[1,2,4,6,5,8,3,7]=>[5,1,1,1]=>1344
[5,4,2,3,1,7,8,6]=>[3,3,2]=>1120
[5,8,6,1,7,2,3,4]=>[8]=>5040
[5,1,4,3,8,2,6,7]=>[6,2]=>3360
[8,4,7,5,6,2,1,3]=>[4,4]=>1260
[3,8,6,7,5,2,4,1]=>[5,2,1]=>4032
[8,2,5,4,7,3,6,1]=>[4,2,1,1]=>2520
[4,2,8,7,3,6,5,1]=>[6,1,1]=>3360
[3,7,8,6,1,4,5,2]=>[6,2]=>3360
[4,6,7,8,2,1,5,3]=>[8]=>5040
[4,7,6,3,8,1,5,2]=>[4,4]=>1260
[3,8,1,4,6,2,5,7]=>[5,2,1]=>4032
[2,4,5,3,8,7,1,6]=>[8]=>5040
[4,7,5,6,2,8,1,3]=>[8]=>5040
[8,7,5,1,6,3,2,4]=>[3,3,2]=>1120
[7,8,6,2,3,5,1,4]=>[3,3,2]=>1120
[2,8,4,6,7,3,5,1]=>[3,3,2]=>1120
[4,1,6,7,8,2,5,3]=>[8]=>5040
[8,6,3,4,1,2,7,5]=>[3,2,1,1,1]=>1120
[2,5,8,4,6,1,3,7]=>[4,3,1]=>3360
[4,7,8,6,5,1,3,2]=>[4,3,1]=>3360
[6,8,4,7,3,5,2,1]=>[8]=>5040
[7,4,5,8,3,6,2,1]=>[5,2,1]=>4032
[8,4,7,3,5,6,2,1]=>[4,2,1,1]=>2520
[3,6,4,2,8,1,7,5]=>[5,2,1]=>4032
[3,4,8,6,2,1,7,5]=>[7,1]=>5760
[3,8,6,2,1,7,4,5]=>[8]=>5040
[3,1,8,2,4,6,5,7]=>[7,1]=>5760
[8,1,7,6,2,5,4,3]=>[8]=>5040
[8,5,4,3,7,6,1,2]=>[5,2,1]=>4032
[4,8,1,3,6,7,5,2]=>[3,3,2]=>1120
[3,5,8,6,1,7,4,2]=>[5,3]=>2688
[8,1,4,7,5,2,6,3]=>[7,1]=>5760
[1,4,8,6,7,3,5,2]=>[5,2,1]=>4032
[4,1,6,7,8,5,3,2]=>[8]=>5040
[3,7,8,6,4,1,5,2]=>[8]=>5040
[5,4,2,3,6,7,8,9,1]=>[6,3]=>20160
[6,5,4,2,3,7,8,9,1]=>[5,4]=>18144
[7,6,5,4,2,3,8,9,1]=>[4,4,1]=>11340
[4,6,1,5,7,2,3,8]=>[5,2,1]=>4032
[4,8,5,3,2,7,1,6]=>[8]=>5040
[5,4,8,1,3,7,2,6]=>[8]=>5040
[8,4,5,3,1,7,2,6]=>[8]=>5040
[7,4,5,3,1,8,6,2]=>[8]=>5040
[5,6,8,7,2,4,3,1]=>[8]=>5040
[5,7,8,6,4,2,3,1]=>[8]=>5040
[6,8,7,5,1,3,2,4]=>[8]=>5040
[3,8,2,6,7,5,1,4]=>[8]=>5040
[4,7,6,3,8,2,5,1]=>[8]=>5040
[6,7,4,1,8,2,5,3]=>[8]=>5040
[5,7,6,8,3,2,4,1]=>[8]=>5040
[7,6,4,2,8,1,5,3]=>[8]=>5040
[6,3,4,8,7,1,2,5]=>[6,2]=>3360
[2,7,4,8,1,6,3,5]=>[7,1]=>5760
[5,3,1,6,7,8,2,4]=>[5,3]=>2688
[3,4,7,8,6,1,2,5]=>[8]=>5040
[2,1,4,7,8,6,3,5]=>[3,2,2,1]=>1680
[2,4,5,8,1,6,3,7]=>[7,1]=>5760
[3,4,6,8,2,5,7,1]=>[7,1]=>5760
[1,8,5,6,4,2,3,7]=>[7,1]=>5760
[1,8,7,6,2,4,5,3]=>[5,2,1]=>4032
[6,4,8,5,7,3,1,2]=>[8]=>5040
[1,6,4,7,2,5,8,3]=>[4,3,1]=>3360
[2,7,5,1,8,6,3,4]=>[7,1]=>5760
[4,7,1,6,5,3,8,2]=>[4,3,1]=>3360
[1,7,5,6,4,8,2,3]=>[5,2,1]=>4032
[8,3,1,4,6,2,7,5]=>[6,1,1]=>3360
[7,2,6,4,5,8,1,3]=>[3,2,1,1,1]=>1120
[4,6,7,8,9,1,2,3,5]=>[7,2]=>25920
[5,7,8,9,1,2,3,4,6]=>[7,2]=>25920
[6,4,5,7,3,8,2,9,1,10]=>[4,3,2,1]=>151200
[2,7,1,5,3,8,6,4]=>[8]=>5040
[3,5,7,2,8,4,1,6]=>[5,3]=>2688
[2,4,3,8,5,1,7,6]=>[5,1,1,1]=>1344
[7,3,2,1,4,8,6,5]=>[6,2]=>3360
[2,8,3,4,1,7,6,5]=>[4,2,1,1]=>2520
[4,7,6,8,2,5,3,1]=>[5,3]=>2688
[2,6,7,1,4,5,8,3]=>[5,3]=>2688
[8,7,2,6,1,5,3,4]=>[5,3]=>2688
[6,2,5,3,4,7,1,8]=>[3,3,1,1]=>1120
[2,7,3,4,1,5,8,6]=>[6,1,1]=>3360
[2,5,8,1,6,7,3,4]=>[8]=>5040
[6,2,8,3,4,5,1,7]=>[7,1]=>5760
[3,6,4,1,2,5,8,7]=>[3,3,2]=>1120
[3,5,4,1,6,2,8,7]=>[3,3,2]=>1120
[4,5,7,2,8,3,1,6]=>[8]=>5040
[8,3,6,2,7,5,4,1]=>[6,2]=>3360
[8,4,2,6,5,3,7,1]=>[4,2,1,1]=>2520
[5,4,2,7,1,8,6,3]=>[6,2]=>3360
[4,1,7,6,5,3,2,8]=>[6,1,1]=>3360
[2,3,6,7,1,8,5,4]=>[8]=>5040
[3,6,1,2,7,8,5,4]=>[4,2,2]=>1260
[4,5,1,8,7,6,3,2]=>[7,1]=>5760
[8,4,5,2,7,6,3,1]=>[3,2,2,1]=>1680
[4,1,3,6,7,5,2,8]=>[6,1,1]=>3360
[3,1,4,5,7,6,2,8]=>[6,1,1]=>3360
[4,5,1,3,6,8,7,2]=>[4,3,1]=>3360
[3,8,5,1,2,4,6,7]=>[8]=>5040
[8,5,1,2,4,3,6,7]=>[5,3]=>2688
[5,8,4,1,2,3,6,7]=>[8]=>5040
[3,5,8,1,4,2,7,6]=>[7,1]=>5760
[2,8,5,7,1,4,3,6]=>[8]=>5040
[4,8,7,5,1,2,3,6]=>[3,3,2]=>1120
[8,1,2,4,6,3,7,5]=>[6,1,1]=>3360
[7,6,1,4,2,3,8,5]=>[7,1]=>5760
[6,1,2,7,8,4,3,5]=>[6,2]=>3360
[7,8,1,2,5,3,4,6]=>[7,1]=>5760
[1,8,4,7,5,2,3,6]=>[3,3,1,1]=>1120
[8,4,7,2,1,6,3,5]=>[3,2,2,1]=>1680
[4,5,8,2,1,6,7,3]=>[4,2,1,1]=>2520
[4,8,1,5,3,6,7,2]=>[4,2,1,1]=>2520
[7,1,5,3,6,8,2,4]=>[5,3]=>2688
[4,5,2,6,1,8,3,7]=>[8]=>5040
[5,1,8,6,7,3,4,2]=>[8]=>5040
[6,5,2,4,1,7,8,3]=>[7,1]=>5760
[5,4,8,2,1,3,6,7]=>[4,2,2]=>1260
[1,4,8,3,2,6,5,7]=>[6,1,1]=>3360
[1,3,8,4,2,7,5,6]=>[6,1,1]=>3360
[7,2,8,3,1,4,5,6]=>[4,3,1]=>3360
[8,1,3,2,7,5,4,6]=>[7,1]=>5760
[9,8,7,5,6,4,3,2,10,1]=>[3,3,2,2]=>25200
[8,7,5,4,6,3,2,9,1]=>[3,3,2,1]=>10080
[8,7,4,6,5,3,2,9,1]=>[3,3,2,1]=>10080
[2,3,4,7,8,9,6,5,1]=>[7,2]=>25920
[2,3,6,7,8,9,5,4,1]=>[5,4]=>18144
[2,5,6,7,8,9,4,3,1]=>[7,2]=>25920
[2,3,4,5,6,1,9,8,7]=>[6,2,1]=>30240
[2,3,4,5,1,9,8,7,6]=>[5,2,2]=>9072
[2,3,4,5,6,9,10,8,7,1]=>[9,1]=>403200
[2,3,4,1,8,9,7,6,5]=>[4,4,1]=>11340
[2,3,4,5,8,9,10,7,6,1]=>[8,2]=>226800
[2,3,1,7,8,9,6,5,4]=>[4,3,2]=>15120
[2,3,4,7,8,9,10,6,5,1]=>[6,4]=>151200
[2,1,6,7,8,9,5,4,3]=>[4,3,2]=>15120
[2,3,6,7,8,9,10,5,4,1]=>[8,2]=>226800
[2,5,6,7,8,9,10,4,3,1]=>[7,3]=>172800
[9,10,2,4,6,8,1,3,5,7]=>[9,1]=>403200
[7,8,2,4,6,10,1,3,5,9]=>[4,3,2,1]=>151200
[9,7,10,2,4,6,8,1,3,5]=>[9,1]=>403200
[8,9,10,7,2,4,6,1,3,5]=>[5,3,2]=>120960
[5,6,2,4,8,10,1,3,7,9]=>[9,1]=>403200
[5,6,9,10,2,4,8,1,3,7]=>[8,2]=>226800
[7,5,8,2,4,6,10,1,3,9]=>[6,3,1]=>201600
[7,9,5,10,2,4,6,8,1,3]=>[9,1]=>403200
[5,8,9,10,7,2,4,6,1,3]=>[7,3]=>172800
[6,7,8,5,2,4,10,1,3,9]=>[10]=>362880
[9,6,7,5,10,2,4,8,1,3]=>[5,2,2,1]=>90720
[8,9,6,10,5,7,2,4,1,3]=>[9,1]=>403200
[7,8,9,10,6,5,2,4,1,3]=>[8,2]=>226800
[3,4,2,6,8,10,1,5,7,9]=>[8,2]=>226800
[3,4,9,10,2,6,8,1,5,7]=>[9,1]=>403200
[3,4,7,8,2,6,10,1,5,9]=>[9,1]=>403200
[9,3,4,7,10,2,6,8,1,5]=>[5,2,2,1]=>90720
[8,9,10,3,4,7,2,6,1,5]=>[6,4]=>151200
[5,3,6,2,4,8,10,1,7,9]=>[7,3]=>172800
[5,3,6,9,10,2,4,8,1,7]=>[6,3,1]=>201600
[5,7,3,8,2,4,6,10,1,9]=>[9,1]=>403200
[5,7,9,3,10,2,4,6,8,1]=>[7,3]=>172800
[8,5,9,10,3,7,2,4,6,1]=>[6,4]=>151200
[3,6,7,8,5,2,4,10,1,9]=>[7,2,1]=>259200
[9,3,6,7,5,10,2,4,8,1]=>[9,1]=>403200
[6,8,3,9,10,5,7,2,4,1]=>[4,2,2,1,1]=>56700
[7,8,9,10,3,6,5,2,4,1]=>[7,2,1]=>259200
[4,5,6,3,2,8,10,1,7,9]=>[5,3,2]=>120960
[4,5,6,3,9,10,2,8,1,7]=>[9,1]=>403200
[7,4,5,3,8,2,6,10,1,9]=>[10]=>362880
[7,4,5,9,3,10,2,6,8,1]=>[8,2]=>226800
[4,8,5,9,10,3,7,2,6,1]=>[7,2,1]=>259200
[6,7,4,8,3,5,2,10,1,9]=>[8,2]=>226800
[6,7,9,4,3,5,10,2,8,1]=>[9,1]=>403200
[8,6,9,4,10,3,5,7,2,1]=>[5,4,1]=>181440
[7,4,8,9,10,6,3,5,2,1]=>[6,3,1]=>201600
[5,6,7,8,4,3,2,10,1,9]=>[6,4]=>151200
[9,5,6,7,4,3,10,2,8,1]=>[8,2]=>226800
[8,9,5,6,4,10,3,7,2,1]=>[8,2]=>226800
[7,8,9,5,10,4,6,3,2,1]=>[6,4]=>151200
[11,12,2,4,6,8,10,1,3,5,7,9]=>[7,4,1]=>17107200
[7,8,11,12,2,4,6,10,1,3,5,9]=>[6,6]=>6652800
[11,8,9,7,12,2,4,6,10,1,3,5]=>[5,3,2,2]=>3991680
[9,10,11,12,8,7,2,4,6,1,3,5]=>[6,4,2]=>9979200
[5,6,11,12,2,4,8,10,1,3,7,9]=>[7,5]=>13685760
[11,5,6,9,12,2,4,8,10,1,3,7]=>[11,1]=>43545600
[10,11,12,5,6,9,2,4,8,1,3,7]=>[5,5,2]=>4790016
[7,5,8,11,12,2,4,6,10,1,3,9]=>[12]=>39916800
[7,9,11,5,12,2,4,6,8,10,1,3]=>[7,4,1]=>17107200
[5,8,9,10,7,2,4,6,12,1,3,11]=>[5,4,3]=>7983360
[8,10,5,11,12,7,9,2,4,6,1,3]=>[9,3]=>17740800
[6,7,8,5,2,4,10,12,1,3,9,11]=>[12]=>39916800
[6,7,8,5,11,12,2,4,10,1,3,9]=>[5,5,2]=>4790016
[6,10,7,11,12,5,9,2,4,8,1,3]=>[9,3]=>17740800
[8,9,6,10,5,7,2,4,12,1,3,11]=>[7,4,1]=>17107200
[8,9,11,6,5,7,12,2,4,10,1,3]=>[10,1,1]=>23950080
[9,6,10,11,12,8,5,7,2,4,1,3]=>[12]=>39916800
[7,8,9,10,6,5,2,4,12,1,3,11]=>[6,4,2]=>9979200
[11,7,8,9,6,5,12,2,4,10,1,3]=>[5,2,2,2,1]=>1995840
[10,11,7,8,6,12,5,9,2,4,1,3]=>[7,5]=>13685760
[9,10,11,7,12,6,8,5,2,4,1,3]=>[11,1]=>43545600
[3,4,2,6,8,10,12,1,5,7,9,11]=>[12]=>39916800
[3,4,11,12,2,6,8,10,1,5,7,9]=>[11,1]=>43545600
[3,4,9,10,2,6,8,12,1,5,7,11]=>[4,4,3,1]=>4989600
[11,3,4,9,12,2,6,8,10,1,5,7]=>[11,1]=>43545600
[3,4,7,8,2,6,10,12,1,5,9,11]=>[11,1]=>43545600
[3,10,11,12,4,7,9,2,6,8,1,5]=>[3,3,3,3]=>246400
[8,9,10,3,4,7,2,6,12,1,5,11]=>[12]=>39916800
[10,11,8,12,3,4,7,9,2,6,1,5]=>[11,1]=>43545600
[9,10,11,12,8,3,4,7,2,6,1,5]=>[7,5]=>13685760
[5,3,6,11,12,2,4,8,10,1,7,9]=>[5,3,3,1]=>5322240
[5,3,6,9,10,2,4,8,12,1,7,11]=>[5,3,3,1]=>5322240
[5,11,3,6,9,12,2,4,8,10,1,7]=>[10,1,1]=>23950080
[5,10,11,12,3,6,9,2,4,8,1,7]=>[4,4,3,1]=>4989600
[5,7,3,8,11,12,2,4,6,10,1,9]=>[3,3,2,2,1,1]=>1663200
[5,7,9,3,10,2,4,6,8,12,1,11]=>[7,5]=>13685760
[5,7,9,11,3,12,2,4,6,8,10,1]=>[6,4,2]=>9979200
[10,5,7,11,12,3,9,2,4,6,8,1]=>[12]=>39916800
[8,5,9,10,3,7,2,4,6,12,1,11]=>[6,6]=>6652800
[3,6,7,8,5,11,12,2,4,10,1,9]=>[10,1,1]=>23950080
[9,3,6,7,5,10,2,4,8,12,1,11]=>[11,1]=>43545600
[9,3,6,7,11,5,12,2,4,8,10,1]=>[7,5]=>13685760
[6,8,9,3,11,5,7,12,2,4,10,1]=>[11,1]=>43545600
[9,6,10,11,12,3,8,5,7,2,4,1]=>[6,4,2]=>9979200
[11,7,8,9,3,6,5,12,2,4,10,1]=>[11,1]=>43545600
[10,11,7,8,3,6,12,5,9,2,4,1]=>[10,1,1]=>23950080
[9,10,11,7,12,3,6,8,5,2,4,1]=>[5,4,2,1]=>11975040
[4,5,6,3,11,12,2,8,10,1,7,9]=>[7,4,1]=>17107200
[7,4,5,3,8,2,6,10,12,1,9,11]=>[9,3]=>17740800
[7,4,5,9,11,3,12,2,6,8,10,1]=>[9,3]=>17740800
[7,10,4,5,11,12,3,9,2,6,8,1]=>[12]=>39916800
[4,8,11,5,9,3,7,12,2,6,10,1]=>[7,4,1]=>17107200
[6,7,4,8,3,5,11,12,2,10,1,9]=>[11,1]=>43545600
[6,7,9,4,3,5,10,2,8,12,1,11]=>[11,1]=>43545600
[6,7,9,4,11,3,5,12,2,8,10,1]=>[11,1]=>43545600
[10,6,7,4,11,12,3,5,9,2,8,1]=>[5,3,2,1,1]=>7983360
[8,6,9,4,10,3,5,7,2,12,1,11]=>[7,4,1]=>17107200
[8,6,9,11,4,3,5,7,12,2,10,1]=>[12]=>39916800
[8,10,6,11,4,12,3,5,7,9,2,1]=>[12]=>39916800
[6,9,4,10,11,12,8,3,5,7,2,1]=>[5,4,3]=>7983360
[9,7,10,4,11,12,6,8,3,5,2,1]=>[10,1,1]=>23950080
[5,6,7,8,4,3,2,10,12,1,9,11]=>[5,4,3]=>7983360
[5,6,7,8,4,3,11,12,2,10,1,9]=>[11,1]=>43545600
[9,5,6,7,4,11,3,12,2,8,10,1]=>[12]=>39916800
[5,10,6,7,4,11,12,3,9,2,8,1]=>[5,4,2,1]=>11975040
[10,8,5,6,11,4,12,3,7,9,2,1]=>[5,5,2]=>4790016
[7,8,9,11,5,4,6,3,12,2,10,1]=>[11,1]=>43545600
[8,9,5,10,11,12,7,4,6,3,2,1]=>[11,1]=>43545600
[6,7,8,9,10,5,4,3,2,12,1,11]=>[6,4,2]=>9979200
[8,9,10,11,6,12,5,7,4,3,2,1]=>[6,4,2]=>9979200
[7,6,1,8,2,5,4,3]=>[5,3]=>2688
[8,4,1,6,7,3,5,2]=>[6,2]=>3360
[5,8,4,2,1,6,3,7]=>[5,2,1]=>4032
[7,6,4,1,2,5,3,8]=>[4,3,1]=>3360
[5,4,2,8,1,6,3,7]=>[5,2,1]=>4032
[8,7,2,6,4,5,3,1]=>[3,3,2]=>1120
[4,8,6,3,5,2,1,7]=>[7,1]=>5760
[5,8,6,3,2,7,1,4]=>[8]=>5040
[5,7,6,3,2,4,8,1]=>[5,3]=>2688
[4,5,1,6,8,2,7,3]=>[7,1]=>5760
[1,2,4,5,6,8,10,9,3,7]=>[6,2,1,1]=>151200
[1,2,3,5,7,8,10,6,9,4]=>[4,2,1,1,1,1]=>18900
[1,2,4,5,7,8,10,3,9,6]=>[7,1,1,1]=>86400
[1,2,4,6,7,5,10,8,3,9]=>[7,1,1,1]=>86400
[1,3,4,2,7,8,10,5,9,6]=>[5,3,1,1]=>120960
[1,3,4,6,7,2,10,8,5,9]=>[4,4,1,1]=>56700
[1,2,3,5,6,9,8,10,7,4]=>[7,1,1,1]=>86400
[1,2,4,5,6,9,8,10,3,7]=>[5,3,1,1]=>120960
[1,2,3,5,7,9,6,10,8,4]=>[7,1,1,1]=>86400
[1,2,4,5,7,9,3,10,8,6]=>[4,4,1,1]=>56700
[1,2,4,6,5,9,7,10,3,8]=>[4,2,1,1,1,1]=>18900
[1,3,4,2,7,9,5,10,8,6]=>[4,3,2,1]=>151200
[1,3,4,6,2,9,7,10,5,8]=>[6,2,1,1]=>151200
[1,2,3,5,8,7,9,6,10,4]=>[7,1,1,1]=>86400
[1,2,4,5,8,7,9,3,10,6]=>[4,4,1,1]=>56700
[1,2,4,6,8,5,9,3,10,7]=>[5,3,1,1]=>120960
[1,2,4,7,6,8,5,9,3,10]=>[7,1,1,1]=>86400
[1,3,4,2,8,7,9,5,10,6]=>[4,3,2,1]=>151200
[1,3,4,6,8,2,9,5,10,7]=>[4,3,2,1]=>151200
[1,3,4,7,6,8,2,9,5,10]=>[4,4,1,1]=>56700
[1,2,3,6,5,9,7,10,8,4]=>[5,1,1,1,1,1]=>6048
[1,2,4,6,3,9,7,10,8,5]=>[7,1,1,1]=>86400
[1,2,5,4,6,9,7,10,3,8]=>[4,2,1,1,1,1]=>18900
[1,3,2,6,4,9,7,10,8,5]=>[6,2,1,1]=>151200
[1,3,5,2,6,9,7,10,4,8]=>[6,2,1,1]=>151200
[1,2,3,6,8,5,9,7,10,4]=>[7,1,1,1]=>86400
[1,2,4,6,8,3,9,7,10,5]=>[5,3,1,1]=>120960
[1,2,5,4,8,6,9,3,10,7]=>[3,3,1,1,1,1]=>8400
[1,2,5,7,4,8,6,9,3,10]=>[7,1,1,1]=>86400
[1,3,2,6,8,4,9,7,10,5]=>[5,2,2,1]=>90720
[1,3,5,2,8,6,9,4,10,7]=>[5,3,1,1]=>120960
[1,3,5,7,2,8,6,9,4,10]=>[5,3,1,1]=>120960
[1,4,3,5,8,2,9,6,10,7]=>[5,3,1,1]=>120960
[1,4,3,7,5,8,2,9,6,10]=>[3,3,1,1,1,1]=>8400
[2,1,3,6,4,9,7,10,8,5]=>[6,2,1,1]=>151200
[2,1,5,3,6,9,7,10,4,8]=>[5,2,2,1]=>90720
[2,1,3,6,8,4,9,7,10,5]=>[5,2,2,1]=>90720
[2,1,5,3,8,6,9,4,10,7]=>[4,3,2,1]=>151200
[2,1,5,7,3,8,6,9,4,10]=>[5,2,2,1]=>90720
[2,4,1,5,8,3,9,6,10,7]=>[7,3]=>172800
[2,4,1,7,5,8,3,9,6,10]=>[5,3,1,1]=>120960
[1,6,3,7,2,4,8,5]=>[6,1,1]=>3360
[8,9,7,6,5,4,3,1,2]=>[2,2,2,2,1]=>945
[8,6,7,5,4,3,2,1,9]=>[4,2,2,1]=>11340
[8,7,9,6,5,4,3,1,2]=>[4,2,2,1]=>11340
[9,7,8,6,5,4,3,1,2]=>[6,2,1]=>30240
[4,3,1,6,7,2,5,8]=>[5,2,1]=>4032
[6,3,1,5,7,2,4,8]=>[4,3,1]=>3360
[8,7,5,4,3,6,9,2,1]=>[5,2,1,1]=>18144
[8,7,6,9,5,3,4,2,1]=>[6,2,1]=>30240
[8,7,9,6,5,4,2,3,1]=>[4,2,2,1]=>11340
[5,2,1,4,8,6,7,3]=>[4,1,1,1,1]=>420
[4,5,2,1,3,7,6,8]=>[3,2,2,1]=>1680
[8,2,7,4,1,6,5,3]=>[5,1,1,1]=>1344
[3,2,8,4,1,6,5,7]=>[5,1,1,1]=>1344
[7,1,6,5,4,2,8,3]=>[6,2]=>3360
[7,1,8,4,2,3,6,5]=>[7,1]=>5760
[2,7,6,4,5,1,8,3]=>[6,1,1]=>3360
[3,6,8,1,5,7,4,2]=>[7,1]=>5760
[2,8,3,1,6,7,4,5]=>[7,1]=>5760
[4,5,6,8,2,1,7,3]=>[5,2,1]=>4032
[4,5,6,8,1,3,7,2]=>[5,2,1]=>4032
[4,5,8,3,2,1,7,6]=>[5,2,1]=>4032
[4,5,1,3,2,6,7,8]=>[3,2,1,1,1]=>1120
[4,7,3,2,1,6,5,8]=>[5,1,1,1]=>1344
[4,7,8,3,5,1,6,2]=>[7,1]=>5760
[4,7,1,3,5,6,2,8]=>[3,2,1,1,1]=>1120
[4,8,3,2,1,6,7,5]=>[5,1,1,1]=>1344
[5,2,8,1,4,6,7,3]=>[3,2,1,1,1]=>1120
[5,6,3,7,8,1,4,2]=>[5,2,1]=>4032
[5,7,1,4,3,6,2,8]=>[3,2,1,1,1]=>1120
[6,2,3,7,1,5,4,8]=>[3,2,1,1,1]=>1120
[6,2,8,1,5,4,7,3]=>[3,2,1,1,1]=>1120
[6,1,3,4,5,2,7,8]=>[3,1,1,1,1,1]=>112
[7,1,3,4,5,6,2,8]=>[3,1,1,1,1,1]=>112
[6,5,2,7,8,4,3,1]=>[8]=>5040
[7,5,3,6,4,2,1,8]=>[4,2,1,1]=>2520
[2,3,6,5,8,4,7,1]=>[7,1]=>5760
[1,3,6,7,5,2,4,8]=>[3,2,1,1,1]=>1120
[1,5,2,6,8,7,3,4]=>[7,1]=>5760
[6,5,4,3,2,1,8,9,7]=>[3,2,2,2]=>2520
[6,3,4,1,2,7,8,9,10,5]=>[10]=>362880
[5,3,4,7,2,1,6,8]=>[7,1]=>5760
[4,2,3,7,6,1,8,5]=>[6,1,1]=>3360
[4,2,6,3,1,5,7,8]=>[5,1,1,1]=>1344
[2,1,8,7,4,3,6,5,10,9]=>[6,2,2]=>75600
[6,5,2,1,4,3,12,11,8,7,10,9]=>[6,6]=>6652800
[4,6,3,2,5,8,7,1]=>[5,1,1,1]=>1344
[5,8,4,3,2,6,1,7]=>[5,2,1]=>4032
[6,1,5,7,3,8,2,4]=>[6,2]=>3360
[1,2,7,8,6,4,3,5]=>[4,2,1,1]=>2520
[3,5,1,7,8,6,2,4]=>[5,2,1]=>4032
[2,1,4,3,6,5,7,9,10,8]=>[3,2,2,2,1]=>25200
[2,1,4,3,5,7,8,6,10,9]=>[3,2,2,2,1]=>25200
[2,1,4,3,5,7,6,9,10,8]=>[3,2,2,2,1]=>25200
[2,1,4,3,5,6,8,9,10,7]=>[4,2,2,1,1]=>56700
[2,1,3,5,6,4,8,7,10,9]=>[3,2,2,2,1]=>25200
[2,1,3,5,6,4,7,9,10,8]=>[3,3,2,1,1]=>50400
[2,1,3,5,4,7,8,6,10,9]=>[3,2,2,2,1]=>25200
[2,1,3,5,4,7,6,9,10,8]=>[3,2,2,2,1]=>25200
[2,1,3,5,4,6,8,9,10,7]=>[4,2,2,1,1]=>56700
[2,1,3,4,6,7,8,5,10,9]=>[4,2,2,1,1]=>56700
[2,1,3,4,6,7,5,9,10,8]=>[3,3,2,1,1]=>50400
[2,1,3,4,6,5,8,9,10,7]=>[4,2,2,1,1]=>56700
[2,1,3,4,5,7,8,9,10,6]=>[5,2,1,1,1]=>60480
[1,3,4,2,6,5,7,9,10,8]=>[3,3,2,1,1]=>50400
[1,3,4,2,5,7,8,6,10,9]=>[3,3,2,1,1]=>50400
[1,3,4,2,5,7,6,9,10,8]=>[3,3,2,1,1]=>50400
[1,3,4,2,5,6,8,9,10,7]=>[4,3,1,1,1]=>50400
[1,3,2,5,6,4,8,7,10,9]=>[3,2,2,2,1]=>25200
[1,3,2,5,6,4,7,9,10,8]=>[3,3,2,1,1]=>50400
[1,3,2,5,4,7,8,6,10,9]=>[3,2,2,2,1]=>25200
[1,3,2,5,4,7,6,9,10,8]=>[3,2,2,2,1]=>25200
[1,3,2,5,4,6,8,9,10,7]=>[4,2,2,1,1]=>56700
[1,3,2,4,6,7,8,5,10,9]=>[4,2,2,1,1]=>56700
[1,3,2,4,6,7,5,9,10,8]=>[3,3,2,1,1]=>50400
[1,3,2,4,6,5,8,9,10,7]=>[4,2,2,1,1]=>56700
[1,3,2,4,5,7,8,9,10,6]=>[5,2,1,1,1]=>60480
[1,2,4,5,6,3,8,7,10,9]=>[4,2,2,1,1]=>56700
[1,2,4,5,6,3,7,9,10,8]=>[4,3,1,1,1]=>50400
[1,2,4,5,3,7,8,6,10,9]=>[3,3,2,1,1]=>50400
[1,2,4,5,3,7,6,9,10,8]=>[3,3,2,1,1]=>50400
[1,2,4,5,3,6,8,9,10,7]=>[4,3,1,1,1]=>50400
[1,2,4,3,6,7,8,5,10,9]=>[4,2,2,1,1]=>56700
[1,2,4,3,6,7,5,9,10,8]=>[3,3,2,1,1]=>50400
[1,2,4,3,6,5,8,9,10,7]=>[4,2,2,1,1]=>56700
[1,2,4,3,5,7,8,9,10,6]=>[5,2,1,1,1]=>60480
[1,2,3,5,6,7,8,4,10,9]=>[5,2,1,1,1]=>60480
[1,2,3,5,6,7,4,9,10,8]=>[4,3,1,1,1]=>50400
[1,2,3,5,6,4,8,9,10,7]=>[4,3,1,1,1]=>50400
[1,2,3,5,4,7,8,9,10,6]=>[5,2,1,1,1]=>60480
[2,1,4,3,6,5,8,7,9,11,12,10]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,6,5,7,9,10,8,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,6,5,7,9,8,11,12,10]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,5,7,8,6,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,5,7,8,6,9,11,12,10]=>[3,3,2,2,1,1]=>1663200
[2,1,4,3,5,7,6,9,10,8,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,5,7,6,9,8,11,12,10]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,5,6,8,9,7,11,12,10]=>[3,3,2,2,1,1]=>1663200
[2,1,4,3,5,6,7,9,10,11,12,8]=>[5,2,2,1,1,1]=>1995840
[2,1,3,5,6,4,8,7,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,3,5,6,4,8,7,9,11,12,10]=>[3,3,2,2,1,1]=>1663200
[2,1,3,5,6,4,7,9,10,8,12,11]=>[3,3,2,2,1,1]=>1663200
[2,1,3,5,6,4,7,9,8,11,12,10]=>[3,3,2,2,1,1]=>1663200
[2,1,3,5,4,7,8,6,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,3,5,4,7,8,6,9,11,12,10]=>[3,3,2,2,1,1]=>1663200
[2,1,3,5,4,7,6,9,10,8,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,3,5,4,7,6,9,8,11,12,10]=>[3,2,2,2,2,1]=>415800
[2,1,3,5,4,6,8,9,7,11,12,10]=>[3,3,2,2,1,1]=>1663200
[2,1,3,5,4,6,7,9,10,11,12,8]=>[5,2,2,1,1,1]=>1995840
[2,1,3,4,6,7,5,9,10,8,12,11]=>[3,3,2,2,1,1]=>1663200
[2,1,3,4,6,7,5,9,8,11,12,10]=>[3,3,2,2,1,1]=>1663200
[2,1,3,4,6,5,8,9,7,11,12,10]=>[3,3,2,2,1,1]=>1663200
[2,1,3,4,6,5,7,9,10,11,12,8]=>[5,2,2,1,1,1]=>1995840
[2,1,3,4,5,7,8,9,10,6,12,11]=>[5,2,2,1,1,1]=>1995840
[2,1,3,4,5,7,6,9,10,11,12,8]=>[5,2,2,1,1,1]=>1995840
[1,3,4,2,6,5,8,7,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[1,3,4,2,6,5,8,7,9,11,12,10]=>[3,3,2,2,1,1]=>1663200
[1,3,4,2,6,5,7,9,10,8,12,11]=>[3,3,2,2,1,1]=>1663200
[1,3,4,2,6,5,7,9,8,11,12,10]=>[3,3,2,2,1,1]=>1663200
[1,3,4,2,5,7,8,6,10,9,12,11]=>[3,3,2,2,1,1]=>1663200
[1,3,4,2,5,7,6,9,10,8,12,11]=>[3,3,2,2,1,1]=>1663200
[1,3,4,2,5,7,6,9,8,11,12,10]=>[3,3,2,2,1,1]=>1663200
[1,3,2,5,6,4,8,7,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[1,3,2,5,6,4,8,7,9,11,12,10]=>[3,3,2,2,1,1]=>1663200
[1,3,2,5,6,4,7,9,10,8,12,11]=>[3,3,2,2,1,1]=>1663200
[1,3,2,5,6,4,7,9,8,11,12,10]=>[3,3,2,2,1,1]=>1663200
[1,3,2,5,4,7,8,6,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[1,3,2,5,4,7,8,6,9,11,12,10]=>[3,3,2,2,1,1]=>1663200
[1,3,2,5,4,7,6,9,10,8,12,11]=>[3,2,2,2,2,1]=>415800
[1,3,2,5,4,7,6,9,8,11,12,10]=>[3,2,2,2,2,1]=>415800
[1,3,2,5,4,6,8,9,7,11,12,10]=>[3,3,2,2,1,1]=>1663200
[1,3,2,5,4,6,7,9,10,11,12,8]=>[5,2,2,1,1,1]=>1995840
[1,3,2,4,6,7,5,9,10,8,12,11]=>[3,3,2,2,1,1]=>1663200
[1,3,2,4,6,7,5,9,8,11,12,10]=>[3,3,2,2,1,1]=>1663200
[1,3,2,4,6,5,8,9,7,11,12,10]=>[3,3,2,2,1,1]=>1663200
[1,3,2,4,6,5,7,9,10,11,12,8]=>[5,2,2,1,1,1]=>1995840
[1,3,2,4,5,7,8,9,10,6,12,11]=>[5,2,2,1,1,1]=>1995840
[1,3,2,4,5,7,6,9,10,11,12,8]=>[5,2,2,1,1,1]=>1995840
[1,2,4,5,3,7,8,6,10,9,12,11]=>[3,3,2,2,1,1]=>1663200
[1,2,4,5,3,7,6,9,10,8,12,11]=>[3,3,2,2,1,1]=>1663200
[1,2,4,5,3,7,6,9,8,11,12,10]=>[3,3,2,2,1,1]=>1663200
[1,2,4,3,6,7,5,9,10,8,12,11]=>[3,3,2,2,1,1]=>1663200
[1,2,4,3,6,7,5,9,8,11,12,10]=>[3,3,2,2,1,1]=>1663200
[1,2,4,3,6,5,8,9,7,11,12,10]=>[3,3,2,2,1,1]=>1663200
[1,2,4,3,6,5,7,9,10,11,12,8]=>[5,2,2,1,1,1]=>1995840
[1,2,4,3,5,7,8,9,10,6,12,11]=>[5,2,2,1,1,1]=>1995840
[1,2,4,3,5,7,6,9,10,11,12,8]=>[5,2,2,1,1,1]=>1995840
[1,2,3,5,6,7,8,4,10,9,12,11]=>[5,2,2,1,1,1]=>1995840
[1,2,3,5,4,7,8,9,10,6,12,11]=>[5,2,2,1,1,1]=>1995840
[1,2,3,5,4,7,6,9,10,11,12,8]=>[5,2,2,1,1,1]=>1995840
[2,3,4,9,6,7,8,5,1]=>[5,4]=>18144
[2,3,9,5,6,7,8,4,1]=>[5,4]=>18144
[2,9,4,5,6,7,8,3,1]=>[6,3]=>20160
[9,3,4,5,6,7,8,2,1]=>[7,2]=>25920
[2,3,4,5,6,10,8,9,7,1]=>[7,3]=>172800
[2,3,4,1,9,7,8,6,5]=>[4,3,2]=>15120
[2,3,4,5,10,7,8,9,6,1]=>[6,4]=>151200
[2,3,1,9,6,7,8,5,4]=>[4,3,2]=>15120
[2,3,4,10,6,7,8,9,5,1]=>[5,5]=>72576
[2,1,9,5,6,7,8,4,3]=>[5,2,2]=>9072
[2,3,10,5,6,7,8,9,4,1]=>[6,4]=>151200
[1,9,4,5,6,7,8,3,2]=>[6,2,1]=>30240
[2,10,4,5,6,7,8,9,3,1]=>[7,3]=>172800
[10,3,4,5,6,7,8,9,2,1]=>[8,2]=>226800
[5,6,4,7,3,9,1,8,2]=>[5,3,1]=>24192
[5,6,4,9,1,8,2,7,3]=>[4,3,2]=>15120
[5,9,1,8,2,7,3,6,4]=>[9]=>40320
[9,1,8,2,7,3,6,4,5]=>[9]=>40320
[5,4,3,8,1,7,2,6]=>[5,2,1]=>4032
[5,4,9,1,8,2,7,3,6]=>[8,1]=>45360
[5,4,6,3,9,1,8,2,7]=>[9]=>40320
[5,4,6,3,7,2,9,1,8]=>[5,4]=>18144
[6,5,7,4,8,3,10,1,9,2]=>[8,1,1]=>226800
[5,6,4,8,2,9,1,7,3]=>[9]=>40320
[6,5,7,4,10,1,9,2,8,3]=>[7,2,1]=>259200
[5,7,3,9,1,8,2,6,4]=>[2,2,2,2,1]=>945
[6,5,10,1,9,2,8,3,7,4]=>[10]=>362880
[6,4,9,1,8,2,7,3,5]=>[4,4,1]=>11340
[4,5,9,1,8,2,7,3,6]=>[6,2,1]=>30240
[5,10,1,9,2,8,3,7,4,6]=>[8,2]=>226800
[6,4,5,3,9,1,8,2,7]=>[7,2]=>25920
[5,6,4,10,1,9,2,8,3,7]=>[7,2,1]=>259200
[5,4,7,3,6,2,9,1,8]=>[9]=>40320
[5,6,4,7,3,10,1,9,2,8]=>[5,5]=>72576
[5,6,4,7,3,8,2,10,1,9]=>[10]=>362880
[7,3,1,5,6,8,4,2]=>[8]=>5040
[2,10,1,3,4,5,6,9,7,8]=>[10]=>362880
[2,9,1,3,4,5,6,7,10,8]=>[10]=>362880
[12,1,2,3,4,5,6,7,8,11,9,10]=>[12]=>39916800
[2,11,1,3,4,5,6,7,10,8,9]=>[11]=>3628800
[10,3,1,2,4,5,6,9,7,8]=>[10]=>362880
[3,1,10,2,4,5,6,9,7,8]=>[10]=>362880
[9,3,1,2,4,5,6,7,10,8]=>[10]=>362880
[3,1,9,2,4,5,6,7,10,8]=>[10]=>362880
[2,10,1,3,4,5,6,7,8,11,9]=>[11]=>3628800
[5,7,8,1,6,2,3,4]=>[8]=>5040
[1,6,4,2,7,3,8,5]=>[4,3,1]=>3360
[1,4,2,5,8,6,3,7]=>[6,1,1]=>3360
[5,4,3,2,1,8,9,7,6]=>[4,2,2,1]=>11340
[4,3,2,1,8,9,7,6,5]=>[4,2,2,1]=>11340
[3,2,1,8,9,7,6,5,4]=>[4,2,2,1]=>11340
[2,1,8,9,7,6,5,4,3]=>[4,2,2,1]=>11340
[9,8,3,4,5,6,7,1,2]=>[4,1,1,1,1,1]=>756
[9,8,2,3,4,5,6,1,7]=>[9]=>40320
[6,2,8,7,3,4,5,1]=>[7,1]=>5760
[9,4,5,6,7,8,2,1,3]=>[9]=>40320
[9,3,4,5,6,7,2,1,8]=>[6,3]=>20160
[11,2,1,3,4,5,6,7,8,9,10]=>[10,1]=>3991680
[12,11,1,2,3,4,5,6,7,8,9,10]=>[12]=>39916800
[10,9,3,4,5,6,7,8,1,2]=>[4,1,1,1,1,1,1]=>1260
[10,9,2,3,4,5,6,7,1,8]=>[10]=>362880
[7,2,9,8,3,4,5,6,1]=>[5,3,1]=>24192
[9,8,2,3,4,5,1,6,7]=>[6,3]=>20160
[7,3,4,8,5,6,2,1]=>[6,1,1]=>3360
[9,5,6,7,8,2,1,3,4]=>[5,4]=>18144
[7,3,6,8,4,5,2,1]=>[8]=>5040
[8,3,9,4,5,6,7,2,1]=>[5,1,1,1,1]=>3024
[10,4,5,6,7,8,9,2,1,3]=>[6,4]=>151200
[9,3,4,5,6,2,1,7,8]=>[5,4]=>18144
[10,3,4,5,6,7,8,2,1,9]=>[7,3]=>172800
[12,2,1,3,4,5,6,7,8,9,10,11]=>[11,1]=>43545600
[5,6,2,8,3,1,7,4]=>[5,2,1]=>4032
[1,4,7,5,6,2,8,3]=>[4,3,1]=>3360
[1,7,4,8,3,5,6,2]=>[7,1]=>5760
[5,3,1,4,8,6,2,7]=>[6,1,1]=>3360
[5,2,4,8,3,1,6,7]=>[7,1]=>5760
[7,4,5,1,8,6,2,3]=>[4,3,1]=>3360
[8,1,5,7,6,3,2,4]=>[5,3]=>2688
[1,8,6,7,5,3,2,4]=>[4,2,1,1]=>2520
[7,4,8,3,1,6,5,2]=>[4,3,1]=>3360
[8,1,5,3,7,6,2,4]=>[7,1]=>5760
[6,1,4,2,3,5,7,8]=>[6,1,1]=>3360
[6,5,1,8,3,7,4,2]=>[8]=>5040
[7,1,4,3,8,6,5,2]=>[5,2,1]=>4032
[8,5,4,1,7,3,2,6]=>[5,3]=>2688
[4,5,3,8,1,7,6,2]=>[5,2,1]=>4032
[4,7,6,3,2,8,5,1]=>[5,3]=>2688
[5,7,6,3,8,2,4,1]=>[5,3]=>2688
[6,8,4,7,1,2,5,3]=>[8]=>5040
[1,3,7,6,8,4,5,2]=>[5,2,1]=>4032
[6,1,5,7,2,8,3,4]=>[8]=>5040
[1,8,7,2,5,6,3,4]=>[3,2,1,1,1]=>1120
[1,8,2,6,7,4,3,5]=>[5,2,1]=>4032
[2,5,4,8,7,6,1,3]=>[4,3,1]=>3360
[1,8,7,6,3,5,4,2]=>[5,2,1]=>4032
[1,8,5,7,6,4,3,2]=>[5,2,1]=>4032
[1,6,2,7,3,8,4,9,5]=>[6,2,1]=>30240
[1,8,5,2,9,6,3,10,7,4]=>[4,4,1,1]=>56700
[7,2,4,1,8,5,3,6]=>[4,3,1]=>3360
[4,7,2,6,1,8,3,5]=>[5,3]=>2688
[7,5,3,2,1,6,8,4]=>[6,1,1]=>3360
[6,8,1,3,4,2,5,7]=>[8]=>5040
[3,6,1,4,7,8,2,5]=>[5,2,1]=>4032
[2,5,7,1,3,6,4,8]=>[6,1,1]=>3360
[1,4,7,2,5,3,6,8]=>[3,2,1,1,1]=>1120
[4,5,3,1,2,6,8,7]=>[2,2,2,1,1]=>420
[4,5,1,3,8,2,6,7]=>[5,3]=>2688
[4,1,5,3,2,7,6,8]=>[5,2,1]=>4032
[7,3,5,1,4,2,6,8]=>[7,1]=>5760
[6,2,1,7,4,3,8,5]=>[4,3,1]=>3360
[2,4,3,6,7,1,5,8]=>[4,2,1,1]=>2520
[7,3,5,2,1,6,4,8]=>[6,1,1]=>3360
[4,6,5,2,1,3,7,8]=>[6,1,1]=>3360
[2,5,6,1,4,3,7,8]=>[4,2,1,1]=>2520
[6,1,5,3,7,2,4,8]=>[4,3,1]=>3360
[3,6,5,4,1,7,2,8]=>[3,3,1,1]=>1120
[10,9,3,8,7,6,5,4,2,1]=>[2,2,2,2,1,1]=>4725
[10,9,8,6,5,4,7,3,2,1]=>[2,2,2,2,1,1]=>4725
[9,11,1,2,3,4,5,6,7,8,10]=>[6,5]=>1330560
[6,7,1,9,2,3,4,5,8]=>[6,3]=>20160
[6,1,8,9,2,3,4,5,7]=>[6,3]=>20160
[8,1,9,10,2,3,4,5,6,7]=>[4,3,3]=>50400
[6,8,7,5,4,2,1,3]=>[6,2]=>3360
[1,6,8,7,3,2,4,5]=>[3,2,2,1]=>1680
[8,7,5,4,6,1,3,2]=>[7,1]=>5760
[1,7,8,2,4,6,3,5]=>[6,1,1]=>3360
[7,5,4,8,1,3,6,2]=>[8]=>5040
[5,6,1,8,4,3,7,2]=>[7,1]=>5760
[1,8,2,6,7,5,4,3]=>[4,3,1]=>3360
[2,7,5,1,6,8,3,4]=>[8]=>5040
[3,8,6,1,2,4,5,7]=>[4,4]=>1260
[1,8,5,3,2,7,4,6]=>[7,1]=>5760
[1,8,4,7,2,3,5,6]=>[7,1]=>5760
[3,2,8,1,7,5,4,6]=>[7,1]=>5760
[3,4,5,6,2,1,7,8,9]=>[6,1,1,1]=>10080
[3,4,5,2,1,6,7,8,9]=>[3,2,1,1,1,1]=>2520
[7,1,5,6,2,3,4,8]=>[7,1]=>5760
[6,5,1,7,2,3,4,8]=>[3,2,2,1]=>1680
[1,6,8,2,7,3,4,5]=>[7,1]=>5760
[1,6,8,7,3,4,2,5]=>[4,3,1]=>3360
[4,1,3,6,7,8,5,2]=>[5,2,1]=>4032
[7,4,1,5,6,8,3,2]=>[5,3]=>2688
[4,1,2,6,7,8,5,3]=>[6,2]=>3360
[3,4,5,8,9,1,2,6,7]=>[9]=>40320
[3,4,7,8,9,1,2,5,6]=>[9]=>40320
[3,6,7,8,9,1,2,4,5]=>[5,2,2]=>9072
[3,4,5,6,1,7,2,8,9]=>[4,3,1,1]=>15120
[3,4,5,1,6,2,7,8,9]=>[6,1,1,1]=>10080
[3,4,5,6,7,10,1,2,8,9]=>[6,4]=>151200
[3,4,1,5,9,2,6,7,8]=>[7,2]=>25920
[3,4,5,6,9,10,1,2,7,8]=>[5,5]=>72576
[3,4,5,8,9,10,1,2,6,7]=>[7,3]=>172800
[1,3,7,8,9,2,4,5,6]=>[8,1]=>45360
[3,4,7,8,9,10,1,2,5,6]=>[3,3,2,2]=>25200
[2,6,7,8,9,1,3,4,5]=>[3,2,2,2]=>2520
[3,6,7,8,9,10,1,2,4,5]=>[7,3]=>172800
[3,7,8,2,1,4,5,6]=>[8]=>5040
[6,3,7,1,8,2,4,5]=>[6,2]=>3360
[2,1,4,3,6,5,10,7,9,8]=>[3,2,2,2,1]=>25200
[2,1,4,3,8,5,7,6,10,9]=>[3,2,2,2,1]=>25200
[2,1,4,3,10,9,7,5,6,8]=>[3,2,2,2,1]=>25200
[2,1,4,3,10,5,6,8,9,7]=>[4,2,2,1,1]=>56700
[2,1,6,3,5,4,8,7,10,9]=>[3,2,2,2,1]=>25200
[2,1,6,3,5,4,10,7,9,8]=>[3,3,2,1,1]=>50400
[2,1,8,7,5,3,4,6,10,9]=>[3,2,2,2,1]=>25200
[2,1,10,7,5,9,4,3,6,8]=>[3,2,2,2,1]=>25200
[2,1,10,8,5,3,6,4,9,7]=>[4,2,2,1,1]=>56700
[2,1,8,3,4,6,7,5,10,9]=>[4,2,2,1,1]=>56700
[2,1,10,9,4,6,7,3,5,8]=>[3,3,2,1,1]=>50400
[2,1,10,3,9,6,4,8,5,7]=>[4,2,2,1,1]=>56700
[2,1,10,3,4,5,7,8,9,6]=>[5,2,1,1,1]=>60480
[4,1,3,2,6,5,8,7,10,9]=>[3,2,2,2,1]=>25200
[4,1,3,2,6,5,10,7,9,8]=>[3,3,2,1,1]=>50400
[4,1,3,2,8,5,7,6,10,9]=>[3,3,2,1,1]=>50400
[4,1,3,2,10,9,7,5,6,8]=>[3,3,2,1,1]=>50400
[4,1,3,2,10,5,6,8,9,7]=>[4,3,1,1,1]=>50400
[6,5,3,1,2,4,10,7,9,8]=>[3,3,2,1,1]=>50400
[8,5,3,7,2,1,4,6,10,9]=>[3,2,2,2,1]=>25200
[10,5,3,7,2,9,4,1,6,8]=>[3,2,2,2,1]=>25200
[10,5,3,8,2,1,6,4,9,7]=>[4,2,2,1,1]=>56700
[8,6,3,1,4,2,7,5,10,9]=>[4,2,2,1,1]=>56700
[10,6,3,9,4,2,7,1,5,8]=>[3,3,2,1,1]=>50400
[10,6,3,1,9,2,4,8,5,7]=>[4,2,2,1,1]=>56700
[10,7,3,1,4,5,2,8,9,6]=>[5,2,1,1,1]=>60480
[6,1,2,4,5,3,8,7,10,9]=>[4,2,2,1,1]=>56700
[6,1,2,4,5,3,10,7,9,8]=>[4,3,1,1,1]=>50400
[8,7,2,4,5,1,3,6,10,9]=>[3,3,2,1,1]=>50400
[10,7,2,4,5,9,3,1,6,8]=>[3,3,2,1,1]=>50400
[10,8,2,4,5,1,6,3,9,7]=>[4,3,1,1,1]=>50400
[8,1,7,4,2,6,3,5,10,9]=>[4,2,2,1,1]=>56700
[10,9,7,4,2,6,3,1,5,8]=>[3,3,2,1,1]=>50400
[10,1,8,4,9,6,2,3,5,7]=>[4,2,2,1,1]=>56700
[10,1,8,4,2,5,7,3,9,6]=>[5,2,1,1,1]=>60480
[8,1,2,3,5,6,7,4,10,9]=>[5,2,1,1,1]=>60480
[10,9,2,3,5,6,7,1,4,8]=>[4,3,1,1,1]=>50400
[10,1,9,3,5,6,2,8,4,7]=>[4,3,1,1,1]=>50400
[10,1,2,9,5,3,7,8,4,6]=>[5,2,1,1,1]=>60480
[2,1,4,3,6,5,8,7,12,9,11,10]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,6,5,10,7,9,8,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,6,5,12,11,9,7,8,10]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,8,5,7,6,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,8,5,7,6,12,9,11,10]=>[3,3,2,2,1,1]=>1663200
[2,1,4,3,10,9,7,5,6,8,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,12,9,7,11,6,5,8,10]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,12,11,6,8,9,5,7,10]=>[3,3,2,2,1,1]=>1663200
[2,1,4,3,12,5,6,7,9,10,11,8]=>[5,2,2,1,1,1]=>1995840
[2,1,6,3,5,4,8,7,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,6,3,5,4,8,7,12,9,11,10]=>[3,3,2,2,1,1]=>1663200
[2,1,6,3,5,4,10,7,9,8,12,11]=>[3,3,2,2,1,1]=>1663200
[2,1,6,3,5,4,12,11,9,7,8,10]=>[3,3,2,2,1,1]=>1663200
[2,1,8,7,5,3,4,6,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,8,7,5,3,4,6,12,9,11,10]=>[3,3,2,2,1,1]=>1663200
[2,1,10,7,5,9,4,3,6,8,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,12,7,5,9,4,11,6,3,8,10]=>[3,2,2,2,2,1]=>415800
[2,1,12,8,5,11,6,4,9,3,7,10]=>[3,3,2,2,1,1]=>1663200
[2,1,12,9,5,3,6,7,4,10,11,8]=>[5,2,2,1,1,1]=>1995840
[2,1,10,9,4,6,7,3,5,8,12,11]=>[3,3,2,2,1,1]=>1663200
[2,1,12,9,4,6,7,11,5,3,8,10]=>[3,3,2,2,1,1]=>1663200
[2,1,12,11,9,6,4,8,5,3,7,10]=>[3,3,2,2,1,1]=>1663200
[2,1,12,3,10,6,4,7,9,5,11,8]=>[5,2,2,1,1,1]=>1995840
[2,1,10,3,4,5,7,8,9,6,12,11]=>[5,2,2,1,1,1]=>1995840
[2,1,12,3,4,11,7,5,9,10,6,8]=>[5,2,2,1,1,1]=>1995840
[4,1,3,2,6,5,8,7,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[4,1,3,2,6,5,8,7,12,9,11,10]=>[3,3,2,2,1,1]=>1663200
[4,1,3,2,6,5,10,7,9,8,12,11]=>[3,3,2,2,1,1]=>1663200
[4,1,3,2,6,5,12,11,9,7,8,10]=>[3,3,2,2,1,1]=>1663200
[4,1,3,2,8,5,7,6,10,9,12,11]=>[3,3,2,2,1,1]=>1663200
[4,1,3,2,10,9,7,5,6,8,12,11]=>[3,3,2,2,1,1]=>1663200
[4,1,3,2,12,9,7,11,6,5,8,10]=>[3,3,2,2,1,1]=>1663200
[6,5,3,1,2,4,8,7,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[6,5,3,1,2,4,8,7,12,9,11,10]=>[3,3,2,2,1,1]=>1663200
[6,5,3,1,2,4,10,7,9,8,12,11]=>[3,3,2,2,1,1]=>1663200
[6,5,3,1,2,4,12,11,9,7,8,10]=>[3,3,2,2,1,1]=>1663200
[8,5,3,7,2,1,4,6,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[8,5,3,7,2,1,4,6,12,9,11,10]=>[3,3,2,2,1,1]=>1663200
[10,5,3,7,2,9,4,1,6,8,12,11]=>[3,2,2,2,2,1]=>415800
[12,5,3,7,2,9,4,11,6,1,8,10]=>[3,2,2,2,2,1]=>415800
[12,5,3,8,2,11,6,4,9,1,7,10]=>[3,3,2,2,1,1]=>1663200
[12,5,3,9,2,1,6,7,4,10,11,8]=>[5,2,2,1,1,1]=>1995840
[10,6,3,9,4,2,7,1,5,8,12,11]=>[3,3,2,2,1,1]=>1663200
[12,6,3,9,4,2,7,11,5,1,8,10]=>[3,3,2,2,1,1]=>1663200
[12,6,3,11,9,2,4,8,5,1,7,10]=>[3,3,2,2,1,1]=>1663200
[12,6,3,1,10,2,4,7,9,5,11,8]=>[5,2,2,1,1,1]=>1995840
[10,7,3,1,4,5,2,8,9,6,12,11]=>[5,2,2,1,1,1]=>1995840
[12,7,3,1,4,11,2,5,9,10,6,8]=>[5,2,2,1,1,1]=>1995840
[8,7,2,4,5,1,3,6,10,9,12,11]=>[3,3,2,2,1,1]=>1663200
[10,7,2,4,5,9,3,1,6,8,12,11]=>[3,3,2,2,1,1]=>1663200
[12,7,2,4,5,9,3,11,6,1,8,10]=>[3,3,2,2,1,1]=>1663200
[10,9,7,4,2,6,3,1,5,8,12,11]=>[3,3,2,2,1,1]=>1663200
[12,9,7,4,2,6,3,11,5,1,8,10]=>[3,3,2,2,1,1]=>1663200
[12,11,8,4,9,6,2,3,5,1,7,10]=>[3,3,2,2,1,1]=>1663200
[12,1,9,4,10,6,2,7,3,5,11,8]=>[5,2,2,1,1,1]=>1995840
[10,1,8,4,2,5,7,3,9,6,12,11]=>[5,2,2,1,1,1]=>1995840
[12,1,9,4,2,11,7,5,3,10,6,8]=>[5,2,2,1,1,1]=>1995840
[8,1,2,3,5,6,7,4,10,9,12,11]=>[5,2,2,1,1,1]=>1995840
[10,1,2,9,5,3,7,8,4,6,12,11]=>[5,2,2,1,1,1]=>1995840
[12,1,2,10,5,11,7,3,9,4,6,8]=>[5,2,2,1,1,1]=>1995840
[1,5,4,7,8,3,6,2]=>[4,3,1]=>3360
[5,1,4,7,8,3,6,2]=>[4,4]=>1260
[4,8,1,5,6,2,3,7]=>[8]=>5040
[5,6,4,1,7,3,8,2]=>[8]=>5040
[4,3,7,8,2,5,1,6]=>[8]=>5040
[3,7,8,5,4,2,1,6]=>[6,2]=>3360
[1,7,4,5,6,8,3,2]=>[7,1]=>5760
[7,2,4,5,6,8,3,1]=>[7,1]=>5760
[2,7,4,5,6,8,3,1]=>[8]=>5040
[2,4,7,8,3,1,6,5]=>[8]=>5040
[5,4,3,6,8,1,7,2]=>[6,1,1]=>3360
[3,7,4,5,8,1,6,2]=>[8]=>5040
[1,4,3,5,6,8,2,7]=>[6,1,1]=>3360
[1,4,6,5,8,2,7,3]=>[6,1,1]=>3360
[4,6,1,7,3,2,8,5]=>[6,2]=>3360
[1,7,3,6,4,2,8,5]=>[6,1,1]=>3360
[4,7,3,5,1,2,8,6]=>[4,3,1]=>3360
[1,6,4,2,3,5,8,7]=>[5,2,1]=>4032
[4,8,3,5,2,1,6,7]=>[7,1]=>5760
[10,9,7,6,5,4,3,8,2,1]=>[2,2,2,2,1,1]=>4725
[1,6,8,4,7,5,3,2]=>[6,1,1]=>3360
[4,7,1,6,8,2,3,5]=>[6,2]=>3360
[4,6,5,8,2,3,7,1]=>[4,3,1]=>3360
[7,1,8,2,4,5,3,6]=>[8]=>5040
[5,7,8,2,3,4,1,6]=>[8]=>5040
[5,2,3,8,7,1,4,6]=>[6,1,1]=>3360
[11,10,9,8,6,7,5,4,3,2,1]=>[3,2,2,2,2]=>34650
[2,7,6,4,8,3,1,5]=>[3,2,2,1]=>1680
[2,6,3,7,5,8,4,1]=>[4,2,1,1]=>2520
[7,5,1,2,3,8,4,6]=>[6,2]=>3360
[4,3,5,2,6,1,7,8,9]=>[6,1,1,1]=>10080
[4,5,3,6,2,7,1,8,9]=>[4,2,1,1,1]=>7560
[3,2,4,1,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]=>240
[3,4,2,5,1,6,7,8,9,10]=>[5,1,1,1,1,1]=>6048
[4,3,5,2,6,1,7,8,9,10]=>[6,1,1,1,1]=>25200
[4,5,3,6,2,7,1,8,9,10]=>[4,2,1,1,1,1]=>18900
[5,4,6,3,7,2,8,1,9,10]=>[4,4,1,1]=>56700
[8,6,2,1,3,7,4,5]=>[8]=>5040
[4,2,3,6,8,5,7,1]=>[5,1,1,1]=>1344
[4,7,3,2,6,5,1,8]=>[4,2,1,1]=>2520
[6,3,5,8,4,1,2,7]=>[6,2]=>3360
[4,5,3,6,8,1,2,7]=>[4,3,1]=>3360
[5,2,8,4,7,1,3,6]=>[6,1,1]=>3360
[7,3,1,2,8,6,5,4]=>[7,1]=>5760
[8,7,1,3,2,4,5,6]=>[5,3]=>2688
[6,8,2,1,4,5,3,7]=>[4,4]=>1260
[2,1,4,3,6,5,10,7,8,9]=>[4,2,2,2]=>18900
[2,1,4,3,8,5,6,7,10,9]=>[4,2,2,2]=>18900
[2,1,4,3,10,9,6,5,8,7]=>[6,2,2]=>75600
[2,1,4,3,10,5,6,7,8,9]=>[6,2,2]=>75600
[2,1,6,3,4,5,8,7,10,9]=>[4,2,2,2]=>18900
[2,1,6,3,4,5,10,7,8,9]=>[4,4,2]=>56700
[2,1,10,7,4,9,6,3,8,5]=>[8,2]=>226800
[2,1,10,9,4,3,6,7,8,5]=>[8,2]=>226800
[2,1,8,3,4,5,6,7,10,9]=>[6,2,2]=>75600
[2,1,10,9,4,5,6,3,8,7]=>[8,2]=>226800
[2,1,10,3,8,5,4,7,6,9]=>[8,2]=>226800
[4,1,2,3,6,5,10,7,8,9]=>[4,4,2]=>56700
[4,1,2,3,8,5,6,7,10,9]=>[4,4,2]=>56700
[4,1,2,3,10,9,6,5,8,7]=>[6,4]=>151200
[6,5,2,1,4,3,8,7,10,9]=>[6,2,2]=>75600
[6,5,2,1,4,3,10,7,8,9]=>[6,4]=>151200
[8,5,2,7,4,1,6,3,10,9]=>[8,2]=>226800
[10,5,2,7,4,9,6,1,8,3]=>[10]=>362880
[10,5,2,9,4,1,6,7,8,3]=>[10]=>362880
[8,7,2,1,4,5,6,3,10,9]=>[8,2]=>226800
[10,7,2,9,4,5,6,1,8,3]=>[10]=>362880
[10,9,2,1,8,5,4,7,6,3]=>[10]=>362880
[10,9,2,1,4,5,6,7,8,3]=>[10]=>362880
[6,1,2,3,4,5,8,7,10,9]=>[6,2,2]=>75600
[8,7,2,3,4,1,6,5,10,9]=>[8,2]=>226800
[10,7,2,3,4,9,6,1,8,5]=>[10]=>362880
[10,9,2,3,4,1,6,7,8,5]=>[10]=>362880
[8,1,6,3,2,5,4,7,10,9]=>[8,2]=>226800
[10,9,6,3,2,5,4,1,8,7]=>[10]=>362880
[10,1,6,3,8,5,2,7,4,9]=>[10]=>362880
[10,1,8,3,2,5,6,7,4,9]=>[10]=>362880
[10,9,2,3,4,5,6,1,8,7]=>[10]=>362880
[10,1,8,3,4,5,2,7,6,9]=>[10]=>362880
[10,1,2,7,4,3,6,5,8,9]=>[10]=>362880
[2,1,4,3,8,5,6,7,12,9,10,11]=>[4,4,2,2]=>1871100
[2,1,6,3,4,5,8,7,12,9,10,11]=>[4,4,2,2]=>1871100
[2,1,6,3,4,5,10,7,8,9,12,11]=>[4,4,2,2]=>1871100
[2,1,6,3,4,5,12,11,8,7,10,9]=>[6,4,2]=>9979200
[2,1,6,3,4,5,12,7,8,9,10,11]=>[6,4,2]=>9979200
[2,1,8,7,4,3,6,5,12,9,10,11]=>[6,4,2]=>9979200
[2,1,8,3,4,5,6,7,12,9,10,11]=>[6,4,2]=>9979200
[4,1,2,3,6,5,8,7,12,9,10,11]=>[4,4,2,2]=>1871100
[4,1,2,3,6,5,10,7,8,9,12,11]=>[4,4,2,2]=>1871100
[4,1,2,3,6,5,12,11,8,7,10,9]=>[6,4,2]=>9979200
[4,1,2,3,6,5,12,7,8,9,10,11]=>[6,4,2]=>9979200
[4,1,2,3,8,5,6,7,10,9,12,11]=>[4,4,2,2]=>1871100
[4,1,2,3,8,5,6,7,12,9,10,11]=>[4,4,4]=>1247400
[4,1,2,3,10,9,6,5,8,7,12,11]=>[6,4,2]=>9979200
[4,1,2,3,10,5,6,7,8,9,12,11]=>[6,4,2]=>9979200
[6,5,2,1,4,3,8,7,12,9,10,11]=>[6,4,2]=>9979200
[6,5,2,1,4,3,10,7,8,9,12,11]=>[6,4,2]=>9979200
[6,5,2,1,4,3,12,7,8,9,10,11]=>[6,6]=>6652800
[12,5,2,7,4,9,6,11,8,1,10,3]=>[12]=>39916800
[12,5,2,7,4,11,6,1,8,9,10,3]=>[12]=>39916800
[12,5,2,9,4,11,6,7,8,1,10,3]=>[12]=>39916800
[12,5,2,11,4,1,10,7,6,9,8,3]=>[12]=>39916800
[12,5,2,11,4,1,6,7,8,9,10,3]=>[12]=>39916800
[12,7,2,9,4,5,6,11,8,1,10,3]=>[12]=>39916800
[12,7,2,11,4,5,6,1,8,9,10,3]=>[12]=>39916800
[12,9,2,11,8,5,4,7,6,1,10,3]=>[12]=>39916800
[12,11,2,1,8,5,10,7,4,9,6,3]=>[12]=>39916800
[12,11,2,1,10,5,4,7,8,9,6,3]=>[12]=>39916800
[12,9,2,11,4,5,6,7,8,1,10,3]=>[12]=>39916800
[12,11,2,1,10,5,6,7,4,9,8,3]=>[12]=>39916800
[12,11,2,1,4,9,6,5,8,7,10,3]=>[12]=>39916800
[12,11,2,1,4,5,6,7,8,9,10,3]=>[12]=>39916800
[6,1,2,3,4,5,8,7,12,9,10,11]=>[6,4,2]=>9979200
[6,1,2,3,4,5,10,7,8,9,12,11]=>[6,4,2]=>9979200
[6,1,2,3,4,5,12,11,8,7,10,9]=>[6,6]=>6652800
[6,1,2,3,4,5,12,7,8,9,10,11]=>[6,6]=>6652800
[12,7,2,3,4,9,6,11,8,1,10,5]=>[12]=>39916800
[12,7,2,3,4,11,6,1,8,9,10,5]=>[12]=>39916800
[12,9,2,3,4,11,6,7,8,1,10,5]=>[12]=>39916800
[12,11,2,3,4,1,10,7,6,9,8,5]=>[12]=>39916800
[12,11,2,3,4,1,6,7,8,9,10,5]=>[12]=>39916800
[12,9,6,3,2,5,4,11,8,1,10,7]=>[12]=>39916800
[12,11,6,3,2,5,4,1,8,9,10,7]=>[12]=>39916800
[12,11,6,3,8,5,2,7,4,1,10,9]=>[12]=>39916800
[12,1,6,3,8,5,10,7,2,9,4,11]=>[12]=>39916800
[12,1,6,3,10,5,2,7,8,9,4,11]=>[12]=>39916800
[12,11,8,3,2,5,6,7,4,1,10,9]=>[12]=>39916800
[12,1,8,3,10,5,6,7,2,9,4,11]=>[12]=>39916800
[12,1,10,3,2,9,6,5,8,7,4,11]=>[12]=>39916800
[12,1,10,3,2,5,6,7,8,9,4,11]=>[12]=>39916800
[12,9,2,3,4,5,6,11,8,1,10,7]=>[12]=>39916800
[12,11,2,3,4,5,6,1,8,9,10,7]=>[12]=>39916800
[12,11,8,3,4,5,2,7,6,1,10,9]=>[12]=>39916800
[12,1,8,3,4,5,10,7,2,9,6,11]=>[12]=>39916800
[12,1,10,3,4,5,2,7,8,9,6,11]=>[12]=>39916800
[12,11,2,7,4,3,6,5,8,1,10,9]=>[12]=>39916800
[12,1,10,7,4,3,6,5,2,9,8,11]=>[12]=>39916800
[12,1,2,7,4,9,6,3,8,5,10,11]=>[12]=>39916800
[12,1,2,9,4,3,6,7,8,5,10,11]=>[12]=>39916800
[12,11,2,3,4,5,6,7,8,1,10,9]=>[12]=>39916800
[12,1,10,3,4,5,6,7,2,9,8,11]=>[12]=>39916800
[12,1,2,9,4,5,6,3,8,7,10,11]=>[12]=>39916800
[12,1,2,3,8,5,4,7,6,9,10,11]=>[12]=>39916800
[12,1,2,3,4,5,6,7,8,9,10,11]=>[12]=>39916800
[1,5,4,8,7,3,2,6]=>[4,3,1]=>3360
[4,3,1,2,6,5,7,8]=>[4,2,1,1]=>2520
[7,5,8,1,2,4,6,3]=>[4,2,2]=>1260
[6,1,5,2,8,7,4,3]=>[5,3]=>2688
[1,4,7,2,6,5,8,3]=>[3,2,2,1]=>1680
[1,5,7,2,6,4,8,3]=>[4,3,1]=>3360
[7,2,4,6,1,8,3,5]=>[7,1]=>5760
[1,2,7,8,3,5,4,6]=>[6,1,1]=>3360
[1,7,6,2,8,5,4,3]=>[4,3,1]=>3360
[1,2,7,8,3,4,6,5]=>[6,1,1]=>3360
[1,7,6,8,3,4,2,5]=>[5,2,1]=>4032
[3,4,1,7,8,6,5,2]=>[5,2,1]=>4032
[2,4,8,6,5,7,1,3]=>[5,2,1]=>4032
[5,1,3,4,8,2,7,6]=>[5,1,1,1]=>1344
[8,7,3,6,1,4,2,5]=>[3,2,2,1]=>1680
[6,5,1,8,3,4,7,2]=>[7,1]=>5760
[8,2,1,5,6,4,7,3]=>[3,3,1,1]=>1120
[7,5,6,1,3,4,8,2]=>[8]=>5040
[5,7,2,4,6,1,8,3]=>[4,3,1]=>3360
[2,1,5,6,3,8,7,4]=>[3,2,2,1]=>1680
[3,2,7,5,8,6,4,1]=>[6,1,1]=>3360
[2,4,5,3,8,1,7,6]=>[7,1]=>5760
[7,2,5,4,3,8,6,1]=>[4,2,1,1]=>2520
[8,5,3,1,2,6,7,4]=>[3,2,1,1,1]=>1120
[7,2,5,1,3,6,8,4]=>[4,2,1,1]=>2520
[8,4,7,3,1,2,6,5]=>[5,3]=>2688
[1,8,7,3,5,2,6,4]=>[6,1,1]=>3360
[2,4,8,3,6,5,7,1]=>[5,2,1]=>4032
[3,1,8,2,6,5,7,4]=>[5,2,1]=>4032
[6,7,2,4,8,5,1,3]=>[7,1]=>5760
[6,7,3,2,8,5,1,4]=>[7,1]=>5760
[1,7,3,8,5,4,2,6]=>[3,2,1,1,1]=>1120
[2,8,6,4,3,1,7,5]=>[6,1,1]=>3360
[1,7,3,4,8,2,5,6]=>[5,1,1,1]=>1344
[1,5,8,3,4,6,2,7]=>[6,1,1]=>3360
[1,3,8,4,2,5,7,6]=>[5,1,1,1]=>1344
[1,4,7,6,2,3,8,5]=>[7,1]=>5760
[1,8,4,6,7,2,3,5]=>[7,1]=>5760
[1,4,2,3,7,8,6,5]=>[4,3,1]=>3360
[5,7,1,6,4,8,3,2]=>[8]=>5040
[1,2,9,7,5,3,10,8,6,4]=>[3,3,1,1,1,1]=>8400
[1,4,3,6,2,5,8,7]=>[4,2,1,1]=>2520
[1,3,6,5,8,2,4,7]=>[4,3,1]=>3360
[1,4,6,3,2,8,5,7]=>[7,1]=>5760
[6,8,4,1,5,7,2,3]=>[7,1]=>5760
[5,2,6,7,4,1,8,3]=>[7,1]=>5760
[8,5,6,4,1,7,3,2]=>[4,3,1]=>3360
[7,8,3,1,6,4,5,2]=>[5,2,1]=>4032
[5,8,2,6,3,1,7,4]=>[7,1]=>5760
[4,5,8,1,6,3,7,2]=>[5,2,1]=>4032
[8,1,4,6,2,5,7,3]=>[7,1]=>5760
[4,5,8,1,6,2,7,3]=>[3,2,2,1]=>1680
[5,2,6,8,1,4,3,7]=>[5,2,1]=>4032
[6,7,3,8,2,1,4,5]=>[5,2,1]=>4032
[2,4,1,5,6,7,8,10,3,9]=>[10]=>362880
[2,7,3,5,4,1,8,6]=>[5,2,1]=>4032
[2,6,3,7,4,1,8,5]=>[4,3,1]=>3360
[2,1,4,8,5,3,7,6]=>[4,2,1,1]=>2520
[2,7,3,8,4,1,6,5]=>[4,3,1]=>3360
[2,6,3,1,5,4,8,7]=>[4,2,1,1]=>2520
[1,5,8,3,4,7,2,6]=>[7,1]=>5760
[5,3,8,1,4,6,2,7]=>[4,3,1]=>3360
[4,5,8,1,3,6,2,7]=>[5,2,1]=>4032
[7,4,6,5,2,8,3,1]=>[5,3]=>2688
[4,1,3,8,5,7,6,2]=>[4,2,1,1]=>2520
[4,1,3,7,2,8,6,5]=>[7,1]=>5760
[4,6,3,1,7,2,8,5]=>[3,2,2,1]=>1680
[7,2,6,3,1,8,5,4]=>[4,3,1]=>3360
[4,8,7,2,5,3,1,6]=>[7,1]=>5760
[1,6,3,2,8,7,4,5]=>[4,2,1,1]=>2520
[2,8,1,7,5,4,6,3]=>[4,3,1]=>3360
[6,8,3,1,5,7,2,4]=>[6,1,1]=>3360
[8,7,3,1,2,5,6,4]=>[4,3,1]=>3360
[7,4,5,1,2,6,8,3]=>[7,1]=>5760
[1,3,5,7,2,8,4,9,6]=>[3,3,2,1]=>10080
[1,3,5,6,2,7,4,9,8]=>[3,3,2,1]=>10080
[1,3,4,5,2,7,6,9,8]=>[4,2,2,1]=>11340
[3,5,7,1,2,4,6,9,8]=>[5,2,2]=>9072
[1,3,5,7,2,9,4,6,8,10]=>[3,3,2,1,1]=>50400
[3,5,7,8,1,9,2,4,6]=>[5,2,2]=>9072
[1,3,5,7,2,9,4,10,6,8]=>[3,2,2,2,1]=>25200
[3,5,6,7,1,8,2,9,4]=>[9]=>40320
[1,3,5,7,2,8,4,9,6,10]=>[3,3,2,1,1]=>50400
[1,3,5,6,2,7,4,9,8,10]=>[3,3,2,1,1]=>50400
[1,3,4,5,2,7,6,9,8,10]=>[4,2,2,1,1]=>56700
[5,4,3,6,1,7,8,2]=>[5,2,1]=>4032
[3,2,7,8,5,6,1,4]=>[3,2,1,1,1]=>1120
[4,8,3,2,1,7,5,6]=>[7,1]=>5760
[1,9,8,7,6,4,3,2,5]=>[8,1]=>45360
[1,9,8,7,5,4,3,2,6]=>[7,1,1]=>25920
[1,9,8,6,5,4,3,2,7]=>[5,2,1,1]=>18144
[1,9,7,6,5,4,3,2,8]=>[3,2,2,1,1]=>7560
[1,9,8,7,6,5,2,3,4]=>[4,2,2,1]=>11340
[1,10,9,8,7,6,5,3,2,4]=>[6,2,1,1]=>151200
[1,9,8,7,6,3,4,2,5]=>[6,2,1]=>30240
[1,10,9,8,7,6,4,3,2,5]=>[8,1,1]=>226800
[1,9,8,7,4,5,3,2,6]=>[8,1]=>45360
[1,10,9,8,7,5,4,3,2,6]=>[9,1]=>403200
[1,9,8,5,6,4,3,2,7]=>[5,3,1]=>24192
[1,10,9,8,6,5,4,3,2,7]=>[7,2,1]=>259200
[1,8,4,5,6,3,2,7]=>[4,3,1]=>3360
[1,9,6,7,5,4,3,2,8]=>[4,3,1,1]=>15120
[1,10,9,7,6,5,4,3,2,8]=>[5,2,2,1]=>90720
[1,7,8,6,5,4,3,2,9]=>[4,2,1,1,1]=>7560
[1,10,8,7,6,5,4,3,2,9]=>[3,2,2,2,1]=>25200
[8,5,1,7,4,6,3,2]=>[7,1]=>5760
[1,3,7,8,4,6,2,5]=>[3,3,1,1]=>1120
[4,8,7,3,6,1,2,5]=>[8]=>5040
[5,8,4,3,7,1,2,6]=>[6,2]=>3360
[5,6,4,8,7,2,1,3]=>[3,3,2]=>1120
[4,8,3,7,6,1,2,5]=>[7,1]=>5760
[2,8,4,7,1,3,6,5]=>[4,4]=>1260
[8,9,2,3,4,5,6,1,7]=>[7,2]=>25920
[7,8,9,2,3,4,5,1,6]=>[9]=>40320
[6,7,8,9,2,3,4,1,5]=>[5,4]=>18144
[5,6,7,8,9,2,3,1,4]=>[5,2,2]=>9072
[9,10,2,3,4,5,6,7,1,8]=>[8,2]=>226800
[8,9,10,2,3,4,5,6,1,7]=>[6,4]=>151200
[7,8,9,2,3,4,1,5,6]=>[7,2]=>25920
[7,8,9,10,2,3,4,5,1,6]=>[7,3]=>172800
[6,7,8,9,2,3,1,4,5]=>[9]=>40320
[5,6,7,8,9,10,2,3,1,4]=>[7,3]=>172800
[4,5,6,7,8,1,9,2,3]=>[6,3]=>20160
[4,5,6,7,8,9,10,2,1,3]=>[7,3]=>172800
[6,8,3,4,5,2,1,7]=>[5,1,1,1]=>1344
[3,7,1,4,5,6,2,8]=>[2,2,1,1,1,1]=>210
[7,9,3,4,5,6,2,1,8]=>[5,1,1,1,1]=>3024
[3,9,2,1,5,6,7,8,4]=>[5,1,1,1,1]=>3024
[3,6,1,4,5,2,7,8]=>[2,2,1,1,1,1]=>210
[3,8,1,4,5,6,7,2,9]=>[2,2,1,1,1,1,1]=>378
[8,10,3,4,5,6,7,2,1,9]=>[5,1,1,1,1,1]=>6048
[6,9,3,4,5,2,7,1,8]=>[5,1,1,1,1]=>3024
[3,8,2,4,5,1,7,6]=>[5,1,1,1]=>1344
[3,9,2,4,1,6,7,8,5]=>[5,1,1,1,1]=>3024
[3,7,2,1,5,6,4,8]=>[5,1,1,1]=>1344
[3,6,8,1,5,4,7,2]=>[6,1,1]=>3360
[3,8,9,1,5,6,7,4,2]=>[6,1,1,1]=>10080
[3,10,2,1,5,6,7,8,9,4]=>[5,1,1,1,1,1]=>6048
[3,7,1,4,5,6,2,8,9]=>[2,2,1,1,1,1,1]=>378
[3,9,1,4,5,6,7,8,2,10]=>[2,2,1,1,1,1,1,1]=>630
[1,7,4,6,3,5,2,8]=>[4,2,1,1]=>2520
[1,3,6,5,7,2,4,8]=>[3,3,1,1]=>1120
[1,7,2,5,6,4,3,8]=>[3,3,1,1]=>1120
[1,6,8,5,4,3,7,2]=>[4,2,1,1]=>2520
[2,5,7,8,4,3,1,6]=>[8]=>5040
[6,8,5,3,2,4,1,7]=>[8]=>5040
[1,6,8,5,3,2,7,4]=>[4,2,1,1]=>2520
[4,6,1,8,7,5,3,2]=>[8]=>5040
[1,3,7,6,8,5,2,4]=>[4,3,1]=>3360
[4,1,7,8,6,5,2,3]=>[6,2]=>3360
[5,4,3,7,6,1,2,8]=>[3,3,1,1]=>1120
[4,7,6,1,2,3,8,5]=>[4,2,2]=>1260
[2,8,7,6,5,4,3,1,9]=>[3,2,2,1,1]=>7560
[2,1,4,9,8,7,6,5,3]=>[3,2,2,2]=>2520
[3,7,6,5,4,2,1,9,8]=>[5,2,2]=>9072
[3,2,1,6,9,8,7,5,4]=>[5,2,1,1]=>18144
[4,6,5,3,2,1,9,8,7]=>[6,2,1]=>30240
[1,7,6,2,3,8,5,4]=>[7,1]=>5760
[1,5,4,3,8,6,2,7]=>[4,2,1,1]=>2520
[1,3,7,5,8,4,6,2]=>[7,1]=>5760
[5,8,1,2,7,6,4,3]=>[7,1]=>5760
[1,6,7,4,5,3,2,8]=>[4,1,1,1,1]=>420
[1,4,2,6,7,5,3,8]=>[6,1,1]=>3360
[1,8,2,4,6,5,3,7]=>[4,2,1,1]=>2520
[1,4,8,7,2,3,6,5]=>[7,1]=>5760
[4,1,3,6,5,8,2,7]=>[6,1,1]=>3360
[4,3,7,1,5,8,2,6]=>[3,2,2,1]=>1680
[1,8,6,5,2,7,4,3]=>[7,1]=>5760
[6,4,1,8,3,7,5,2]=>[5,3]=>2688
[4,5,8,7,3,6,2,1]=>[7,1]=>5760
[3,5,4,1,7,8,6,2]=>[5,3]=>2688
[6,8,7,2,1,5,4,3]=>[5,3]=>2688
[8,1,6,3,7,5,4,2]=>[5,3]=>2688
[8,5,1,3,7,6,4,2]=>[7,1]=>5760
[8,3,6,5,4,2,1,7]=>[3,3,2]=>1120
[6,1,3,5,7,2,8,4]=>[4,3,1]=>3360
[7,4,1,6,5,2,8,3]=>[4,3,1]=>3360
[7,4,2,8,6,5,3,1]=>[6,2]=>3360
[6,8,4,7,3,2,5,1]=>[4,4]=>1260
[5,8,7,3,2,1,6,4]=>[8]=>5040
[5,8,7,2,6,4,3,1]=>[6,2]=>3360
[6,8,7,3,5,1,4,2]=>[3,2,2,1]=>1680
[7,2,5,6,8,3,4,1]=>[7,1]=>5760
[1,6,5,7,8,3,2,4]=>[7,1]=>5760
[8,6,7,2,3,5,4,1]=>[6,2]=>3360
[5,4,8,6,7,3,1,2]=>[5,3]=>2688
[4,2,7,3,1,6,8,5]=>[6,1,1]=>3360
[7,3,6,4,2,1,8,5]=>[7,1]=>5760
[4,8,5,2,7,3,1,6]=>[8]=>5040
[6,4,3,1,8,5,2,7]=>[7,1]=>5760
[7,4,3,1,5,8,6,2]=>[6,1,1]=>3360
[7,4,8,6,5,3,1,2]=>[5,2,1]=>4032
[4,8,5,2,6,7,3,1]=>[4,4]=>1260
[7,3,2,1,8,5,6,4]=>[6,2]=>3360
[7,8,1,9,2,3,4,5,6]=>[6,3]=>20160
[6,7,8,1,9,2,3,4,5]=>[7,2]=>25920
[5,6,7,8,1,9,2,3,4]=>[7,2]=>25920
[9,1,2,3,4,5,7,6,8]=>[8,1]=>45360
[2,1,3,4,5,9,6,7,8]=>[4,2,1,1,1]=>7560
[5,1,3,8,2,7,4,6]=>[4,3,1]=>3360
[7,1,2,6,4,3,8,5]=>[8]=>5040
[8,1,6,3,2,4,7,5]=>[4,3,1]=>3360
[2,1,4,3,10,5,7,6,9,8]=>[4,2,2,1,1]=>56700
[2,1,4,3,9,6,10,5,8,7]=>[3,2,2,2,1]=>25200
[2,1,8,3,5,4,7,6,10,9]=>[4,2,2,1,1]=>56700
[2,1,10,3,5,4,7,6,9,8]=>[5,2,1,1,1]=>60480
[2,1,9,6,10,3,5,4,8,7]=>[5,3,2]=>120960
[2,1,7,4,8,3,6,5,10,9]=>[3,2,2,2,1]=>25200
[2,1,7,4,10,3,6,5,9,8]=>[3,3,2,1,1]=>50400
[2,1,10,3,6,5,9,4,8,7]=>[6,2,2]=>75600
[2,1,9,4,8,5,10,3,7,6]=>[7,2,1]=>259200
[4,1,3,2,10,5,7,6,9,8]=>[4,3,1,1,1]=>50400
[4,1,3,2,9,6,10,5,8,7]=>[3,3,2,1,1]=>50400
[6,1,3,2,5,4,8,7,10,9]=>[4,2,2,1,1]=>56700
[6,1,3,2,5,4,10,7,9,8]=>[4,3,1,1,1]=>50400
[8,1,3,2,5,4,7,6,10,9]=>[5,2,1,1,1]=>60480
[9,6,10,1,3,2,5,4,8,7]=>[4,4,2]=>56700
[7,4,8,1,3,2,6,5,10,9]=>[5,3,2]=>120960
[7,4,10,1,3,2,6,5,9,8]=>[5,4,1]=>181440
[10,1,3,2,6,5,9,4,8,7]=>[7,2,1]=>259200
[9,4,8,5,10,1,3,2,7,6]=>[10]=>362880
[5,2,6,1,4,3,8,7,10,9]=>[3,2,2,2,1]=>25200
[5,2,6,1,4,3,10,7,9,8]=>[3,3,2,1,1]=>50400
[5,2,8,1,4,3,7,6,10,9]=>[3,3,2,1,1]=>50400
[5,2,10,1,4,3,7,6,9,8]=>[4,3,1,1,1]=>50400
[5,2,9,6,10,1,4,3,8,7]=>[6,3,1]=>201600
[8,1,4,3,7,2,6,5,10,9]=>[6,2,2]=>75600
[10,1,4,3,7,2,6,5,9,8]=>[7,2,1]=>259200
[9,2,6,5,10,1,4,3,8,7]=>[5,4,1]=>181440
[10,1,4,3,8,5,9,2,7,6]=>[6,2,2]=>75600
[7,2,6,3,8,1,5,4,10,9]=>[7,2,1]=>259200
[7,2,6,3,10,1,5,4,9,8]=>[8,1,1]=>226800
[10,1,5,4,9,2,6,3,8,7]=>[5,4,1]=>181440
[8,3,10,1,5,4,9,2,7,6]=>[7,2,1]=>259200
[8,3,9,2,7,4,10,1,6,5]=>[5,3,2]=>120960
[2,1,4,3,6,5,11,8,12,7,10,9]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,12,5,7,6,9,8,11,10]=>[5,2,2,1,1,1]=>1995840
[2,1,4,3,11,8,12,5,7,6,10,9]=>[5,3,2,2]=>3991680
[2,1,4,3,9,6,10,5,8,7,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,4,3,9,6,12,5,8,7,11,10]=>[3,3,2,2,1,1]=>1663200
[2,1,6,3,5,4,11,8,12,7,10,9]=>[3,3,2,2,1,1]=>1663200
[2,1,10,3,5,4,7,6,9,8,12,11]=>[5,2,2,1,1,1]=>1995840
[2,1,11,8,12,3,5,4,7,6,10,9]=>[4,4,2,2]=>1871100
[2,1,9,6,10,3,5,4,8,7,12,11]=>[5,3,2,2]=>3991680
[2,1,9,6,12,3,5,4,8,7,11,10]=>[5,4,2,1]=>11975040
[2,1,7,4,8,3,6,5,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[2,1,7,4,8,3,6,5,12,9,11,10]=>[3,3,2,2,1,1]=>1663200
[2,1,7,4,10,3,6,5,9,8,12,11]=>[3,3,2,2,1,1]=>1663200
[2,1,11,4,8,7,12,3,6,5,10,9]=>[5,4,2,1]=>11975040
[2,1,12,3,7,6,11,4,8,5,10,9]=>[5,4,2,1]=>11975040
[2,1,10,5,11,4,9,6,12,3,8,7]=>[5,3,2,2]=>3991680
[4,1,3,2,6,5,11,8,12,7,10,9]=>[3,3,2,2,1,1]=>1663200
[4,1,3,2,11,8,12,5,7,6,10,9]=>[5,3,3,1]=>5322240
[4,1,3,2,9,6,10,5,8,7,12,11]=>[3,3,2,2,1,1]=>1663200
[8,1,3,2,5,4,7,6,10,9,12,11]=>[5,2,2,1,1,1]=>1995840
[11,8,12,1,3,2,5,4,7,6,10,9]=>[7,5]=>13685760
[9,6,10,1,3,2,5,4,8,7,12,11]=>[4,4,2,2]=>1871100
[9,6,12,1,3,2,5,4,8,7,11,10]=>[5,4,2,1]=>11975040
[7,4,8,1,3,2,6,5,10,9,12,11]=>[5,3,2,2]=>3991680
[7,4,8,1,3,2,6,5,12,9,11,10]=>[5,3,3,1]=>5322240
[7,4,10,1,3,2,6,5,9,8,12,11]=>[5,4,2,1]=>11975040
[7,4,11,8,12,1,3,2,6,5,10,9]=>[9,3]=>17740800
[11,4,8,7,12,1,3,2,6,5,10,9]=>[7,5]=>13685760
[9,4,8,5,12,1,3,2,7,6,11,10]=>[11,1]=>43545600
[5,2,6,1,4,3,8,7,10,9,12,11]=>[3,2,2,2,2,1]=>415800
[5,2,6,1,4,3,8,7,12,9,11,10]=>[3,3,2,2,1,1]=>1663200
[5,2,6,1,4,3,10,7,9,8,12,11]=>[3,3,2,2,1,1]=>1663200
[5,2,6,1,4,3,11,8,12,7,10,9]=>[3,3,2,2,1,1]=>1663200
[5,2,8,1,4,3,7,6,10,9,12,11]=>[3,3,2,2,1,1]=>1663200
[5,2,11,8,12,1,4,3,7,6,10,9]=>[11,1]=>43545600
[5,2,11,6,10,7,12,1,4,3,9,8]=>[11,1]=>43545600
[11,8,12,1,4,3,7,2,6,5,10,9]=>[5,4,2,1]=>11975040
[9,2,6,5,10,1,4,3,8,7,12,11]=>[5,4,2,1]=>11975040
[11,2,6,5,10,7,12,1,4,3,9,8]=>[11,1]=>43545600
[11,2,7,6,12,1,4,3,8,5,10,9]=>[11,1]=>43545600
[10,5,11,2,7,6,12,1,4,3,9,8]=>[11,1]=>43545600
[10,5,12,1,4,3,9,6,11,2,8,7]=>[7,5]=>13685760
[7,2,6,3,11,8,12,1,5,4,10,9]=>[11,1]=>43545600
[10,1,5,4,9,2,6,3,8,7,12,11]=>[5,4,2,1]=>11975040
[11,2,6,3,8,7,12,1,5,4,10,9]=>[11,1]=>43545600
[12,1,5,4,10,7,11,2,6,3,9,8]=>[4,4,3,1]=>4989600
[8,3,11,2,7,6,12,1,5,4,10,9]=>[5,4,2,1]=>11975040
[11,2,7,6,12,1,5,4,10,3,9,8]=>[11,1]=>43545600
[12,1,5,4,10,3,9,6,11,2,8,7]=>[11,1]=>43545600
[8,3,9,2,7,4,10,1,6,5,12,11]=>[5,3,2,2]=>3991680
[8,3,9,2,7,4,12,1,6,5,11,10]=>[5,4,2,1]=>11975040
[12,1,6,5,11,2,7,4,10,3,9,8]=>[11,1]=>43545600
[10,3,9,4,12,1,6,5,11,2,8,7]=>[11,1]=>43545600
[10,3,9,4,11,2,8,5,12,1,7,6]=>[5,4,2,1]=>11975040
[4,7,6,2,3,1,5,8]=>[7,1]=>5760
[4,7,6,1,3,2,8,5]=>[6,2]=>3360
[7,2,6,5,4,3,1,9,8]=>[2,2,2,2,1]=>945
[3,2,1,9,5,8,7,6,4]=>[2,2,2,1,1,1]=>1260
[6,3,5,4,2,1,9,8,7]=>[3,2,2,1,1]=>7560
[4,3,2,1,9,7,8,6,5]=>[3,2,2,2]=>2520
[7,6,3,1,8,5,2,4]=>[7,1]=>5760
[7,2,5,8,6,1,3,4]=>[5,2,1]=>4032
[4,1,3,6,2,5,8,7]=>[5,2,1]=>4032
[7,1,4,6,3,2,5,8]=>[7,1]=>5760
[7,4,5,8,6,2,3,1]=>[8]=>5040
[6,7,2,3,8,4,1,5]=>[6,2]=>3360
[1,5,2,6,8,7,4,3]=>[4,3,1]=>3360
[1,2,3,4,5,6,8,9,7,10]=>[3,1,1,1,1,1,1,1]=>240
[3,1,6,7,5,2,8,4]=>[4,3,1]=>3360
[8,6,2,4,5,1,7,3]=>[5,1,1,1]=>1344
[8,6,7,5,2,1,4,3]=>[8]=>5040
[4,1,6,2,3,8,7,5]=>[4,3,1]=>3360
[4,1,7,6,5,2,8,3]=>[4,3,1]=>3360
[8,4,1,5,6,2,7,3]=>[4,3,1]=>3360
[8,4,5,3,6,1,7,2]=>[7,1]=>5760
[2,8,4,7,3,5,6,1]=>[5,3]=>2688
[1,5,4,8,3,2,6,7]=>[7,1]=>5760
[1,5,7,6,3,8,2,4]=>[4,3,1]=>3360
[2,6,3,1,7,8,4,5]=>[7,1]=>5760
[2,1,7,8,3,5,4,6]=>[6,2]=>3360
[1,5,8,6,7,4,2,3]=>[3,2,2,1]=>1680
[8,7,1,3,5,2,6,4]=>[4,3,1]=>3360
[3,7,8,2,5,4,1,6]=>[7,1]=>5760
[4,7,6,5,8,1,3,2]=>[8]=>5040
[4,7,8,6,2,1,5,3]=>[3,3,2]=>1120
[4,8,6,3,2,1,7,5]=>[4,3,1]=>3360
[5,1,4,7,6,8,3,2]=>[5,3]=>2688
[5,6,4,7,1,8,3,2]=>[3,3,2]=>1120
[5,3,7,4,6,1,8,2]=>[4,3,1]=>3360
[4,1,5,7,8,6,3,2]=>[7,1]=>5760
[3,6,7,1,5,4,8,2]=>[7,1]=>5760
[3,6,4,7,5,8,2,1]=>[7,1]=>5760
[9,1,2,3,4,8,6,5,7]=>[9]=>40320
[9,1,2,3,8,5,6,4,7]=>[9]=>40320
[8,1,2,9,4,5,6,3,7]=>[5,4]=>18144
[9,1,8,3,4,5,6,2,7]=>[9]=>40320
[7,1,2,3,4,9,5,8,6]=>[6,2,1]=>30240
[10,1,2,3,4,5,9,7,6,8]=>[10]=>362880
[6,1,2,3,8,4,5,9,7]=>[5,4]=>18144
[10,1,2,3,4,9,6,7,5,8]=>[10]=>362880
[5,1,2,8,3,4,6,9,7]=>[5,4]=>18144
[9,1,2,3,10,5,6,7,4,8]=>[5,5]=>72576
[4,1,9,2,3,5,6,8,7]=>[5,3,1]=>24192
[10,1,2,9,4,5,6,7,3,8]=>[10]=>362880
[3,8,1,2,4,5,6,9,7]=>[7,2]=>25920
[10,1,9,3,4,5,6,7,2,8]=>[10]=>362880
[8,2,1,3,4,5,6,9,7]=>[8,1]=>45360
[8,1,2,3,4,5,10,6,9,7]=>[7,2,1]=>259200
[11,1,2,3,4,5,6,10,8,7,9]=>[11]=>3628800
[9,1,2,3,8,5,4,7,6]=>[9]=>40320
[7,1,2,3,4,9,5,6,10,8]=>[6,4]=>151200
[11,1,2,3,4,5,10,7,8,6,9]=>[11]=>3628800
[6,1,2,3,9,4,7,8,5]=>[5,2,1,1]=>18144
[6,1,2,3,9,4,5,7,10,8]=>[5,5]=>72576
[10,1,2,3,4,11,6,7,8,5,9]=>[6,5]=>1330560
[5,1,2,8,3,6,4,9,7]=>[4,4,1]=>11340
[5,1,2,10,3,4,6,7,9,8]=>[5,4,1]=>181440
[11,1,2,3,10,5,6,7,8,4,9]=>[11]=>3628800
[9,8,2,1,4,5,6,7,3]=>[9]=>40320
[8,1,7,3,2,4,5,6]=>[8]=>5040
[4,1,8,2,5,3,6,9,7]=>[5,3,1]=>24192
[4,1,9,2,3,5,6,7,10,8]=>[7,3]=>172800
[11,1,2,10,4,5,6,7,8,3,9]=>[11]=>3628800
[3,9,1,4,2,5,6,8,7]=>[5,2,1,1]=>18144
[3,9,1,2,4,5,6,7,10,8]=>[8,2]=>226800
[10,1,11,3,4,5,6,7,8,2,9]=>[8,3]=>1663200
[8,2,3,1,4,5,6,9,7]=>[7,1,1]=>25920
[10,2,1,3,4,5,6,7,9,8]=>[8,1,1]=>226800
[11,10,2,3,4,5,6,7,8,1,9]=>[11]=>3628800
[6,4,7,1,5,2,8,3]=>[4,3,1]=>3360
[1,6,5,2,8,7,4,3]=>[4,3,1]=>3360
[2,3,4,5,7,8,1,9,6]=>[6,3]=>20160
[1,3,4,5,2,6,7,8,9]=>[4,1,1,1,1,1]=>756
[1,2,3,4,5,7,8,6,9,10]=>[3,1,1,1,1,1,1,1]=>240
[2,3,4,5,7,9,1,6,8]=>[6,3]=>20160
[1,2,3,4,5,7,8,9,6,10]=>[4,1,1,1,1,1,1]=>1260
[2,3,4,5,1,6,7,9,8]=>[5,2,1,1]=>18144
[4,5,6,1,7,8,9,2,3]=>[7,2]=>25920
[2,1,4,5,3,6,7,8,9]=>[3,2,1,1,1,1]=>2520
[2,4,5,6,1,7,8,9,10,3]=>[10]=>362880
[1,3,2,5,4,6,7,8,9]=>[2,2,1,1,1,1,1]=>378
[2,3,5,6,1,7,8,9,10,4]=>[6,4]=>151200
[4,1,7,2,5,8,3,6]=>[3,2,2,1]=>1680
[3,2,5,8,6,1,7,4]=>[4,2,1,1]=>2520
[4,5,1,7,2,8,6,3]=>[6,2]=>3360
[4,7,1,8,5,3,6,2]=>[7,1]=>5760
[7,1,4,3,6,8,2,5]=>[3,3,2]=>1120
[4,1,6,2,8,3,5,7,9]=>[3,3,2,1]=>10080
[4,1,6,2,8,3,9,5,7]=>[3,2,2,2]=>2520
[4,1,6,2,7,3,8,5,9]=>[3,3,2,1]=>10080
[4,8,7,3,5,1,6,2]=>[5,2,1]=>4032
[5,3,8,7,1,6,2,4]=>[5,2,1]=>4032
[5,2,6,7,4,3,1,8]=>[4,2,1,1]=>2520
[8,5,1,6,4,3,2,7]=>[8]=>5040
[8,6,3,5,2,7,1,4]=>[7,1]=>5760
[8,4,6,2,1,5,7,3]=>[5,2,1]=>4032
[8,5,2,1,6,4,7,3]=>[7,1]=>5760
[1,7,2,8,5,4,6,3]=>[6,1,1]=>3360
[6,7,1,4,8,5,3,2]=>[7,1]=>5760
[7,3,2,8,5,1,4,6]=>[5,2,1]=>4032
[4,1,7,3,2,8,5,6]=>[6,2]=>3360
[8,3,5,2,4,7,1,6]=>[4,4]=>1260
[4,3,7,8,6,1,5,2]=>[8]=>5040
[1,2,6,3,7,8,5,4]=>[4,2,1,1]=>2520
[6,1,3,7,8,5,4,2]=>[5,2,1]=>4032
[8,7,9,1,4,5,6,2,3]=>[7,2]=>25920
[7,6,9,1,4,5,2,8,3]=>[6,2,1]=>30240
[9,8,10,1,4,5,6,7,2,3]=>[8,2]=>226800
[11,10,2,1,4,5,6,7,8,9,3]=>[11]=>3628800
[4,5,1,8,6,2,7,3]=>[4,3,1]=>3360
[5,6,1,8,7,2,3,4]=>[4,2,2]=>1260
[4,5,1,6,8,7,3,2]=>[5,3]=>2688
[3,8,6,1,5,2,4,7]=>[7,1]=>5760
[3,2,8,1,5,6,4,7]=>[5,1,1,1]=>1344
[5,8,7,3,2,1,4,6]=>[5,3]=>2688
[3,4,7,6,8,2,1,5]=>[3,3,2]=>1120
[2,8,1,3,7,5,6,4]=>[5,3]=>2688
[1,8,7,2,5,6,4,3]=>[5,1,1,1]=>1344
[3,4,7,1,5,8,2,6]=>[5,2,1]=>4032
[4,2,7,1,5,8,3,6]=>[2,2,2,1,1]=>420
[1,3,5,2,4,6,7,8,9]=>[4,1,1,1,1,1]=>756
[4,1,2,3,5,6,8,7,9]=>[4,2,1,1,1]=>7560
[1,2,4,7,3,5,6,8,9]=>[5,1,1,1,1]=>3024
[5,1,2,3,4,7,6,8,9]=>[5,2,1,1]=>18144
[1,4,7,5,2,3,6,8]=>[3,3,1,1]=>1120
[2,5,7,6,8,3,4,1]=>[4,4]=>1260
[3,1,6,7,2,8,5,4]=>[8]=>5040
[1,5,3,6,8,4,7,2]=>[3,2,1,1,1]=>1120
[6,5,1,3,8,4,7,2]=>[4,3,1]=>3360
[1,7,4,8,5,3,2,6]=>[4,2,1,1]=>2520
[7,3,1,6,8,4,5,2]=>[6,2]=>3360
[8,5,1,4,6,7,3,2]=>[7,1]=>5760
[3,4,7,5,6,8,2,1]=>[8]=>5040
[3,4,7,8,5,2,6,1]=>[7,1]=>5760
[4,8,1,7,5,6,3,2]=>[4,2,1,1]=>2520
[1,8,7,5,2,6,3,4]=>[4,2,1,1]=>2520
[1,7,6,3,4,5,8,2]=>[4,3,1]=>3360
[1,8,7,4,5,6,2,3]=>[4,1,1,1,1]=>420
[1,8,7,3,6,4,2,5]=>[7,1]=>5760
[1,4,7,5,8,2,6,3]=>[7,1]=>5760
[1,4,7,2,3,6,5,8]=>[3,2,1,1,1]=>1120
[1,7,2,5,6,3,4,8]=>[6,1,1]=>3360
[1,2,6,5,8,3,4,7]=>[4,2,1,1]=>2520
[1,5,8,2,6,3,4,7]=>[7,1]=>5760
[6,8,3,2,7,5,1,4]=>[4,3,1]=>3360
[4,1,5,7,2,6,3,8]=>[6,1,1]=>3360
[5,7,2,1,3,6,4,8]=>[6,1,1]=>3360
[10,11,8,1,2,3,4,5,6,7,9]=>[7,4]=>1425600
[7,1,10,9,2,3,4,5,6,8]=>[10]=>362880
[6,7,9,1,2,3,4,5,10,8]=>[10]=>362880
[2,8,1,9,10,3,4,5,6,7]=>[10]=>362880
[8,7,1,10,2,3,4,5,6,9]=>[10]=>362880
[3,5,6,7,2,4,1,8]=>[5,2,1]=>4032
[6,4,7,5,2,3,1,8]=>[4,3,1]=>3360
[1,5,6,4,8,3,2,7]=>[4,2,1,1]=>2520
[2,1,5,6,4,8,3,7]=>[6,2]=>3360
[5,1,4,7,8,6,2,3]=>[7,1]=>5760
[1,6,7,2,8,5,4,3]=>[7,1]=>5760
[5,3,2,1,7,8,6,4]=>[6,2]=>3360
[7,4,3,8,6,1,5,2]=>[4,3,1]=>3360
[4,3,7,1,5,8,6,2]=>[5,2,1]=>4032
[8,2,4,5,3,1,7,6]=>[3,3,1,1]=>1120
[1,4,3,2,7,5,8,6]=>[4,2,1,1]=>2520
[1,5,2,8,6,3,10,9,7,4]=>[5,4,1]=>181440
[4,1,5,2,8,6,3,10,9,7]=>[5,3,1,1]=>120960
[1,7,5,2,8,6,3,10,9,4]=>[7,1,1,1]=>86400
[4,1,7,5,2,8,3,10,9,6]=>[4,3,2,1]=>151200
[6,4,1,7,5,2,8,3,10,9]=>[7,2,1]=>259200
[3,4,1,7,2,8,5,10,9,6]=>[4,3,2,1]=>151200
[3,6,4,1,7,2,8,5,10,9]=>[3,3,2,2]=>25200
[1,5,2,9,8,6,3,10,7,4]=>[8,1,1]=>226800
[4,1,5,2,9,8,6,3,10,7]=>[7,3]=>172800
[1,7,5,2,9,6,3,10,8,4]=>[8,1,1]=>226800
[4,1,7,5,2,9,3,10,8,6]=>[4,4,2]=>56700
[4,1,9,6,5,2,7,3,10,8]=>[4,4,1,1]=>56700
[3,4,1,7,2,9,5,10,8,6]=>[4,4,2]=>56700
[3,6,1,9,4,2,7,5,10,8]=>[5,2,2,1]=>90720
[1,8,7,5,2,9,6,3,10,4]=>[9,1]=>403200
[4,1,8,7,5,2,9,3,10,6]=>[7,2,1]=>259200
[6,4,1,8,5,2,9,3,10,7]=>[6,3,1]=>201600
[7,6,4,1,8,5,2,9,3,10]=>[9,1]=>403200
[3,4,1,8,7,2,9,5,10,6]=>[8,2]=>226800
[3,6,4,1,8,2,9,5,10,7]=>[3,3,2,2]=>25200
[3,7,6,4,1,8,2,9,5,10]=>[6,2,1,1]=>151200
[1,9,6,5,2,7,3,10,8,4]=>[6,3,1]=>201600
[6,1,9,4,2,7,3,10,8,5]=>[9,1]=>403200
[5,4,1,9,6,2,7,3,10,8]=>[9,1]=>403200
[9,3,1,6,2,7,4,10,8,5]=>[7,3]=>172800
[9,5,3,1,6,2,7,4,10,8]=>[5,3,1,1]=>120960
[6,1,8,5,2,9,7,3,10,4]=>[7,2,1]=>259200
[6,4,1,8,2,9,7,3,10,5]=>[9,1]=>403200
[8,5,4,1,6,2,9,3,10,7]=>[4,3,3]=>50400
[5,7,4,1,8,6,2,9,3,10]=>[6,2,1,1]=>151200
[3,6,1,8,2,9,7,4,10,5]=>[5,2,2,1]=>90720
[5,8,3,1,6,2,9,4,10,7]=>[6,3,1]=>201600
[5,3,7,1,8,6,2,9,4,10]=>[5,3,1,1]=>120960
[4,3,8,1,9,5,2,6,10,7]=>[8,2]=>226800
[7,4,3,5,1,8,2,9,6,10]=>[5,3,1,1]=>120960
[9,6,2,1,3,7,4,10,8,5]=>[10]=>362880
[5,9,2,1,6,3,7,4,10,8]=>[9,1]=>403200
[6,8,2,1,3,9,7,4,10,5]=>[9,1]=>403200
[8,2,5,1,6,3,9,4,10,7]=>[3,3,3,1]=>22400
[2,5,7,1,8,6,3,9,4,10]=>[6,2,1,1]=>151200
[2,4,8,1,9,5,3,6,10,7]=>[7,3]=>172800
[4,8,7,2,6,1,3,5]=>[6,2]=>3360
[4,5,8,2,1,7,3,6]=>[4,4]=>1260
[6,8,4,1,7,3,2,5]=>[4,4]=>1260
[5,6,4,3,2,1,7,8,9]=>[4,2,1,1,1]=>7560
[5,6,4,3,2,1,7,8,9,10]=>[4,2,1,1,1,1]=>18900
[4,5,3,2,1,6,7,8,9]=>[4,1,1,1,1,1]=>756
[6,7,5,4,3,2,1,8,9,10]=>[4,2,1,1,1,1]=>18900
[6,7,4,3,2,1,5,8,9]=>[3,2,2,1,1]=>7560
[5,6,4,3,2,7,1,8,9]=>[5,2,1,1]=>18144
[7,5,4,3,1,2,6,8,9]=>[5,2,1,1]=>18144
[6,5,4,3,7,1,2,8,9]=>[3,2,2,1,1]=>7560
[6,7,9,8,5,4,3,2,1]=>[8,1]=>45360
[7,6,8,9,5,4,3,2,1]=>[8,1]=>45360
[7,8,10,9,6,5,4,3,2,1]=>[8,2]=>226800
[6,7,5,9,8,4,3,2,1]=>[5,4]=>18144
[5,7,9,8,6,4,3,2,1]=>[9]=>40320
[7,6,8,5,9,4,3,2,1]=>[9]=>40320
[6,5,8,9,7,4,3,2,1]=>[5,4]=>18144
[8,7,9,10,6,5,4,3,2,1]=>[8,2]=>226800
[4,1,7,8,3,2,5,6]=>[5,3]=>2688
[7,6,2,8,4,5,3,1]=>[8]=>5040
[5,8,2,1,3,6,4,7]=>[7,1]=>5760
[8,5,1,7,3,4,6,2]=>[5,3]=>2688
[5,7,6,3,4,1,8,2]=>[5,3]=>2688
[7,8,9,10,1,5,6,3,4,2]=>[6,4]=>151200
[9,8,6,1,2,3,4,5,7]=>[4,3,2]=>15120
[9,8,7,5,1,2,3,4,6]=>[7,2]=>25920
[9,8,7,6,4,1,2,3,5]=>[5,4]=>18144
[9,8,7,6,5,3,1,2,4]=>[6,2,1]=>30240
[7,1,2,6,4,3,5,8]=>[7,1]=>5760
[7,1,2,6,5,3,4,8]=>[6,1,1]=>3360
[4,7,8,6,2,3,5,1]=>[5,3]=>2688
[7,1,2,4,8,6,5,3]=>[6,1,1]=>3360
[2,7,5,6,4,8,1,3]=>[5,3]=>2688
[2,8,3,6,5,7,1,4]=>[6,1,1]=>3360
[9,8,4,7,6,5,3,2,1]=>[3,2,2,2]=>2520
[9,8,3,7,6,5,4,2,1]=>[2,2,2,2,1]=>945
[9,3,8,7,6,5,4,2,1]=>[3,2,2,2]=>2520
[9,2,8,7,6,5,4,3,1]=>[2,2,2,2,1]=>945
[10,9,8,5,7,6,4,3,2,1]=>[3,2,2,2,1]=>25200
[9,8,4,6,5,7,3,2,1]=>[4,2,2,1]=>11340
[10,9,8,4,7,6,5,3,2,1]=>[2,2,2,2,1,1]=>4725
[9,8,3,6,5,4,7,2,1]=>[2,2,2,1,1,1]=>1260
[10,9,4,8,7,6,5,3,2,1]=>[3,2,2,2,1]=>25200
[9,3,7,6,5,4,8,2,1]=>[4,2,2,1]=>11340
[9,2,7,6,5,4,3,8,1]=>[2,2,2,1,1,1]=>1260
[10,3,9,8,7,6,5,4,2,1]=>[3,2,2,2,1]=>25200
[10,2,9,8,7,6,5,4,3,1]=>[2,2,2,2,1,1]=>4725
[7,4,3,1,6,5,2,8]=>[4,2,1,1]=>2520
[3,5,1,2,6,8,7,4]=>[5,2,1]=>4032
[3,1,2,4,8,7,5,6]=>[4,3,1]=>3360
[5,4,1,2,3,7,8,6]=>[3,3,2]=>1120
[1,6,7,2,5,8,3,4]=>[4,2,1,1]=>2520
[7,8,5,6,2,4,3,1]=>[6,2]=>3360
[5,3,8,6,2,4,1,7]=>[6,2]=>3360
[2,7,4,6,3,8,1,5]=>[5,3]=>2688
[5,4,7,8,6,2,1,3]=>[8]=>5040
[2,7,4,8,3,1,5,6]=>[8]=>5040
[8,2,1,3,7,4,6,5]=>[7,1]=>5760
[6,5,8,2,3,4,7,1]=>[7,1]=>5760
[7,8,2,3,6,4,5,1]=>[8]=>5040
[8,1,2,7,5,3,4,6]=>[5,2,1]=>4032
[4,2,8,1,3,7,5,6]=>[5,2,1]=>4032
[7,5,1,8,2,3,4,6]=>[6,2]=>3360
[8,2,4,1,3,7,5,6]=>[7,1]=>5760
[8,1,6,2,3,7,4,5]=>[8]=>5040
[7,1,8,2,3,6,4,5]=>[4,3,1]=>3360
[4,2,6,7,5,1,8,3]=>[6,1,1]=>3360
[4,7,2,5,3,8,1,6]=>[6,2]=>3360
[3,5,7,4,2,8,1,6]=>[3,2,2,1]=>1680
[2,4,7,6,3,8,1,5]=>[8]=>5040
[4,6,8,5,1,2,3,7]=>[3,3,2]=>1120
[4,6,5,7,1,2,3,8]=>[5,2,1]=>4032
[4,6,5,7,1,3,8,2]=>[8]=>5040
[3,4,7,6,1,8,2,5]=>[8]=>5040
[8,5,2,1,6,3,4,7]=>[4,4]=>1260
[7,1,8,5,3,2,4,6]=>[8]=>5040
[9,10,2,1,6,4,3,5,7,8]=>[10]=>362880
[7,10,2,1,8,4,3,5,6,9]=>[8,2]=>226800
[2,9,1,10,7,4,3,5,6,8]=>[10]=>362880
[2,8,1,9,4,3,10,5,6,7]=>[8,2]=>226800
[10,8,5,2,1,6,3,4,7,9]=>[6,3,1]=>201600
[9,5,2,1,10,6,3,4,7,8]=>[9,1]=>403200
[10,7,2,1,8,5,3,4,6,9]=>[7,3]=>172800
[9,2,1,10,7,5,3,4,6,8]=>[6,3,1]=>201600
[2,8,1,9,3,10,5,4,6,7]=>[10]=>362880
[10,6,2,1,7,3,8,4,5,9]=>[7,3]=>172800
[9,2,1,10,6,3,7,4,5,8]=>[5,3,1,1]=>120960
[8,2,1,9,3,10,6,4,5,7]=>[6,3,1]=>201600
[7,2,1,8,3,9,4,10,5,6]=>[9,1]=>403200
[10,8,6,3,1,4,2,5,7,9]=>[7,3]=>172800
[3,9,1,10,6,4,2,5,7,8]=>[5,3,2]=>120960
[10,7,3,1,8,4,2,5,6,9]=>[5,2,2,1]=>90720
[9,3,1,10,7,4,2,5,6,8]=>[10]=>362880
[8,3,1,9,4,2,10,5,6,7]=>[8,2]=>226800
[10,8,5,1,6,3,2,4,7,9]=>[7,3]=>172800
[9,5,1,10,6,3,2,4,7,8]=>[7,3]=>172800
[10,7,1,8,5,3,2,4,6,9]=>[5,2,2,1]=>90720
[9,1,10,7,5,3,2,4,6,8]=>[9,1]=>403200
[8,3,1,9,2,10,5,4,6,7]=>[10]=>362880
[10,6,1,7,3,2,8,4,5,9]=>[5,3,2]=>120960
[9,1,10,6,3,2,7,4,5,8]=>[9,1]=>403200
[8,1,9,3,2,10,6,4,5,7]=>[7,3]=>172800
[7,1,8,3,2,9,4,10,5,6]=>[10]=>362880
[10,8,4,1,5,2,6,3,7,9]=>[9,1]=>403200
[9,4,1,10,5,2,6,3,7,8]=>[9,1]=>403200
[10,7,1,8,4,2,5,3,6,9]=>[10]=>362880
[9,1,10,7,4,2,5,3,6,8]=>[4,3,3]=>50400
[8,1,9,4,2,10,5,3,6,7]=>[9,1]=>403200
[10,6,1,7,2,8,4,3,5,9]=>[8,2]=>226800
[9,1,10,6,2,7,4,3,5,8]=>[4,3,3]=>50400
[8,1,9,2,10,6,4,3,5,7]=>[9,1]=>403200
[7,1,8,2,9,4,3,10,5,6]=>[8,2]=>226800
[10,5,1,6,2,7,3,8,4,9]=>[7,2,1]=>259200
[9,1,10,5,2,6,3,7,4,8]=>[5,4,1]=>181440
[8,1,9,2,10,5,3,6,4,7]=>[10]=>362880
[7,1,8,2,9,3,10,5,4,6]=>[10]=>362880
[11,12,8,2,1,6,4,3,5,7,9,10]=>[5,4,2,1]=>11975040
[12,2,9,1,10,6,4,3,5,7,8,11]=>[10,1,1]=>23950080
[10,2,4,1,11,3,12,6,5,7,8,9]=>[11,1]=>43545600
[2,11,7,1,12,8,4,3,5,6,9,10]=>[12]=>39916800
[9,12,2,1,10,7,4,3,5,6,8,11]=>[7,5]=>13685760
[2,11,1,12,9,7,4,3,5,6,8,10]=>[5,5,2]=>4790016
[10,11,2,1,4,3,12,7,5,6,8,9]=>[12]=>39916800
[8,12,2,1,9,4,3,10,5,6,7,11]=>[5,5,2]=>4790016
[2,11,1,12,8,4,3,9,5,6,7,10]=>[5,4,3]=>7983360
[5,11,2,1,12,8,6,3,4,7,9,10]=>[12]=>39916800
[11,5,2,1,12,9,6,3,4,7,8,10]=>[12]=>39916800
[12,10,7,2,1,8,5,3,4,6,9,11]=>[12]=>39916800
[11,2,1,12,9,7,5,3,4,6,8,10]=>[7,4,1]=>17107200
[8,9,2,1,12,3,10,5,4,6,7,11]=>[12]=>39916800
[11,8,2,1,12,3,9,5,4,6,7,10]=>[7,5]=>13685760
[2,10,1,11,3,12,8,5,4,6,7,9]=>[12]=>39916800
[2,9,1,10,3,11,5,4,12,6,7,8]=>[12]=>39916800
[11,6,2,1,12,7,3,8,4,5,9,10]=>[4,4,3,1]=>4989600
[11,2,1,12,8,3,9,6,4,5,7,10]=>[11,1]=>43545600
[10,2,1,11,3,12,8,6,4,5,7,9]=>[7,4,1]=>17107200
[12,7,2,1,8,3,9,4,10,5,6,11]=>[12]=>39916800
[8,2,1,9,3,10,4,11,5,12,6,7]=>[11,1]=>43545600
[12,10,8,6,3,1,4,2,5,7,9,11]=>[12]=>39916800
[11,12,3,1,8,6,4,2,5,7,9,10]=>[10,1,1]=>23950080
[3,11,1,12,9,6,4,2,5,7,8,10]=>[4,3,2,2,1]=>4989600
[3,10,4,1,11,2,12,6,5,7,8,9]=>[9,3]=>17740800
[12,10,7,3,1,8,4,2,5,6,9,11]=>[5,4,3]=>7983360
[11,7,3,1,12,8,4,2,5,6,9,10]=>[11,1]=>43545600
[12,9,3,1,10,7,4,2,5,6,8,11]=>[11,1]=>43545600
[11,3,1,12,9,7,4,2,5,6,8,10]=>[5,5,2]=>4790016
[11,3,1,12,8,4,2,9,5,6,7,10]=>[5,4,3]=>7983360
[5,11,1,12,8,6,3,2,4,7,9,10]=>[11,1]=>43545600
[12,9,5,1,10,6,3,2,4,7,8,11]=>[7,4,1]=>17107200
[11,5,1,12,9,6,3,2,4,7,8,10]=>[11,1]=>43545600
[12,10,7,1,8,5,3,2,4,6,9,11]=>[5,5,2]=>4790016
[11,7,1,12,8,5,3,2,4,6,9,10]=>[12]=>39916800
[12,9,1,10,7,5,3,2,4,6,8,11]=>[12]=>39916800
[11,1,12,9,7,5,3,2,4,6,8,10]=>[6,4,2]=>9979200
[11,8,1,12,3,2,9,5,4,6,7,10]=>[12]=>39916800
[10,3,1,11,2,12,8,5,4,6,7,9]=>[12]=>39916800
[9,3,1,10,2,11,5,4,12,6,7,8]=>[12]=>39916800
[12,10,6,1,7,3,2,8,4,5,9,11]=>[5,4,2,1]=>11975040
[11,6,1,12,7,3,2,8,4,5,9,10]=>[11,1]=>43545600
[12,9,1,10,6,3,2,7,4,5,8,11]=>[12]=>39916800
[11,1,12,9,6,3,2,7,4,5,8,10]=>[5,5,2]=>4790016
[10,1,11,6,3,2,12,7,4,5,8,9]=>[12]=>39916800
[11,1,12,7,3,2,8,4,9,5,6,10]=>[4,4,3,1]=>4989600
[10,1,11,3,2,12,7,4,8,5,6,9]=>[7,4,1]=>17107200
[8,1,9,3,2,10,4,11,5,12,6,7]=>[12]=>39916800
[4,11,1,12,8,5,2,6,3,7,9,10]=>[9,3]=>17740800
[12,9,4,1,10,5,2,6,3,7,8,11]=>[12]=>39916800
[11,4,1,12,9,5,2,6,3,7,8,10]=>[7,5]=>13685760
[11,7,1,12,8,4,2,5,3,6,9,10]=>[4,4,2,2]=>1871100
[12,9,1,10,7,4,2,5,3,6,8,11]=>[9,3]=>17740800
[11,1,12,9,7,4,2,5,3,6,8,10]=>[6,6]=>6652800
[12,8,1,9,4,2,10,5,3,6,7,11]=>[12]=>39916800
[11,1,12,8,4,2,9,5,3,6,7,10]=>[9,3]=>17740800
[10,1,11,4,2,12,8,5,3,6,7,9]=>[11,1]=>43545600
[9,1,10,4,2,11,5,3,12,6,7,8]=>[11,1]=>43545600
[12,10,6,1,7,2,8,4,3,5,9,11]=>[12]=>39916800
[11,6,1,12,7,2,8,4,3,5,9,10]=>[6,4,2]=>9979200
[12,9,1,10,6,2,7,4,3,5,8,11]=>[11,1]=>43545600
[11,1,12,9,6,2,7,4,3,5,8,10]=>[11,1]=>43545600
[10,1,11,6,2,12,7,4,3,5,8,9]=>[7,4,1]=>17107200
[12,8,1,9,2,10,6,4,3,5,7,11]=>[12]=>39916800
[10,1,11,2,12,8,6,4,3,5,7,9]=>[12]=>39916800
[12,7,1,8,2,9,4,3,10,5,6,11]=>[12]=>39916800
[10,1,11,2,12,7,4,3,8,5,6,9]=>[12]=>39916800
[8,1,9,2,10,4,3,11,5,12,6,7]=>[6,6]=>6652800
[12,10,5,1,6,2,7,3,8,4,9,11]=>[11,1]=>43545600
[11,5,1,12,6,2,7,3,8,4,9,10]=>[5,3,3,1]=>5322240
[12,9,1,10,5,2,6,3,7,4,8,11]=>[5,4,2,1]=>11975040
[11,1,12,9,5,2,6,3,7,4,8,10]=>[11,1]=>43545600
[10,1,11,5,2,12,6,3,7,4,8,9]=>[5,4,3]=>7983360
[11,1,12,8,2,9,5,3,6,4,7,10]=>[5,5,2]=>4790016
[12,7,1,8,2,9,3,10,5,4,6,11]=>[9,3]=>17740800
[11,1,12,7,2,8,3,9,5,4,6,10]=>[7,5]=>13685760
[10,1,11,2,12,7,3,8,5,4,6,9]=>[4,4,3,1]=>4989600
[9,1,10,2,11,3,12,7,5,4,6,8]=>[9,3]=>17740800
[8,1,9,2,10,3,11,5,4,12,6,7]=>[12]=>39916800
[12,6,1,7,2,8,3,9,4,10,5,11]=>[11,1]=>43545600
[11,1,12,6,2,7,3,8,4,9,5,10]=>[7,4,1]=>17107200
[10,1,11,2,12,6,3,7,4,8,5,9]=>[11,1]=>43545600
[9,1,10,2,11,3,12,6,4,7,5,8]=>[6,4,2]=>9979200
[8,2,7,5,4,1,6,3]=>[5,2,1]=>4032
[4,2,8,5,7,1,6,3]=>[5,2,1]=>4032
[6,8,7,4,5,3,2,1]=>[6,1,1]=>3360
[5,2,6,7,4,8,3,1]=>[7,1]=>5760
[6,5,8,1,7,3,2,4]=>[5,3]=>2688
[6,4,8,1,5,2,3,7]=>[4,3,1]=>3360
[7,2,4,1,6,3,5,8]=>[6,1,1]=>3360
[2,6,1,5,3,4,8,7]=>[6,2]=>3360
[3,8,7,5,4,2,6,1]=>[6,2]=>3360
[5,7,8,2,3,6,4,1]=>[4,3,1]=>3360
[2,8,7,3,1,4,5,6]=>[8]=>5040
[5,6,1,2,4,7,8,3]=>[8]=>5040
[10,2,3,1,4,5,6,7,8,9]=>[8,1,1]=>226800
[9,2,3,4,1,5,6,7,8]=>[6,1,1,1]=>10080
[9,8,4,5,7,6,3,2,1]=>[4,2,2,1]=>11340
[9,8,5,4,6,7,3,2,1]=>[4,2,2,1]=>11340
[10,9,8,6,5,7,4,3,2,1]=>[3,2,2,2,1]=>25200
[11,10,9,8,5,7,6,4,3,2,1]=>[2,2,2,2,2,1]=>10395
[10,9,8,4,5,7,6,3,2,1]=>[2,2,2,2,1,1]=>4725
[9,8,4,5,3,7,6,2,1]=>[3,2,2,2]=>2520
[9,8,3,5,7,6,4,2,1]=>[3,2,2,1,1]=>7560
[9,8,5,4,6,3,7,2,1]=>[3,2,2,1,1]=>7560
[9,8,4,3,6,7,5,2,1]=>[3,2,2,2]=>2520
[10,9,8,5,4,6,7,3,2,1]=>[2,2,2,2,1,1]=>4725
[11,10,9,8,6,5,7,4,3,2,1]=>[2,2,2,2,2,1]=>10395
[3,8,6,7,5,4,2,1]=>[7,1]=>5760
[7,8,5,1,4,6,2,3]=>[7,1]=>5760
[8,2,7,5,4,6,1,3]=>[4,2,1,1]=>2520
[8,4,7,6,3,1,2,5]=>[8]=>5040
[4,6,7,1,3,2,8,5]=>[4,2,2]=>1260
[6,4,7,5,3,2,8,1]=>[8]=>5040
[8,4,6,3,1,5,7,2]=>[7,1]=>5760
[7,3,1,4,5,6,8,2]=>[5,1,1,1]=>1344
[6,7,3,4,2,1,8,5]=>[4,2,1,1]=>2520
[6,4,8,3,1,5,7,2]=>[4,3,1]=>3360
[7,4,2,3,5,1,8,6]=>[4,3,1]=>3360
[3,1,6,5,2,4,8,7]=>[6,2]=>3360
[2,5,3,8,6,4,1,7]=>[7,1]=>5760
[5,8,4,1,3,2,7,6]=>[4,3,1]=>3360
[5,3,4,7,6,1,8,2]=>[5,3]=>2688
[4,5,2,1,6,3,8,7]=>[4,2,2]=>1260
[4,5,2,1,6,7,3,8]=>[5,2,1]=>4032
[5,3,8,6,2,4,7,1]=>[5,2,1]=>4032
[2,5,1,6,4,3,8,7]=>[6,2]=>3360
[3,6,2,8,5,7,1,4]=>[5,2,1]=>4032
[4,6,8,1,5,7,2,3]=>[3,2,2,1]=>1680
[4,1,2,5,7,6,3,8]=>[6,1,1]=>3360
[4,6,5,8,1,7,3,2]=>[8]=>5040
[2,1,3,6,4,8,7,5]=>[4,2,1,1]=>2520
[4,8,1,2,7,5,6,3]=>[5,3]=>2688
[4,5,1,6,8,7,2,3]=>[8]=>5040
[3,4,7,2,5,8,6,1]=>[5,2,1]=>4032
[2,5,1,8,6,4,7,3]=>[7,1]=>5760
[9,8,7,4,3,2,1,5,6]=>[8,1]=>45360
[9,8,7,6,3,2,1,4,5]=>[5,4]=>18144
[3,8,7,2,6,1,4,5]=>[8]=>5040
[8,4,5,1,6,7,2,3]=>[8]=>5040
[8,4,7,3,1,5,2,6]=>[4,4]=>1260
[2,5,1,8,3,6,4,7]=>[4,3,1]=>3360
[5,8,4,7,3,2,1,6]=>[5,3]=>2688
[4,3,8,6,1,2,5,7]=>[8]=>5040
[4,8,6,5,7,1,3,2]=>[6,2]=>3360
[7,2,3,5,6,8,4,1]=>[6,1,1]=>3360
[5,8,1,3,4,7,2,6]=>[4,4]=>1260
[8,7,5,6,4,1,3,2]=>[8]=>5040
[7,2,4,5,3,1,6,8]=>[3,3,1,1]=>1120
[7,6,3,1,4,5,8,2]=>[7,1]=>5760
[3,7,4,6,2,1,8,5]=>[4,4]=>1260
[5,4,1,7,8,6,2,3]=>[4,3,1]=>3360
[5,3,4,7,8,1,6,2]=>[8]=>5040
[4,3,7,6,5,1,8,2]=>[4,3,1]=>3360
[5,1,4,8,2,3,7,6]=>[4,3,1]=>3360
[3,2,8,5,4,1,6,7]=>[5,2,1]=>4032
[7,8,9,1,3,4,5,6,2]=>[9]=>40320
[6,1,2,9,3,4,5,7,8]=>[9]=>40320
[4,1,2,3,5,9,6,7,8]=>[4,4,1]=>11340
[3,1,2,4,5,6,9,7,8]=>[3,3,1,1,1]=>3360
[1,2,8,3,4,6,5,7]=>[5,1,1,1]=>1344
[8,1,2,7,3,5,4,6]=>[6,2]=>3360
[5,7,1,2,6,3,4,8]=>[4,3,1]=>3360
[1,2,7,5,6,3,4,8]=>[5,1,1,1]=>1344
[5,1,4,7,2,3,6,8]=>[4,3,1]=>3360
[4,8,1,2,3,6,5,7]=>[7,1]=>5760
[1,3,4,2,5,6,7,8,9]=>[3,1,1,1,1,1,1]=>168
[1,2,4,5,6,3,7,8,9]=>[4,1,1,1,1,1]=>756
[1,2,3,5,6,7,8,4,9]=>[5,1,1,1,1]=>3024
[2,1,5,3,6,7,4,8,9]=>[5,2,1,1]=>18144
[1,3,5,6,4,2,7,8,9]=>[5,1,1,1,1]=>3024
[3,5,2,1,6,4,7,8,9]=>[6,1,1,1]=>10080
[2,1,3,6,4,7,8,9,5]=>[6,2,1]=>30240
[1,3,4,6,7,2,8,5,9]=>[4,3,1,1]=>15120
[3,2,6,1,4,7,8,5,9]=>[7,1,1]=>25920
[2,4,6,1,7,5,3,8,9]=>[4,3,1,1]=>15120
[4,6,3,2,1,7,5,8,9]=>[6,1,1,1]=>10080
[2,4,1,7,5,8,3,9,6]=>[5,3,1]=>24192
[4,3,7,2,1,5,8,9,6]=>[9]=>40320
[1,3,5,7,8,6,4,2,9]=>[4,2,1,1,1]=>7560
[3,5,7,2,1,8,6,4,9]=>[8,1]=>45360
[5,7,4,3,2,1,8,6,9]=>[6,2,1]=>30240
[2,4,6,8,1,9,7,5,3]=>[5,3,1]=>24192
[4,6,8,3,2,1,9,7,5]=>[9]=>40320
[6,8,5,4,3,2,1,9,7]=>[6,2,1]=>30240
[1,3,4,2,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]=>240
[1,2,4,5,6,3,7,8,9,10]=>[4,1,1,1,1,1,1]=>1260
[1,2,3,5,6,7,8,4,9,10]=>[5,1,1,1,1,1]=>6048
[2,1,5,3,6,7,4,8,9,10]=>[5,2,1,1,1]=>60480
[1,3,5,6,4,2,7,8,9,10]=>[5,1,1,1,1,1]=>6048
[3,5,2,1,6,4,7,8,9,10]=>[6,1,1,1,1]=>25200
[2,1,3,6,4,7,8,9,5,10]=>[6,2,1,1]=>151200
[1,3,4,6,7,2,8,5,9,10]=>[4,3,1,1,1]=>50400
[3,2,6,1,4,7,8,5,9,10]=>[7,1,1,1]=>86400
[2,4,6,1,7,5,3,8,9,10]=>[4,3,1,1,1]=>50400
[4,6,3,2,1,7,5,8,9,10]=>[6,1,1,1,1]=>25200
[1,3,4,2,7,8,5,9,10,6]=>[4,3,2,1]=>151200
[3,2,1,7,4,5,8,9,10,6]=>[7,2,1]=>259200
[1,2,4,5,7,8,9,6,3,10]=>[5,2,1,1,1]=>60480
[4,3,7,2,1,5,8,9,6,10]=>[9,1]=>403200
[1,3,5,7,8,6,4,2,9,10]=>[4,2,1,1,1,1]=>18900
[3,5,7,2,1,8,6,4,9,10]=>[8,1,1]=>226800
[5,7,4,3,2,1,8,6,9,10]=>[6,2,1,1]=>151200
[2,1,5,3,8,6,9,10,7,4]=>[5,2,2,1]=>90720
[1,3,5,6,8,9,4,2,10,7]=>[5,4,1]=>181440
[3,5,2,8,1,6,9,4,10,7]=>[4,3,2,1]=>151200
[5,4,8,3,2,1,6,9,10,7]=>[10]=>362880
[2,4,6,8,1,9,7,5,3,10]=>[5,3,1,1]=>120960
[4,6,8,3,2,1,9,7,5,10]=>[9,1]=>403200
[6,8,5,4,3,2,1,9,7,10]=>[6,2,1,1]=>151200
[3,5,7,9,2,1,10,8,6,4]=>[7,2,1]=>259200
[5,7,9,4,3,2,1,10,8,6]=>[9,1]=>403200
[7,9,6,5,4,3,2,1,10,8]=>[6,2,2]=>75600
[6,2,3,8,7,1,4,5]=>[4,2,1,1]=>2520
[8,2,3,6,4,7,5,1]=>[4,2,1,1]=>2520
[7,2,3,6,4,8,1,5]=>[4,2,1,1]=>2520
[4,5,6,3,7,2,8,1,9]=>[8,1]=>45360
[1,5,6,7,4,8,3,9,2]=>[8,1]=>45360
[4,5,1,3,2,6,8,7]=>[3,2,2,1]=>1680
[6,4,7,5,1,3,2,8]=>[7,1]=>5760
[5,3,1,6,2,7,8,4]=>[4,4]=>1260
[6,7,2,4,1,8,3,5]=>[4,3,1]=>3360
[5,1,6,3,2,7,8,4]=>[5,3]=>2688
[5,2,1,6,4,7,3,8]=>[6,1,1]=>3360
[5,4,1,6,2,7,8,3]=>[8]=>5040
[6,7,2,5,4,1,3,8]=>[3,2,2,1]=>1680
[7,1,3,5,4,2,8,6]=>[5,2,1]=>4032
[7,6,8,2,4,5,3,1]=>[4,4]=>1260
[4,2,8,6,5,1,3,7]=>[3,3,1,1]=>1120
[3,8,5,4,7,1,2,6]=>[7,1]=>5760
[1,4,8,3,6,2,7,5]=>[6,1,1]=>3360
[6,3,2,4,8,7,1,5]=>[3,2,2,1]=>1680
[8,3,2,7,4,1,5,6]=>[3,3,2]=>1120
[7,3,2,6,5,8,1,4]=>[3,2,2,1]=>1680
[3,6,2,5,7,4,8,1]=>[8]=>5040
[2,7,1,5,8,6,4,3]=>[7,1]=>5760
[7,2,4,1,6,8,5,3]=>[7,1]=>5760
[6,4,7,2,3,8,5,1]=>[3,3,2]=>1120
[6,1,8,5,7,4,2,3]=>[6,2]=>3360
[7,1,4,3,6,5,8,2]=>[4,2,2]=>1260
[7,1,5,6,3,4,8,2]=>[4,2,2]=>1260
[6,1,8,5,4,7,3,2]=>[6,2]=>3360
[7,6,1,5,4,2,8,3]=>[4,2,2]=>1260
[5,1,6,8,7,2,4,3]=>[8]=>5040
[4,6,7,5,3,1,8,2]=>[8]=>5040
[5,3,2,6,8,7,4,1]=>[3,3,2]=>1120
[5,4,6,2,8,7,3,1]=>[3,3,2]=>1120
[4,5,8,6,7,2,3,1]=>[8]=>5040
[4,5,7,6,1,2,8,3]=>[5,3]=>2688
[4,6,5,7,2,1,8,3]=>[8]=>5040
[2,3,7,5,6,1,10,9,4,8]=>[10]=>362880
[2,3,4,10,6,9,8,5,1,7]=>[10]=>362880
[2,3,6,5,9,10,8,4,1,7]=>[10]=>362880
[2,3,9,5,8,7,4,1,10,6]=>[10]=>362880
[2,5,4,9,6,10,8,3,1,7]=>[10]=>362880
[2,5,4,8,9,7,3,1,10,6]=>[10]=>362880
[2,3,4,10,6,7,1,9,8,5]=>[8,2]=>226800
[2,3,7,5,6,1,10,9,8,4]=>[8,2]=>226800
[2,3,4,10,6,8,9,1,7,5]=>[8,2]=>226800
[2,3,6,5,8,10,9,1,7,4]=>[8,2]=>226800
[2,3,8,5,7,9,1,10,6,4]=>[8,2]=>226800
[2,5,4,8,6,10,9,1,7,3]=>[8,2]=>226800
[2,5,4,7,8,9,1,10,6,3]=>[8,2]=>226800
[2,3,4,10,6,9,8,7,5,1]=>[5,3,2]=>120960
[2,3,6,5,9,10,8,7,4,1]=>[5,3,2]=>120960
[2,3,7,5,9,8,10,6,4,1]=>[5,3,2]=>120960
[2,3,9,5,8,7,6,4,1,10]=>[4,3,2,1]=>151200
[2,5,4,9,6,10,8,7,3,1]=>[5,3,2]=>120960
[2,5,4,9,7,8,10,6,3,1]=>[5,3,2]=>120960
[2,5,4,8,9,7,6,3,1,10]=>[4,3,2,1]=>151200
[2,3,4,10,7,9,8,1,6,5]=>[8,2]=>226800
[2,3,5,7,10,9,8,1,6,4]=>[8,2]=>226800
[2,3,8,6,9,7,1,10,5,4]=>[8,2]=>226800
[2,4,7,5,10,9,8,1,6,3]=>[8,2]=>226800
[2,4,6,8,9,7,1,10,5,3]=>[8,2]=>226800
[2,3,4,10,7,8,9,6,5,1]=>[5,3,2]=>120960
[2,3,5,7,10,8,9,6,4,1]=>[5,3,2]=>120960
[2,3,7,6,8,9,10,5,4,1]=>[5,3,2]=>120960
[2,3,9,6,7,8,5,4,1,10]=>[4,3,2,1]=>151200
[2,4,7,5,10,8,9,6,3,1]=>[5,3,2]=>120960
[2,4,6,7,8,9,10,5,3,1]=>[5,3,2]=>120960
[2,4,6,9,7,8,5,3,1,10]=>[4,3,2,1]=>151200
[2,6,5,8,9,7,10,4,3,1]=>[5,3,2]=>120960
[2,6,5,7,8,9,4,3,1,10]=>[4,3,2,1]=>151200
[3,7,4,5,10,9,8,1,6,2]=>[8,2]=>226800
[3,6,4,8,9,7,1,10,5,2]=>[8,2]=>226800
[3,7,4,5,10,8,9,6,2,1]=>[5,3,2]=>120960
[3,6,4,7,8,9,10,5,2,1]=>[5,3,2]=>120960
[3,6,4,9,7,8,5,2,1,10]=>[4,3,2,1]=>151200
[3,5,6,8,9,7,10,4,2,1]=>[5,3,2]=>120960
[3,5,6,7,8,9,4,2,1,10]=>[4,3,2,1]=>151200
[7,4,8,6,3,5,1,2]=>[6,2]=>3360
[7,2,4,3,6,1,8,5]=>[5,2,1]=>4032
[2,3,4,7,8,6,1,5]=>[5,2,1]=>4032
[6,3,7,1,4,2,8,5]=>[8]=>5040
[4,6,3,5,1,8,2,7]=>[4,3,1]=>3360
[8,5,7,6,2,3,4,1]=>[4,2,2]=>1260
[3,5,6,7,8,9,2,4,1]=>[5,4]=>18144
[3,4,6,7,8,2,5,1]=>[8]=>5040
[2,4,6,7,8,9,1,3,5]=>[5,4]=>18144
[2,5,6,7,3,8,1,4]=>[8]=>5040
[2,5,6,7,8,9,3,1,4]=>[5,4]=>18144
[5,8,4,6,2,1,7,3]=>[7,1]=>5760
[2,4,7,5,8,6,3,1]=>[5,2,1]=>4032
[1,6,8,3,4,2,7,5]=>[4,2,1,1]=>2520
[4,1,7,6,2,8,3,5]=>[6,2]=>3360
[4,1,8,2,7,5,3,6]=>[5,3]=>2688
[4,1,7,2,8,5,3,6]=>[3,3,2]=>1120
[2,5,6,3,7,4,8,1]=>[5,3]=>2688
[2,6,5,3,8,4,7,1]=>[7,1]=>5760
[2,6,5,3,7,4,8,1]=>[8]=>5040
[7,1,6,3,5,4,8,2]=>[4,3,1]=>3360
[5,7,3,2,8,4,1,6]=>[7,1]=>5760
[2,8,6,1,7,5,3,4]=>[4,4]=>1260
[8,1,5,2,7,4,3,6]=>[5,3]=>2688
[7,1,4,2,8,5,3,6]=>[5,3]=>2688
[2,6,8,1,7,5,3,4]=>[8]=>5040
[1,4,6,5,3,8,2,7]=>[7,1]=>5760
[2,4,5,8,7,1,3,6]=>[5,3]=>2688
[3,1,6,8,7,5,4,2]=>[8]=>5040
[3,1,8,7,5,6,4,2]=>[4,2,1,1]=>2520
[5,1,8,7,6,3,4,2]=>[6,2]=>3360
[8,2,7,5,3,6,4,1]=>[4,2,1,1]=>2520
[8,7,2,3,1,5,6,4]=>[8]=>5040
[2,8,5,7,6,1,3,4]=>[8]=>5040
[1,8,7,2,6,4,5,3]=>[7,1]=>5760
[8,7,2,1,6,4,5,3]=>[8]=>5040
[1,8,4,7,6,2,5,3]=>[7,1]=>5760
[8,7,1,6,4,3,5,2]=>[8]=>5040
[8,4,1,7,3,6,5,2]=>[7,1]=>5760
[5,4,6,3,8,1,7,2,9]=>[7,1,1]=>25920
[1,6,5,7,4,9,2,8,3]=>[7,1,1]=>25920
[5,6,4,7,3,9,1,8,2,10]=>[5,3,1,1]=>120960
[5,4,8,1,7,2,6,3,9]=>[6,2,1]=>30240
[5,4,8,1,6,3,7,2,9]=>[7,1,1]=>25920
[1,6,5,9,2,8,3,7,4]=>[6,2,1]=>30240
[1,6,5,9,2,7,4,8,3]=>[7,1,1]=>25920
[1,6,7,5,8,4,10,2,9,3]=>[5,3,1,1]=>120960
[4,5,6,7,8,9,1,10,2,3]=>[7,3]=>172800
[2,5,6,7,8,1,9,3,4]=>[6,3]=>20160
[4,5,6,7,1,2,8,3,9]=>[8,1]=>45360
[1,3,6,7,8,9,2,4,5]=>[8,1]=>45360
[3,5,6,7,8,1,2,9,4]=>[6,3]=>20160
[3,2,5,4,7,6,8,10,9,1]=>[6,1,1,1,1]=>25200
[3,2,5,4,6,9,7,8,10,1]=>[6,1,1,1,1]=>25200
[3,2,5,4,6,8,7,10,9,1]=>[6,1,1,1,1]=>25200
[3,2,5,4,6,7,10,8,9,1]=>[6,1,1,1,1]=>25200
[3,2,4,7,5,6,9,8,10,1]=>[6,1,1,1,1]=>25200
[3,2,4,7,5,6,8,10,9,1]=>[6,1,1,1,1]=>25200
[3,2,4,6,5,9,7,8,10,1]=>[6,1,1,1,1]=>25200
[3,2,4,6,5,8,7,10,9,1]=>[6,1,1,1,1]=>25200
[3,2,4,6,5,7,10,8,9,1]=>[6,1,1,1,1]=>25200
[3,2,4,5,9,6,7,8,10,1]=>[6,1,1,1,1]=>25200
[3,2,4,5,8,6,7,10,9,1]=>[6,1,1,1,1]=>25200
[3,2,4,5,7,6,10,8,9,1]=>[6,1,1,1,1]=>25200
[3,2,4,5,6,10,7,8,9,1]=>[6,1,1,1,1]=>25200
[2,5,3,4,7,6,9,8,10,1]=>[6,1,1,1,1]=>25200
[2,5,3,4,7,6,8,10,9,1]=>[6,1,1,1,1]=>25200
[2,5,3,4,6,9,7,8,10,1]=>[6,1,1,1,1]=>25200
[2,5,3,4,6,8,7,10,9,1]=>[6,1,1,1,1]=>25200
[2,5,3,4,6,7,10,8,9,1]=>[6,1,1,1,1]=>25200
[2,4,3,7,5,6,9,8,10,1]=>[6,1,1,1,1]=>25200
[2,4,3,7,5,6,8,10,9,1]=>[6,1,1,1,1]=>25200
[2,4,3,6,5,9,7,8,10,1]=>[6,1,1,1,1]=>25200
[2,4,3,6,5,7,10,8,9,1]=>[6,1,1,1,1]=>25200
[2,4,3,5,9,6,7,8,10,1]=>[6,1,1,1,1]=>25200
[2,4,3,5,8,6,7,10,9,1]=>[6,1,1,1,1]=>25200
[2,4,3,5,7,6,10,8,9,1]=>[6,1,1,1,1]=>25200
[2,4,3,5,6,10,7,8,9,1]=>[6,1,1,1,1]=>25200
[2,3,7,4,5,6,9,8,10,1]=>[6,1,1,1,1]=>25200
[2,3,7,4,5,6,8,10,9,1]=>[6,1,1,1,1]=>25200
[2,3,6,4,5,9,7,8,10,1]=>[6,1,1,1,1]=>25200
[2,3,6,4,5,8,7,10,9,1]=>[6,1,1,1,1]=>25200
[2,3,6,4,5,7,10,8,9,1]=>[6,1,1,1,1]=>25200
[2,3,5,4,9,6,7,8,10,1]=>[6,1,1,1,1]=>25200
[2,3,5,4,8,6,7,10,9,1]=>[6,1,1,1,1]=>25200
[2,3,5,4,7,6,10,8,9,1]=>[6,1,1,1,1]=>25200
[2,3,5,4,6,10,7,8,9,1]=>[6,1,1,1,1]=>25200
[2,3,4,9,5,6,7,8,10,1]=>[6,1,1,1,1]=>25200
[2,3,4,8,5,6,7,10,9,1]=>[6,1,1,1,1]=>25200
[2,3,4,7,5,6,10,8,9,1]=>[6,1,1,1,1]=>25200
[2,3,4,6,5,10,7,8,9,1]=>[6,1,1,1,1]=>25200
[4,5,1,8,7,3,6,2]=>[8]=>5040
[3,8,5,2,6,7,4,1]=>[8]=>5040
[4,3,8,5,2,6,1,7]=>[7,1]=>5760
[3,6,4,7,5,2,1,8]=>[4,2,1,1]=>2520
[5,7,4,1,2,6,8,3]=>[7,1]=>5760
[7,4,5,2,6,3,1,8]=>[3,2,2,1]=>1680
[8,6,3,4,5,1,7,2]=>[4,1,1,1,1]=>420
[8,6,3,5,4,1,7,2]=>[4,2,1,1]=>2520
[8,7,4,5,1,3,6,2]=>[8]=>5040
[8,6,2,5,3,1,4,7]=>[8]=>5040
[8,4,7,3,1,2,5,6]=>[8]=>5040
[8,7,3,5,1,6,4,2]=>[6,1,1]=>3360
[4,8,3,2,6,1,7,5]=>[6,1,1]=>3360
[4,3,7,6,1,5,2,8]=>[4,3,1]=>3360
[7,5,4,3,6,1,8,2]=>[6,2]=>3360
[4,6,8,5,3,1,2,7]=>[8]=>5040
[5,6,8,4,3,7,2,1]=>[4,3,1]=>3360
[7,5,8,4,2,1,6,3]=>[3,2,2,1]=>1680
[1,4,8,7,6,2,5,3]=>[5,2,1]=>4032
[7,2,4,1,5,3,8,6]=>[6,1,1]=>3360
[8,5,3,4,1,7,2,6]=>[6,1,1]=>3360
[2,8,5,4,3,6,1,7]=>[4,2,1,1]=>2520
[8,6,5,3,1,2,7,4]=>[5,2,1]=>4032
[7,4,6,5,3,2,8,1]=>[5,3]=>2688
[5,6,7,2,3,8,4,1]=>[8]=>5040
[8,4,2,6,5,7,3,1]=>[5,2,1]=>4032
[1,7,4,2,8,5,6,3]=>[7,1]=>5760
[3,2,1,7,4,6,8,5]=>[4,2,1,1]=>2520
[6,2,5,7,1,4,3,8]=>[6,1,1]=>3360
[4,8,5,3,1,2,6,7]=>[4,4]=>1260
[8,5,2,4,6,1,3,7]=>[7,1]=>5760
[1,5,3,4,7,2,6,8]=>[4,1,1,1,1]=>420
[8,4,6,1,5,7,3,2]=>[4,3,1]=>3360
[6,4,7,2,1,3,8,5]=>[6,2]=>3360
[6,7,3,1,2,4,8,5]=>[4,3,1]=>3360
[3,1,8,7,6,2,5,4]=>[8]=>5040
[1,3,8,6,7,2,5,4]=>[5,2,1]=>4032
[5,2,3,6,1,8,4,7]=>[4,2,1,1]=>2520
[3,2,6,4,7,1,5,8]=>[3,2,1,1,1]=>1120
[2,7,4,6,8,5,3,1]=>[8]=>5040
[2,7,1,8,6,5,3,4]=>[4,2,2]=>1260
[2,3,4,5,7,6,8,9,1]=>[8,1]=>45360
[2,3,4,5,7,8,6,9,1]=>[9]=>40320
[2,3,4,5,8,7,6,9,1]=>[7,2]=>25920
[2,3,4,5,7,9,8,6,1]=>[9]=>40320
[4,5,6,3,7,8,9,2,1]=>[9]=>40320
[3,4,5,6,2,7,8,9,10,1]=>[10]=>362880
[2,4,5,6,3,7,8,9,10,1]=>[8,2]=>226800
[2,3,5,6,4,7,8,9,10,1]=>[10]=>362880
[5,3,4,7,6,2,1,8]=>[7,1]=>5760
[4,1,8,5,7,2,6,3]=>[6,2]=>3360
[4,1,8,2,7,5,6,3]=>[3,3,2]=>1120
[7,6,8,2,4,3,5,1]=>[8]=>5040
[7,4,5,3,8,1,6,2]=>[5,3]=>2688
[7,3,6,1,4,2,8,5]=>[5,3]=>2688
[8,7,2,6,4,5,1,3]=>[5,3]=>2688
[1,2,3,4,7,9,5,6,8]=>[3,2,1,1,1,1]=>2520
[1,2,3,4,6,7,9,5,8]=>[5,1,1,1,1]=>3024
[1,2,3,4,8,5,6,9,7]=>[5,1,1,1,1]=>3024
[1,2,3,4,7,8,5,9,6]=>[3,2,1,1,1,1]=>2520
[1,2,4,8,5,7,3,6]=>[5,1,1,1]=>1344
[7,3,2,5,1,6,8,4]=>[5,2,1]=>4032
[3,5,1,7,6,4,8,2]=>[6,2]=>3360
[8,7,4,2,1,6,5,3]=>[7,1]=>5760
[5,4,7,6,2,1,8,3]=>[5,3]=>2688
[3,5,2,8,7,1,6,4]=>[6,2]=>3360
[3,7,6,5,4,1,8,2]=>[3,3,2]=>1120
[4,6,5,3,1,8,7,2]=>[4,3,1]=>3360
[4,5,2,6,7,3,8,1]=>[8]=>5040
[9,3,10,1,2,4,5,6,7,8]=>[10]=>362880
[10,3,1,9,2,4,5,6,7,8]=>[10]=>362880
[3,1,4,10,2,5,6,7,8,9]=>[10]=>362880
[4,7,1,8,5,3,2,6]=>[5,2,1]=>4032
[8,5,6,1,7,4,2,3]=>[5,3]=>2688
[6,4,1,2,5,7,8,3]=>[5,2,1]=>4032
[6,1,5,4,2,7,3,8]=>[6,1,1]=>3360
[6,4,2,3,1,7,5,8]=>[4,3,1]=>3360
[3,4,6,1,8,2,7,5]=>[5,2,1]=>4032
[5,3,1,4,7,6,2,8]=>[5,1,1,1]=>1344
[6,4,5,2,7,1,3,8]=>[3,2,2,1]=>1680
[7,4,3,5,1,6,2,8]=>[5,1,1,1]=>1344
[7,5,3,6,2,1,4,8]=>[4,2,1,1]=>2520
[6,4,3,7,1,8,2,5]=>[4,3,1]=>3360
[3,1,2,7,6,4,5,8]=>[4,3,1]=>3360
[5,1,2,7,6,3,4,8]=>[5,2,1]=>4032
[5,6,1,7,2,4,3,8]=>[7,1]=>5760
[3,5,6,8,1,2,7,4]=>[5,2,1]=>4032
[2,6,5,7,1,3,4,8]=>[5,2,1]=>4032
[2,3,7,1,5,6,4,8]=>[5,1,1,1]=>1344
[2,6,5,3,4,1,7,8]=>[3,3,1,1]=>1120
[2,6,1,3,5,4,7,8]=>[5,1,1,1]=>1344
[4,6,1,5,2,8,7,3]=>[7,1]=>5760
[6,1,5,4,2,7,8,3]=>[7,1]=>5760
[4,6,1,5,2,7,8,3]=>[8]=>5040
[2,8,6,5,1,3,7,4]=>[5,2,1]=>4032
[5,1,8,6,2,7,4,3]=>[3,3,2]=>1120
[3,6,8,2,7,5,1,4]=>[8]=>5040
[5,6,4,1,7,2,8,3]=>[6,2]=>3360
[3,8,6,1,5,7,4,2]=>[5,2,1]=>4032
[8,1,6,3,4,2,5,7]=>[8]=>5040
[7,4,2,3,1,6,8,5]=>[4,3,1]=>3360
[6,4,2,3,7,8,1,5]=>[5,3]=>2688
[4,3,6,2,5,8,1,7]=>[7,1]=>5760
[9,8,10,7,6,5,4,3,1,2]=>[4,2,2,2]=>18900
[8,7,9,6,5,4,2,1,3]=>[2,2,2,2,1]=>945
[8,9,7,6,5,4,2,1,3]=>[4,2,2,1]=>11340
[8,9,7,6,5,4,2,3,1]=>[6,2,1]=>30240
[8,9,1,2,3,4,5,6,10,11,7]=>[11]=>3628800
[10,7,1,2,3,4,8,9,5,6]=>[10]=>362880
[1,6,4,5,7,3,2,8]=>[6,1,1]=>3360
[1,6,4,5,7,2,8,3]=>[5,2,1]=>4032
[1,7,5,6,4,8,3,2]=>[7,1]=>5760
[1,5,6,7,3,2,4,8]=>[4,2,1,1]=>2520
[7,6,8,2,1,5,3,4]=>[8]=>5040
[8,6,2,5,1,3,7,4]=>[4,3,1]=>3360
[7,1,6,8,3,2,4,5]=>[8]=>5040
[5,7,2,6,4,1,8,3]=>[4,4]=>1260
[4,5,6,1,3,8,2,7]=>[6,2]=>3360
[6,3,5,7,4,2,8,1]=>[8]=>5040
[7,6,4,8,5,3,1,2]=>[5,2,1]=>4032
[8,2,1,6,4,7,3,5]=>[7,1]=>5760
[1,3,8,6,5,2,7,4]=>[5,1,1,1]=>1344
[2,7,3,8,5,6,4,1]=>[5,1,1,1]=>1344
[1,2,8,5,7,4,6,3]=>[4,2,1,1]=>2520
[1,6,8,5,4,7,2,3]=>[3,2,2,1]=>1680
[5,7,1,8,3,2,6,4]=>[3,3,2]=>1120
[8,2,5,4,3,7,1,6]=>[4,2,1,1]=>2520
[5,8,4,3,7,6,2,1]=>[5,2,1]=>4032
[8,1,5,3,4,7,2,6]=>[5,3]=>2688
[6,1,8,7,4,5,3,2]=>[8]=>5040
[1,5,8,6,4,3,7,2]=>[6,1,1]=>3360
[5,8,6,4,2,1,7,3]=>[6,1,1]=>3360
[2,6,1,8,4,7,5,3]=>[8]=>5040
[5,3,8,6,1,2,7,4]=>[5,2,1]=>4032
[5,8,1,4,6,2,7,3]=>[6,1,1]=>3360
[3,7,6,2,1,4,8,5]=>[8]=>5040
[4,6,2,3,7,1,8,5]=>[5,3]=>2688
[6,8,7,5,1,3,4,2]=>[6,2]=>3360
[6,4,3,2,7,8,5,1]=>[3,2,2,1]=>1680
[2,7,6,1,5,3,8,4]=>[5,2,1]=>4032
[7,8,6,4,2,5,3,1]=>[7,1]=>5760
[6,4,5,8,7,1,3,2]=>[3,3,2]=>1120
[6,4,1,7,8,3,2,5]=>[3,3,2]=>1120
[2,3,4,5,8,6,7,9,1]=>[7,1,1]=>25920
[2,3,4,5,9,6,8,7,1]=>[6,2,1]=>30240
[9,3,4,5,2,6,7,8,1]=>[4,2,1,1,1]=>7560
[6,2,3,4,5,7,8,9,10,1]=>[6,1,1,1,1]=>25200
[2,6,3,4,5,7,8,9,10,1]=>[7,1,1,1]=>86400
[2,3,6,4,5,7,8,9,10,1]=>[8,1,1]=>226800
[5,4,7,2,1,3,8,6]=>[4,2,2]=>1260
[2,6,4,5,7,1,8,3]=>[5,3]=>2688
[3,7,4,6,1,5,8,2]=>[5,3]=>2688
[3,4,6,5,2,8,1,7]=>[5,3]=>2688
[4,6,7,5,8,2,1,3]=>[6,2]=>3360
[2,5,7,6,4,1,8,3]=>[5,3]=>2688
[5,1,4,6,2,7,8,3]=>[5,3]=>2688
[1,2,5,3,7,8,6,4]=>[6,1,1]=>3360
[4,8,3,5,1,2,7,6]=>[3,3,1,1]=>1120
[6,1,3,7,2,8,4,5]=>[5,2,1]=>4032
[3,8,5,4,1,7,2,6]=>[4,3,1]=>3360
[3,1,5,8,2,6,7,4]=>[4,2,1,1]=>2520
[2,8,5,3,1,7,4,6]=>[8]=>5040
[6,5,2,3,7,1,8,4]=>[6,2]=>3360
[7,2,1,6,4,8,3,5]=>[4,3,1]=>3360
[2,1,3,7,5,8,4,6]=>[2,2,2,1,1]=>420
[6,2,4,5,7,1,8,3]=>[5,2,1]=>4032
[2,3,8,7,1,4,6,5]=>[5,3]=>2688
[4,2,7,5,6,8,1,3]=>[7,1]=>5760
[2,1,3,4,5,8,6,7,9]=>[3,2,1,1,1,1]=>2520
[6,8,2,5,4,7,3,1]=>[6,2]=>3360
[9,2,3,4,5,1,6,7,8]=>[5,1,1,1,1]=>3024
[7,2,3,4,5,6,9,1,8]=>[4,1,1,1,1,1]=>756
[10,2,3,4,5,6,7,1,8,9]=>[4,1,1,1,1,1,1]=>1260
[6,2,3,4,5,9,1,7,8]=>[5,1,1,1,1]=>3024
[10,2,3,4,5,6,1,7,8,9]=>[5,1,1,1,1,1]=>6048
[5,2,3,4,9,1,6,7,8]=>[6,1,1,1]=>10080
[10,2,3,4,5,1,6,7,8,9]=>[6,1,1,1,1]=>25200
[4,2,3,9,1,5,6,7,8]=>[7,1,1]=>25920
[10,2,3,4,1,5,6,7,8,9]=>[7,1,1,1]=>86400
[3,2,9,1,4,5,6,7,8]=>[8,1]=>45360
[2,8,1,3,4,5,6,10,7,9]=>[10]=>362880
[10,7,1,2,3,4,5,9,6,8]=>[10]=>362880
[5,3,2,7,6,1,8,4]=>[3,3,2]=>1120
[4,5,6,8,2,9,3,10,7,1]=>[4,4,2]=>56700
[10,4,5,6,9,3,8,2,7,1]=>[8,2]=>226800
[4,5,10,6,9,3,8,2,7,1]=>[5,5]=>72576
[4,5,8,2,6,10,9,3,7,1]=>[6,2,2]=>75600
[10,6,9,5,4,3,8,2,7,1]=>[6,2,2]=>75600
[8,2,6,10,9,5,4,3,7,1]=>[9,1]=>403200
[8,2,10,4,5,6,7,1,9,3]=>[2,2,1,1,1,1,1,1]=>630
[4,5,6,8,2,10,7,1,9,3]=>[3,3,2,1,1]=>50400
[10,4,5,6,8,2,7,1,9,3]=>[5,3,1,1]=>120960
[4,5,10,6,8,2,7,1,9,3]=>[6,2,1,1]=>151200
[4,5,10,8,2,6,7,1,9,3]=>[3,2,2,1,1,1]=>25200
[10,6,8,2,7,1,9,5,4,3]=>[10]=>362880
[10,8,2,6,7,1,9,5,4,3]=>[10]=>362880
[8,2,7,1,9,3,10,4,5,6]=>[4,3,2,1]=>151200
[4,5,8,2,7,1,9,3,10,6]=>[8,2]=>226800
[4,5,9,3,10,7,1,8,2,6]=>[9,1]=>403200
[4,5,7,1,9,3,8,2,6,10]=>[7,2,1]=>259200
[8,2,7,1,9,5,4,3,10,6]=>[5,4,1]=>181440
[9,5,4,3,10,7,1,8,2,6]=>[7,2,1]=>259200
[7,1,9,5,4,3,8,2,6,10]=>[4,3,2,1]=>151200
[8,2,6,10,4,5,7,1,9,3]=>[5,2,1,1,1]=>60480
[4,8,2,6,10,5,7,1,9,3]=>[8,1,1]=>226800
[4,10,8,2,5,6,7,1,9,3]=>[6,1,1,1,1]=>25200
[8,2,6,10,5,7,1,9,4,3]=>[8,1,1]=>226800
[10,8,2,5,6,7,1,9,4,3]=>[10]=>362880
[9,3,10,4,5,7,1,8,2,6]=>[7,1,1,1]=>86400
[4,9,3,10,5,7,1,8,2,6]=>[5,2,1,1,1]=>60480
[4,9,3,10,7,1,8,2,5,6]=>[5,4,1]=>181440
[4,7,1,9,3,8,2,5,6,10]=>[7,2,1]=>259200
[9,4,3,10,5,7,1,8,2,6]=>[7,1,1,1]=>86400
[9,4,3,10,7,1,8,2,5,6]=>[9,1]=>403200
[7,1,9,4,3,8,2,5,6,10]=>[5,3,1,1]=>120960
[5,10,7,1,8,2,4,3,9,6]=>[6,3,1]=>201600
[5,7,1,8,2,4,3,9,6,10]=>[5,4,1]=>181440
[10,5,7,1,9,4,2,6,8,3]=>[10]=>362880
[9,4,2,5,6,7,1,10,8,3]=>[10]=>362880
[10,5,7,1,8,3,9,4,2,6]=>[10]=>362880
[10,7,1,8,3,9,4,2,5,6]=>[6,4]=>151200
[7,1,8,3,9,4,2,5,6,10]=>[6,3,1]=>201600
[4,2,5,10,7,1,8,3,9,6]=>[4,4,1,1]=>56700
[4,2,5,7,1,8,3,9,6,10]=>[5,3,1,1]=>120960
[6,1,7,3,8,4,5,2]=>[8]=>5040
[8,2,3,1,6,4,7,5]=>[5,1,1,1]=>1344
[1,8,7,2,3,4,6,5]=>[7,1]=>5760
[1,8,3,7,6,2,5,4]=>[6,1,1]=>3360
[1,3,8,2,5,6,4,7]=>[5,1,1,1]=>1344
[1,3,2,7,4,6,8,5]=>[4,2,1,1]=>2520
[1,3,8,4,6,2,7,5]=>[5,1,1,1]=>1344
[8,2,3,6,7,4,5,1]=>[2,2,2,1,1]=>420
[5,6,4,2,1,7,3,8]=>[5,2,1]=>4032
[2,5,7,6,3,8,4,1]=>[8]=>5040
[6,4,7,1,2,5,3,8]=>[5,2,1]=>4032
[1,2,7,5,8,6,3,4]=>[3,2,1,1,1]=>1120
[2,1,9,8,7,6,5,3,4]=>[4,2,2,1]=>11340
[2,1,9,8,7,6,4,3,5]=>[6,2,1]=>30240
[2,1,9,8,7,6,3,5,4]=>[6,2,1]=>30240
[2,1,10,9,8,7,6,5,3,4]=>[4,2,2,2]=>18900
[7,4,5,1,6,8,2,3]=>[4,4]=>1260
[1,7,8,4,2,6,3,5]=>[5,1,1,1]=>1344
[6,3,2,5,7,4,1,8]=>[5,2,1]=>4032
[6,2,5,1,3,8,7,4]=>[4,2,1,1]=>2520
[6,2,8,5,1,3,7,4]=>[6,1,1]=>3360
[10,9,7,3,6,1,2,4,8,5]=>[6,4]=>151200
[9,7,3,6,1,2,4,10,8,5]=>[5,4,1]=>181440
[7,3,10,9,6,1,2,4,8,5]=>[7,3]=>172800
[7,3,9,6,1,2,4,10,8,5]=>[10]=>362880
[9,6,1,2,4,10,7,3,8,5]=>[5,4,1]=>181440
[8,4,10,9,7,3,6,1,2,5]=>[5,3,2]=>120960
[10,8,4,9,7,3,6,1,2,5]=>[10]=>362880
[7,3,8,4,10,9,6,1,2,5]=>[7,2,1]=>259200
[7,3,10,8,4,9,6,1,2,5]=>[10]=>362880
[10,7,3,8,4,9,6,1,2,5]=>[5,4,1]=>181440
[6,1,2,7,3,8,4,10,9,5]=>[7,2,1]=>259200
[6,1,2,7,3,10,8,4,9,5]=>[6,3,1]=>201600
[6,1,2,10,7,3,8,4,9,5]=>[5,4,1]=>181440
[10,6,1,2,7,3,8,4,9,5]=>[9,1]=>403200
[6,1,3,10,9,7,2,4,8,5]=>[5,4,1]=>181440
[6,1,3,9,7,2,4,10,8,5]=>[6,3,1]=>201600
[10,9,6,1,3,7,2,4,8,5]=>[10]=>362880
[9,6,1,3,7,2,4,10,8,5]=>[8,2]=>226800
[10,7,2,4,9,6,1,3,8,5]=>[8,1,1]=>226800
[6,1,3,8,4,10,9,7,2,5]=>[9,1]=>403200
[6,1,3,10,8,4,9,7,2,5]=>[9,1]=>403200
[8,4,10,9,6,1,3,7,2,5]=>[7,3]=>172800
[10,8,4,9,6,1,3,7,2,5]=>[6,4]=>151200
[9,6,1,3,8,4,10,7,2,5]=>[6,4]=>151200
[7,2,6,1,3,8,4,10,9,5]=>[5,3,1,1]=>120960
[7,2,6,1,3,10,8,4,9,5]=>[4,4,1,1]=>56700
[10,7,2,6,1,3,8,4,9,5]=>[6,3,1]=>201600
[7,2,10,6,1,3,8,4,9,5]=>[8,1,1]=>226800
[8,3,6,1,4,10,9,7,2,5]=>[10]=>362880
[10,8,3,6,1,4,9,7,2,5]=>[4,3,2,1]=>151200
[10,9,6,1,4,8,3,7,2,5]=>[4,4,2]=>56700
[9,6,1,4,10,8,3,7,2,5]=>[7,2,1]=>259200
[8,3,9,6,1,4,10,7,2,5]=>[5,3,2]=>120960
[8,3,7,2,6,1,4,10,9,5]=>[5,4,1]=>181440
[10,8,3,7,2,6,1,4,9,5]=>[7,1,1,1]=>86400
[8,3,10,7,2,6,1,4,9,5]=>[4,4,1,1]=>56700
[7,2,8,3,10,6,1,4,9,5]=>[3,2,2,1,1,1]=>25200
[9,4,10,8,3,7,2,6,1,5]=>[5,3,2]=>120960
[8,3,9,4,10,7,2,6,1,5]=>[7,2,1]=>259200
[7,2,8,3,9,4,10,6,1,5]=>[5,4,1]=>181440
[11,9,5,12,10,7,1,2,4,8,3,6]=>[12]=>39916800
[12,10,7,1,2,4,9,5,11,8,3,6]=>[4,4,4]=>1247400
[8,3,7,1,2,4,12,11,9,5,10,6]=>[11,1]=>43545600
[8,3,7,1,2,4,11,9,5,12,10,6]=>[12]=>39916800
[12,11,8,3,7,1,2,4,9,5,10,6]=>[5,3,3,1]=>5322240
[8,3,12,11,7,1,2,4,9,5,10,6]=>[11,1]=>43545600
[8,3,11,7,1,2,4,9,5,12,10,6]=>[6,4,2]=>9979200
[12,10,7,1,2,5,11,9,4,8,3,6]=>[9,3]=>17740800
[9,4,10,7,1,2,5,12,11,8,3,6]=>[12]=>39916800
[9,4,12,10,7,1,2,5,11,8,3,6]=>[6,6]=>6652800
[12,9,4,10,7,1,2,5,11,8,3,6]=>[9,3]=>17740800
[12,11,9,4,8,3,7,1,2,5,10,6]=>[10,1,1]=>23950080
[11,9,4,8,3,7,1,2,5,12,10,6]=>[6,6]=>6652800
[9,4,11,8,3,7,1,2,5,12,10,6]=>[9,3]=>17740800
[8,3,9,4,12,11,7,1,2,5,10,6]=>[5,3,2,1,1]=>7983360
[8,3,9,4,11,7,1,2,5,12,10,6]=>[11,1]=>43545600
[8,3,11,7,1,2,5,12,9,4,10,6]=>[11,1]=>43545600
[12,10,5,11,9,4,8,3,7,1,2,6]=>[7,5]=>13685760
[9,4,10,5,12,11,8,3,7,1,2,6]=>[6,6]=>6652800
[9,4,12,10,5,11,8,3,7,1,2,6]=>[11,1]=>43545600
[12,9,4,10,5,11,8,3,7,1,2,6]=>[11,1]=>43545600
[8,3,9,4,10,5,12,11,7,1,2,6]=>[11,1]=>43545600
[8,3,9,4,12,10,5,11,7,1,2,6]=>[11,1]=>43545600
[12,8,3,9,4,10,5,11,7,1,2,6]=>[4,4,3,1]=>4989600
[7,1,2,8,3,9,4,10,5,12,11,6]=>[11,1]=>43545600
[7,1,2,8,3,9,4,12,10,5,11,6]=>[11,1]=>43545600
[7,1,2,12,8,3,9,4,10,5,11,6]=>[11,1]=>43545600
[12,7,1,2,8,3,9,4,10,5,11,6]=>[7,4,1]=>17107200
[8,2,4,11,9,5,12,10,7,1,3,6]=>[5,3,3,1]=>5322240
[12,11,8,2,4,9,5,10,7,1,3,6]=>[12]=>39916800
[12,9,5,11,8,2,4,10,7,1,3,6]=>[12]=>39916800
[7,1,3,8,2,4,12,11,9,5,10,6]=>[10,1,1]=>23950080
[7,1,3,8,2,4,11,9,5,12,10,6]=>[11,1]=>43545600
[7,1,3,12,11,8,2,4,9,5,10,6]=>[4,3,3,1,1]=>3326400
[7,1,3,12,9,5,11,8,2,4,10,6]=>[10,1,1]=>23950080
[11,7,1,3,8,2,4,9,5,12,10,6]=>[9,3]=>17740800
[12,9,5,11,7,1,3,8,2,4,10,6]=>[3,3,3,2,1]=>1478400
[12,11,9,4,8,2,5,10,7,1,3,6]=>[11,1]=>43545600
[11,9,4,8,2,5,12,10,7,1,3,6]=>[6,6]=>6652800
[9,4,12,11,8,2,5,10,7,1,3,6]=>[6,6]=>6652800
[11,8,2,5,12,9,4,10,7,1,3,6]=>[6,6]=>6652800
[7,1,3,11,9,4,8,2,5,12,10,6]=>[5,4,2,1]=>11975040
[7,1,3,9,4,11,8,2,5,12,10,6]=>[4,4,3,1]=>4989600
[9,4,12,11,7,1,3,8,2,5,10,6]=>[11,1]=>43545600
[9,4,11,7,1,3,8,2,5,12,10,6]=>[5,4,3]=>7983360
[12,8,2,5,11,7,1,3,9,4,10,6]=>[4,4,3,1]=>4989600
[7,1,3,10,5,12,11,9,4,8,2,6]=>[4,4,2,1,1]=>3742200
[7,1,3,12,10,5,11,9,4,8,2,6]=>[7,4,1]=>17107200
[7,1,3,9,4,10,5,12,11,8,2,6]=>[7,4,1]=>17107200
[9,4,12,10,5,11,7,1,3,8,2,6]=>[10,1,1]=>23950080
[12,9,4,10,5,11,7,1,3,8,2,6]=>[10,1,1]=>23950080
[11,7,1,3,9,4,10,5,12,8,2,6]=>[12]=>39916800
[8,2,7,1,3,9,4,10,5,12,11,6]=>[10,1,1]=>23950080
[8,2,7,1,3,9,4,12,10,5,11,6]=>[10,1,1]=>23950080
[8,2,7,1,3,12,9,4,10,5,11,6]=>[5,3,2,1,1]=>7983360
[12,8,2,7,1,3,9,4,10,5,11,6]=>[11,1]=>43545600
[12,10,7,1,4,8,2,5,11,9,3,6]=>[6,6]=>6652800
[12,11,8,2,5,10,7,1,4,9,3,6]=>[10,1,1]=>23950080
[11,9,3,7,1,4,8,2,5,12,10,6]=>[11,1]=>43545600
[9,3,7,1,4,11,8,2,5,12,10,6]=>[4,4,4]=>1247400
[9,3,12,8,2,5,11,7,1,4,10,6]=>[5,5,2]=>4790016
[10,5,12,11,9,3,7,1,4,8,2,6]=>[5,3,3,1]=>5322240
[12,10,5,11,9,3,7,1,4,8,2,6]=>[11,1]=>43545600
[10,5,12,11,7,1,4,9,3,8,2,6]=>[7,5]=>13685760
[12,10,5,11,7,1,4,9,3,8,2,6]=>[9,3]=>17740800
[11,7,1,4,10,5,12,9,3,8,2,6]=>[11,1]=>43545600
[9,3,11,7,1,4,10,5,12,8,2,6]=>[9,3]=>17740800
[9,3,8,2,7,1,4,10,5,12,11,6]=>[11,1]=>43545600
[9,3,8,2,7,1,4,12,10,5,11,6]=>[11,1]=>43545600
[12,9,3,8,2,7,1,4,10,5,11,6]=>[4,4,2,1,1]=>3742200
[8,2,9,3,12,7,1,4,10,5,11,6]=>[10,1,1]=>23950080
[12,11,9,3,7,1,5,10,4,8,2,6]=>[3,3,2,2,2]=>554400
[10,4,9,3,7,1,5,12,11,8,2,6]=>[5,5,2]=>4790016
[11,7,1,5,12,10,4,9,3,8,2,6]=>[12]=>39916800
[10,4,11,7,1,5,12,9,3,8,2,6]=>[12]=>39916800
[10,4,9,3,8,2,7,1,5,12,11,6]=>[10,1,1]=>23950080
[12,10,4,9,3,8,2,7,1,5,11,6]=>[11,1]=>43545600
[10,4,12,9,3,8,2,7,1,5,11,6]=>[11,1]=>43545600
[9,3,10,4,11,5,12,8,2,7,1,6]=>[10,1,1]=>23950080
[4,1,7,8,3,6,5,2]=>[4,3,1]=>3360
[6,4,2,1,7,3,5,8]=>[5,2,1]=>4032
[5,8,4,2,1,3,6,7]=>[6,2]=>3360
[4,5,3,6,7,8,9,1,2]=>[4,4,1]=>11340
[5,3,4,6,7,8,9,1,2]=>[9]=>40320
[1,7,5,8,4,3,6,2]=>[7,1]=>5760
[5,8,1,6,4,7,2,3]=>[8]=>5040
[2,4,7,5,1,8,6,3]=>[4,4]=>1260
[2,3,7,1,8,5,6,4]=>[8]=>5040
[6,5,1,2,7,4,8,3]=>[8]=>5040
[3,6,5,7,8,2,4,1]=>[4,2,2]=>1260
[3,6,5,1,8,7,4,2]=>[8]=>5040
[7,8,1,2,5,4,3,6]=>[4,3,1]=>3360
[2,8,4,3,5,1,7,6]=>[4,2,1,1]=>2520
[5,2,4,7,6,8,1,3]=>[7,1]=>5760
[3,1,5,7,4,8,6,2]=>[8]=>5040
[4,1,7,6,8,2,5,3]=>[4,4]=>1260
[7,2,6,4,1,5,3,8]=>[5,1,1,1]=>1344
[1,2,6,5,8,3,7,4]=>[3,2,1,1,1]=>1120
[7,3,5,6,1,4,2,8]=>[5,2,1]=>4032
[5,8,3,1,6,7,4,2]=>[5,2,1]=>4032
[4,5,8,1,7,3,6,2]=>[6,2]=>3360
[4,7,1,6,8,5,2,3]=>[6,2]=>3360
[5,8,7,1,6,4,2,3]=>[4,4]=>1260
[8,4,1,3,6,7,5,2]=>[5,3]=>2688
[5,3,1,8,6,7,4,2]=>[8]=>5040
[6,2,7,1,4,3,5,8]=>[6,1,1]=>3360
[9,5,4,3,2,1,6,7,8]=>[5,2,2]=>9072
[10,3,4,1,2,5,6,7,8,9]=>[10]=>362880
[8,3,2,6,5,1,7,4]=>[4,2,1,1]=>2520
[2,6,8,4,7,1,3,5]=>[4,3,1]=>3360
[7,8,6,3,2,5,4,1]=>[8]=>5040
[1,6,4,8,2,3,5,7]=>[7,1]=>5760
[2,8,5,6,4,1,7,3]=>[7,1]=>5760
[1,4,7,3,5,8,6,2]=>[6,1,1]=>3360
[3,7,8,2,5,1,6,4]=>[7,1]=>5760
[8,6,1,4,3,2,7,5]=>[4,2,1,1]=>2520
[7,3,8,2,4,1,5,6]=>[8]=>5040
[6,3,7,8,1,2,5,4]=>[6,2]=>3360
[7,6,1,5,2,3,8,4]=>[8]=>5040
[5,1,8,6,7,2,3,4]=>[8]=>5040
[5,7,1,6,8,2,3,4]=>[8]=>5040
[6,8,4,2,1,7,3,5]=>[8]=>5040
[6,3,2,8,1,7,4,5]=>[6,2]=>3360
[6,4,1,3,7,8,5,2]=>[6,2]=>3360
[6,8,5,4,3,7,1,2]=>[3,2,2,1]=>1680
[5,7,4,8,3,1,2,6]=>[6,2]=>3360
[6,1,2,4,8,3,7,5]=>[4,2,1,1]=>2520
[2,5,6,8,1,4,7,3]=>[4,3,1]=>3360
[7,4,1,6,5,2,3,8]=>[3,3,1,1]=>1120
[4,1,6,5,2,3,8,7]=>[4,2,2]=>1260
[4,5,1,7,8,6,2,3]=>[7,1]=>5760
[8,5,7,3,4,6,2,1]=>[5,2,1]=>4032
[6,8,7,4,3,5,2,1]=>[7,1]=>5760
[6,8,7,5,3,4,2,1]=>[8]=>5040
[5,8,6,2,4,7,3,1]=>[5,3]=>2688
[4,8,6,2,5,7,3,1]=>[4,3,1]=>3360
[1,6,4,7,5,3,2,8]=>[5,1,1,1]=>1344
[1,6,5,3,2,7,4,8]=>[6,1,1]=>3360
[1,6,8,7,4,5,3,2]=>[7,1]=>5760
[1,4,7,5,3,2,6,8]=>[6,1,1]=>3360
[1,7,5,4,3,2,8,6]=>[4,2,1,1]=>2520
[1,4,7,5,3,2,8,6]=>[7,1]=>5760
[1,7,4,6,8,5,3,2]=>[7,1]=>5760
[6,8,7,2,3,5,4,1]=>[8]=>5040
[5,7,6,1,8,2,4,3]=>[8]=>5040
[4,8,6,5,7,2,3,1]=>[8]=>5040
[2,7,8,5,1,4,3,6]=>[8]=>5040
[8,5,6,2,4,7,3,1]=>[3,3,2]=>1120
[8,1,3,6,4,5,2,7]=>[4,3,1]=>3360
[1,2,3,7,4,8,5,9,6]=>[3,3,1,1,1]=>3360
[1,2,3,4,7,5,9,8,6]=>[4,1,1,1,1,1]=>756
[1,2,6,3,7,4,9,8,5]=>[3,3,1,1,1]=>3360
[1,2,3,8,6,4,9,7,5]=>[6,1,1,1]=>10080
[1,2,3,6,4,9,8,7,5]=>[4,2,1,1,1]=>7560
[5,1,6,2,7,3,9,8,4]=>[6,2,1]=>30240
[1,5,2,8,6,3,9,7,4]=>[4,4,1]=>11340
[1,5,2,6,3,9,8,7,4]=>[3,3,2,1]=>10080
[1,2,7,5,3,9,8,6,4]=>[7,1,1]=>25920
[1,2,5,3,9,8,7,6,4]=>[4,2,1,1,1]=>7560
[4,1,7,5,2,9,8,6,3]=>[5,4]=>18144
[4,1,5,2,9,8,7,6,3]=>[3,3,2,1]=>10080
[1,6,4,2,9,8,7,5,3]=>[7,1,1]=>25920
[1,4,2,9,8,7,6,5,3]=>[4,2,2,1]=>11340
[7,5,3,1,9,8,6,4,2]=>[5,3,1]=>24192
[5,3,1,9,8,7,6,4,2]=>[7,2]=>25920
[1,2,3,4,8,5,9,6,10,7]=>[3,3,1,1,1,1]=>8400
[1,2,3,4,5,8,6,10,9,7]=>[4,1,1,1,1,1,1]=>1260
[1,2,3,7,4,8,5,10,9,6]=>[3,3,1,1,1,1]=>8400
[1,2,3,4,9,7,5,10,8,6]=>[6,1,1,1,1]=>25200
[1,2,3,4,7,5,10,9,8,6]=>[4,2,1,1,1,1]=>18900
[1,6,2,7,3,8,4,10,9,5]=>[6,2,1,1]=>151200
[1,2,6,3,9,7,4,10,8,5]=>[4,4,1,1]=>56700
[1,2,6,3,7,4,10,9,8,5]=>[3,3,2,1,1]=>50400
[1,2,3,8,6,4,10,9,7,5]=>[7,1,1,1]=>86400
[1,2,3,6,4,10,9,8,7,5]=>[4,2,1,1,1,1]=>18900
[5,1,6,2,9,7,3,10,8,4]=>[7,3]=>172800
[5,1,6,2,7,3,10,9,8,4]=>[6,2,2]=>75600
[1,5,2,6,3,10,9,8,7,4]=>[3,3,2,1,1]=>50400
[1,2,7,5,3,10,9,8,6,4]=>[7,1,1,1]=>86400
[1,2,5,3,10,9,8,7,6,4]=>[4,2,2,1,1]=>56700
[7,4,1,8,5,2,10,9,6,3]=>[5,4,1]=>181440
[4,1,9,7,5,2,10,8,6,3]=>[8,1,1]=>226800
[4,1,7,5,2,10,9,8,6,3]=>[5,4,1]=>181440
[4,1,5,2,10,9,8,7,6,3]=>[3,3,2,2]=>25200
[1,8,6,4,2,10,9,7,5,3]=>[5,3,1,1]=>120960
[1,6,4,2,10,9,8,7,5,3]=>[7,2,1]=>259200
[1,4,2,10,9,8,7,6,5,3]=>[4,2,2,1,1]=>56700
[7,5,3,1,10,9,8,6,4,2]=>[6,3,1]=>201600
[5,3,1,10,9,8,7,6,4,2]=>[7,2,1]=>259200
[4,3,1,6,2,5,8,7]=>[6,2]=>3360
[7,5,2,1,8,4,3,6]=>[8]=>5040
[5,3,1,4,7,8,2,6]=>[5,2,1]=>4032
[7,1,2,4,8,3,5,6]=>[7,1]=>5760
[8,6,1,3,5,7,4,2]=>[7,1]=>5760
[7,1,5,8,2,3,4,6]=>[8]=>5040
[3,6,8,5,1,4,2,7]=>[8]=>5040
[5,2,4,1,6,8,3,7]=>[7,1]=>5760
[2,5,3,4,6,8,1,7]=>[6,1,1]=>3360
[4,7,1,2,5,6,3,8]=>[5,1,1,1]=>1344
[6,7,3,1,8,2,4,5]=>[5,2,1]=>4032
[7,3,1,4,6,2,8,5]=>[7,1]=>5760
[7,4,1,2,5,6,3,8]=>[3,2,1,1,1]=>1120
[5,4,1,3,6,8,7,2]=>[7,1]=>5760
[5,7,4,8,1,6,3,2]=>[5,2,1]=>4032
[4,3,1,2,5,7,6,8]=>[4,2,1,1]=>2520
[5,3,1,8,4,2,6,7]=>[8]=>5040
[6,1,5,4,7,3,8,2]=>[7,1]=>5760
[5,3,2,8,7,1,6,4]=>[4,2,2]=>1260
[8,6,7,4,1,3,5,2]=>[7,1]=>5760
[4,1,3,6,5,2,8,7]=>[4,2,1,1]=>2520
[4,6,3,2,5,1,8,7]=>[4,2,1,1]=>2520
[4,8,3,2,6,5,7,1]=>[4,2,1,1]=>2520
[4,8,3,6,5,2,7,1]=>[5,1,1,1]=>1344
[8,1,6,2,5,4,7,3]=>[6,1,1]=>3360
[2,4,3,8,6,1,7,5]=>[6,1,1]=>3360
[2,6,3,8,5,4,7,1]=>[5,1,1,1]=>1344
[6,1,3,2,5,8,7,4]=>[5,1,1,1]=>1344
[6,8,4,2,5,3,7,1]=>[6,1,1]=>3360
[6,8,4,3,5,2,7,1]=>[4,2,1,1]=>2520
[8,1,4,6,5,3,7,2]=>[3,3,1,1]=>1120
[1,4,2,5,6,7,9,8,3]=>[7,1,1]=>25920
[2,1,4,5,6,9,7,3,8]=>[6,2,1]=>30240
[3,5,4,6,1,2,8,7]=>[6,2]=>3360
[3,1,5,2,9,6,7,8,4]=>[6,1,1,1]=>10080
[4,5,1,6,8,7,9,2,3]=>[6,3]=>20160
[1,4,2,5,6,7,8,10,9,3]=>[8,1,1]=>226800
[1,3,4,5,6,7,8,9,11,2,10]=>[10,1]=>3991680
[2,1,4,5,6,7,10,8,3,9]=>[7,2,1]=>259200
[2,3,1,5,9,6,7,4,8]=>[4,3,1,1]=>15120
[1,2,4,5,7,9,6,3,8]=>[7,1,1]=>25920
[3,4,6,5,7,1,2,9,8]=>[4,3,2]=>15120
[3,1,9,4,2,6,7,8,5]=>[5,1,1,1,1]=>3024
[7,3,5,6,1,8,2,4]=>[5,3]=>2688
[1,2,5,3,9,6,8,7,4]=>[4,2,1,1,1]=>7560
[3,1,5,2,6,10,7,8,9,4]=>[7,1,1,1]=>86400
[4,5,1,7,6,8,2,9,3]=>[9]=>40320
[4,5,1,6,7,9,8,10,2,3]=>[10]=>362880
[1,4,2,5,6,7,8,9,11,10,3]=>[9,1,1]=>2217600
[5,7,6,3,4,2,8,1]=>[8]=>5040
[4,6,7,2,3,5,8,1]=>[8]=>5040
[6,5,4,8,7,2,3,1]=>[8]=>5040
[7,2,8,3,9,4,10,5,1,6]=>[9,1]=>403200
[7,2,8,3,9,4,10,1,5,6]=>[7,2,1]=>259200
[7,2,8,3,9,10,4,5,1,6]=>[7,2,1]=>259200
[7,2,8,3,9,10,4,1,5,6]=>[5,2,2,1]=>90720
[7,2,8,3,9,10,1,4,5,6]=>[3,2,2,2,1]=>25200
[7,2,8,9,3,4,10,5,1,6]=>[6,3,1]=>201600
[7,2,8,9,3,4,10,1,5,6]=>[9,1]=>403200
[7,2,8,9,3,10,4,5,1,6]=>[4,3,2,1]=>151200
[7,2,8,9,3,10,4,1,5,6]=>[7,2,1]=>259200
[7,2,8,9,3,10,1,4,5,6]=>[5,2,2,1]=>90720
[7,2,8,9,10,3,4,5,1,6]=>[5,4,1]=>181440
[7,2,8,9,10,3,4,1,5,6]=>[9,1]=>403200
[7,2,8,9,10,3,1,4,5,6]=>[7,2,1]=>259200
[7,8,2,3,9,4,10,5,1,6]=>[10]=>362880
[7,8,2,3,9,4,10,1,5,6]=>[8,2]=>226800
[7,8,2,3,9,10,4,5,1,6]=>[8,2]=>226800
[7,8,2,3,9,10,4,1,5,6]=>[6,2,2]=>75600
[7,8,2,3,9,10,1,4,5,6]=>[4,2,2,2]=>18900
[7,8,2,9,3,4,10,5,1,6]=>[6,4]=>151200
[7,8,2,9,3,4,10,1,5,6]=>[10]=>362880
[7,8,2,9,3,10,4,5,1,6]=>[4,4,2]=>56700
[7,8,2,9,3,10,4,1,5,6]=>[8,2]=>226800
[7,8,2,9,3,10,1,4,5,6]=>[6,2,2]=>75600
[7,8,2,9,10,3,4,5,1,6]=>[6,4]=>151200
[7,8,2,9,10,3,4,1,5,6]=>[10]=>362880
[7,8,2,9,10,3,1,4,5,6]=>[8,2]=>226800
[7,8,2,9,10,1,3,4,5,6]=>[10]=>362880
[7,8,9,2,3,4,10,5,1,6]=>[10]=>362880
[7,8,9,2,3,4,10,1,5,6]=>[7,3]=>172800
[7,8,9,2,3,10,4,5,1,6]=>[8,2]=>226800
[7,8,9,2,3,10,4,1,5,6]=>[5,3,2]=>120960
[7,8,9,2,3,10,1,4,5,6]=>[3,3,2,2]=>25200
[7,8,9,2,10,3,4,5,1,6]=>[10]=>362880
[7,8,9,2,10,3,4,1,5,6]=>[5,5]=>72576
[7,8,9,2,10,3,1,4,5,6]=>[5,3,2]=>120960
[7,8,9,2,10,1,3,4,5,6]=>[7,3]=>172800
[7,8,9,10,2,3,4,1,5,6]=>[10]=>362880
[7,8,9,10,2,3,1,4,5,6]=>[8,2]=>226800
[7,8,9,10,2,1,3,4,5,6]=>[10]=>362880
[8,2,9,3,10,4,11,5,12,6,1,7]=>[11,1]=>43545600
[8,2,9,3,10,4,11,5,12,1,6,7]=>[7,4,1]=>17107200
[8,2,9,3,10,4,11,12,5,1,6,7]=>[11,1]=>43545600
[8,2,9,3,10,11,4,5,12,1,6,7]=>[5,4,2,1]=>11975040
[8,2,9,3,10,11,4,12,5,6,1,7]=>[11,1]=>43545600
[8,2,9,3,10,11,12,4,1,5,6,7]=>[5,2,2,2,1]=>1995840
[8,2,9,3,10,11,12,1,4,5,6,7]=>[3,2,2,2,2,1]=>415800
[8,2,9,10,3,4,11,5,12,1,6,7]=>[11,1]=>43545600
[8,2,9,10,3,4,11,12,5,6,1,7]=>[5,3,3,1]=>5322240
[8,2,9,10,3,4,11,12,1,5,6,7]=>[11,1]=>43545600
[8,2,9,10,3,11,4,5,12,6,1,7]=>[11,1]=>43545600
[8,2,9,10,3,11,12,4,5,1,6,7]=>[4,3,2,2,1]=>4989600
[8,2,9,10,3,11,12,1,4,5,6,7]=>[5,2,2,2,1]=>1995840
[8,2,9,10,11,3,4,5,12,6,1,7]=>[7,4,1]=>17107200
[8,2,9,10,11,3,4,5,12,1,6,7]=>[11,1]=>43545600
[8,2,9,10,11,3,4,12,5,6,1,7]=>[11,1]=>43545600
[8,2,9,10,11,3,4,12,1,5,6,7]=>[11,1]=>43545600
[8,2,9,10,11,3,12,4,5,1,6,7]=>[5,4,2,1]=>11975040
[8,2,9,10,11,12,3,4,5,6,1,7]=>[11,1]=>43545600
[8,2,9,10,11,12,3,4,5,1,6,7]=>[7,4,1]=>17107200
[8,2,9,10,11,12,3,4,1,5,6,7]=>[11,1]=>43545600
[8,2,9,10,11,12,1,3,4,5,6,7]=>[11,1]=>43545600
[8,9,2,3,10,4,11,5,12,6,1,7]=>[12]=>39916800
[8,9,2,3,10,4,11,12,5,6,1,7]=>[7,5]=>13685760
[8,9,2,3,10,4,11,12,5,1,6,7]=>[12]=>39916800
[8,9,2,3,10,11,4,5,12,6,1,7]=>[6,6]=>6652800
[8,9,2,3,10,11,4,5,12,1,6,7]=>[6,4,2]=>9979200
[8,9,2,3,10,11,4,12,5,6,1,7]=>[12]=>39916800
[8,9,2,10,3,4,11,5,12,6,1,7]=>[9,3]=>17740800
[8,9,2,10,3,4,11,5,12,1,6,7]=>[12]=>39916800
[8,9,2,10,3,4,11,12,5,6,1,7]=>[5,4,3]=>7983360
[8,9,2,10,3,4,11,12,1,5,6,7]=>[12]=>39916800
[8,9,2,10,3,11,4,5,12,6,1,7]=>[12]=>39916800
[8,9,2,10,3,11,4,12,5,1,6,7]=>[6,4,2]=>9979200
[8,9,2,10,3,11,12,4,5,6,1,7]=>[6,4,2]=>9979200
[8,9,2,10,3,11,12,4,5,1,6,7]=>[4,4,2,2]=>1871100
[8,9,2,10,11,3,4,5,12,1,6,7]=>[12]=>39916800
[8,9,2,10,11,3,4,12,5,6,1,7]=>[12]=>39916800
[8,9,2,10,11,3,4,12,5,1,6,7]=>[6,6]=>6652800
[8,9,2,10,11,3,4,12,1,5,6,7]=>[12]=>39916800
[8,9,2,10,11,3,12,4,5,1,6,7]=>[6,4,2]=>9979200
[8,9,2,10,11,12,3,4,5,6,1,7]=>[12]=>39916800
[8,9,2,10,11,12,3,4,1,5,6,7]=>[12]=>39916800
[8,9,2,10,11,12,1,3,4,5,6,7]=>[12]=>39916800
[8,9,10,2,3,4,11,5,12,6,1,7]=>[12]=>39916800
[8,9,10,2,3,4,11,5,12,1,6,7]=>[7,5]=>13685760
[8,9,10,2,3,4,11,12,5,6,1,7]=>[7,5]=>13685760
[8,9,10,2,3,4,11,12,5,1,6,7]=>[12]=>39916800
[8,9,10,2,3,4,11,12,1,5,6,7]=>[9,3]=>17740800
[8,9,10,2,3,11,4,5,12,6,1,7]=>[7,5]=>13685760
[8,9,10,2,3,11,4,5,12,1,6,7]=>[5,5,2]=>4790016
[8,9,10,2,3,11,4,12,5,6,1,7]=>[12]=>39916800
[8,9,10,2,3,11,12,4,1,5,6,7]=>[5,3,2,2]=>3991680
[8,9,10,2,3,11,12,1,4,5,6,7]=>[3,3,2,2,2]=>554400
[8,9,10,2,11,3,4,5,12,6,1,7]=>[5,4,3]=>7983360
[8,9,10,2,11,3,4,5,12,1,6,7]=>[7,5]=>13685760
[8,9,10,2,11,3,4,12,5,6,1,7]=>[9,3]=>17740800
[8,9,10,2,11,3,4,12,5,1,6,7]=>[12]=>39916800
[8,9,10,2,11,3,4,12,1,5,6,7]=>[7,5]=>13685760
[8,9,10,2,11,3,12,4,1,5,6,7]=>[5,5,2]=>4790016
[8,9,10,2,11,3,12,1,4,5,6,7]=>[5,3,2,2]=>3991680
[8,9,10,2,11,12,3,4,5,6,1,7]=>[7,5]=>13685760
[8,9,10,2,11,12,3,4,5,1,6,7]=>[12]=>39916800
[8,9,10,2,11,12,3,4,1,5,6,7]=>[7,5]=>13685760
[8,9,10,2,11,12,1,3,4,5,6,7]=>[9,3]=>17740800
[8,9,10,11,2,3,4,5,12,6,1,7]=>[9,3]=>17740800
[8,9,10,11,2,3,4,5,12,1,6,7]=>[12]=>39916800
[8,9,10,11,2,3,4,12,5,1,6,7]=>[9,3]=>17740800
[8,9,10,11,2,3,4,12,1,5,6,7]=>[12]=>39916800
[8,9,10,11,2,3,12,4,5,6,1,7]=>[4,3,3,2]=>3326400
[8,9,10,11,2,12,3,4,5,6,1,7]=>[5,4,3]=>7983360
[8,9,10,11,2,12,3,4,5,1,6,7]=>[9,3]=>17740800
[8,9,10,11,2,12,3,4,1,5,6,7]=>[12]=>39916800
[8,9,10,11,2,12,1,3,4,5,6,7]=>[12]=>39916800
[8,9,10,11,12,2,3,4,5,1,6,7]=>[12]=>39916800
[8,9,10,11,12,2,3,4,1,5,6,7]=>[7,5]=>13685760
[8,9,10,11,12,2,3,1,4,5,6,7]=>[5,5,2]=>4790016
[8,9,10,11,12,2,1,3,4,5,6,7]=>[7,5]=>13685760
[4,8,7,6,5,3,2,1,9]=>[7,1,1]=>25920
[5,9,8,7,6,4,3,2,1,10]=>[9,1]=>403200
[5,8,7,4,6,3,2,1,9]=>[7,1,1]=>25920
[8,4,7,6,5,3,2,1,9]=>[5,2,1,1]=>18144
[5,7,4,3,6,2,1,8]=>[5,2,1]=>4032
[6,9,8,5,7,4,1,3,2]=>[5,2,2]=>9072
[9,8,7,5,1,6,4,3,2]=>[8,1]=>45360
[10,9,8,6,1,7,5,4,3,2]=>[10]=>362880
[1,2,8,3,4,5,6,9,7]=>[7,1,1]=>25920
[1,9,5,2,3,8,4,6,7]=>[4,2,2,1]=>11340
[1,2,9,3,4,5,6,7,10,8]=>[8,1,1]=>226800
[1,8,2,9,4,3,5,6,7]=>[4,4,1]=>11340
[1,3,2,4,9,8,5,6,7]=>[3,2,2,1,1]=>7560
[2,1,3,4,5,9,8,6,7]=>[4,2,1,1,1]=>7560
[1,2,3,4,5,9,6,7,10,8]=>[5,1,1,1,1,1]=>6048
[9,1,7,2,3,4,5,8,6]=>[5,3,1]=>24192
[1,10,6,2,3,4,9,5,7,8]=>[7,2,1]=>259200
[1,2,10,3,4,5,6,7,8,11,9]=>[9,1,1]=>2217600
[1,8,5,2,3,4,6,9,7]=>[6,2,1]=>30240
[9,8,1,2,3,5,6,4,7]=>[6,3]=>20160
[1,5,2,9,3,10,4,6,7,8]=>[3,3,3,1]=>22400
[1,4,2,3,9,5,6,8,7]=>[4,3,1,1]=>15120
[1,8,5,6,2,3,7,4]=>[6,1,1]=>3360
[4,9,8,1,2,5,3,6,7]=>[7,2]=>25920
[1,2,4,3,10,9,5,6,7,8]=>[6,2,1,1]=>151200
[1,3,2,4,5,9,6,8,7]=>[3,2,1,1,1,1]=>2520
[1,8,3,9,4,2,5,6,7]=>[4,3,1,1]=>15120
[1,3,2,4,5,10,9,6,7,8]=>[3,2,2,1,1,1]=>25200
[1,2,3,4,5,10,6,7,8,11,9]=>[6,1,1,1,1,1]=>55440
[2,3,1,4,9,8,5,6,7]=>[3,3,2,1]=>10080
[2,1,3,4,5,9,6,10,7,8]=>[3,2,2,1,1,1]=>25200
[8,5,6,1,3,2,7,4]=>[4,3,1]=>3360
[5,3,7,8,2,6,1,4]=>[5,2,1]=>4032
[4,5,8,3,6,1,7,2]=>[7,1]=>5760
[5,7,1,3,6,2,4,8]=>[7,1]=>5760
[4,7,5,2,3,6,8,1]=>[5,2,1]=>4032
[3,6,4,1,2,5,7,8]=>[3,3,1,1]=>1120
[4,7,1,3,2,5,8,6]=>[5,3]=>2688
[4,7,1,3,2,6,8,5]=>[4,3,1]=>3360
[5,7,1,3,6,2,8,4]=>[8]=>5040
[6,8,2,5,7,3,1,4]=>[8]=>5040
[4,8,5,2,3,6,1,7]=>[5,2,1]=>4032
[5,8,6,3,4,7,2,1]=>[8]=>5040
[3,7,5,4,2,8,1,6]=>[5,2,1]=>4032
[4,6,5,1,7,8,2,3]=>[6,2]=>3360
[4,7,1,3,2,8,5,6]=>[3,3,2]=>1120
[3,6,5,1,8,2,4,7]=>[6,2]=>3360
[5,8,7,3,4,2,6,1]=>[8]=>5040
[8,5,2,3,7,4,6,1]=>[6,2]=>3360
[6,3,1,5,4,8,2,7]=>[6,2]=>3360
[4,7,6,3,5,2,8,1]=>[7,1]=>5760
[1,7,5,3,4,8,6,2]=>[4,3,1]=>3360
[5,8,2,3,4,7,6,1]=>[6,2]=>3360
[8,7,3,2,6,4,5,1]=>[5,2,1]=>4032
[8,3,1,4,7,5,2,6]=>[7,1]=>5760
[5,3,1,6,4,8,7,2]=>[7,1]=>5760
[3,4,8,5,7,2,6,1]=>[5,3]=>2688
[8,5,1,2,7,6,4,3]=>[4,3,1]=>3360
[10,7,8,1,2,3,4,5,6,9]=>[10]=>362880
[6,7,10,1,2,3,4,5,8,9]=>[10]=>362880
[3,7,8,5,6,2,4,1]=>[5,3]=>2688
[1,10,2,3,4,7,5,6,8,9]=>[9,1]=>403200
[7,4,3,6,2,5,8,1]=>[4,3,1]=>3360
[4,3,8,7,1,6,2,5]=>[7,1]=>5760
[1,5,3,8,4,7,2,6]=>[6,1,1]=>3360
[8,2,3,1,6,5,7,4]=>[3,2,1,1,1]=>1120
[8,4,2,7,1,3,6,5]=>[5,3]=>2688
[8,4,2,3,1,6,7,5]=>[3,3,1,1]=>1120
[4,7,2,3,6,5,8,1]=>[6,2]=>3360
[3,8,2,6,4,7,1,5]=>[8]=>5040
[1,7,5,8,6,2,4,3]=>[7,1]=>5760
[6,5,1,7,4,8,3,2]=>[8]=>5040
[10,9,8,6,7,5,4,3,2,1]=>[4,2,2,2]=>18900
[7,6,3,5,1,4,8,2]=>[7,1]=>5760
[6,5,4,1,7,2,3,8]=>[7,1]=>5760
[8,3,6,1,7,4,5,2]=>[6,2]=>3360
[7,1,2,6,4,8,3,5]=>[4,4]=>1260
[3,5,1,8,6,2,4,7]=>[3,3,2]=>1120
[8,7,5,6,4,3,2,1,9]=>[4,2,2,1]=>11340
[8,6,5,7,4,3,2,1,9]=>[6,2,1]=>30240
[9,8,7,6,4,3,2,5,1]=>[7,2]=>25920
[9,8,7,6,4,3,5,2,1]=>[5,2,2]=>9072
[8,5,6,7,4,3,2,1,9]=>[4,2,2,1]=>11340
[10,9,7,6,8,5,4,3,2,1]=>[6,2,2]=>75600
[6,7,5,8,4,3,2,1,9]=>[6,2,1]=>30240
[10,8,7,6,9,5,4,3,2,1]=>[8,2]=>226800
[8,9,7,6,4,3,2,1,5]=>[7,2]=>25920
[7,6,5,3,2,1,4,8,9]=>[7,1,1]=>25920
[9,8,7,6,4,3,5,1,2]=>[5,4]=>18144
[9,8,7,6,4,3,2,5,1,10]=>[7,2,1]=>259200
[9,8,7,6,4,5,2,3,1]=>[4,3,2]=>15120
[9,8,7,6,4,3,5,2,1,10]=>[5,2,2,1]=>90720
[9,8,7,6,5,3,4,2,1]=>[4,2,2,1]=>11340
[1,8,7,5,4,6,2,3]=>[4,2,1,1]=>2520
[8,1,6,7,4,5,3,2]=>[5,3]=>2688
[8,1,6,4,7,5,3,2]=>[4,3,1]=>3360
[6,4,8,1,5,3,7,2]=>[6,1,1]=>3360
[1,6,4,3,5,8,2,7]=>[4,2,1,1]=>2520
[5,7,1,8,6,3,2,4]=>[4,2,2]=>1260
[5,7,6,3,4,2,1,8]=>[7,1]=>5760
[8,7,6,5,4,2,3,1,9]=>[4,2,2,1]=>11340
[1,10,9,8,6,5,7,4,3,2]=>[2,2,2,2,1,1]=>4725
[2,9,8,6,5,7,4,3,1]=>[3,3,2,1]=>10080
[3,1,4,5,6,7,9,2,10,8]=>[10]=>362880
[5,8,3,6,7,2,4,1]=>[7,1]=>5760
[8,1,6,2,5,7,4,3]=>[7,1]=>5760
[2,7,1,5,3,6,8,4]=>[7,1]=>5760
[6,8,7,3,4,2,5,1]=>[4,4]=>1260
[1,8,6,2,4,7,5,3]=>[7,1]=>5760
[5,7,3,6,4,2,1,8]=>[6,1,1]=>3360
[5,7,3,6,4,1,8,2]=>[4,3,1]=>3360
[3,7,5,6,4,1,8,2]=>[5,3]=>2688
[7,1,8,2,3,4,5,9,6]=>[9]=>40320
[6,8,1,2,3,4,5,9,7]=>[9]=>40320
[9,8,6,5,4,3,7,2,1]=>[2,2,2,2,1]=>945
[2,8,5,7,3,4,6,1]=>[3,3,2]=>1120
[2,3,6,4,5,1,7,8,9]=>[4,1,1,1,1,1]=>756
[2,3,4,8,5,6,7,1,9]=>[5,1,1,1,1]=>3024
[3,5,4,7,2,6,1,8,9]=>[4,2,1,1,1]=>7560
[2,6,4,1,5,3,7,8,9]=>[5,1,1,1,1]=>3024
[4,5,2,6,3,1,7,8,9]=>[3,3,1,1,1]=>3360
[3,6,4,5,9,2,7,8,1]=>[5,2,1,1]=>18144
[2,5,4,7,8,6,3,1,9]=>[4,3,1,1]=>15120
[4,6,2,5,8,3,7,1,9]=>[4,3,1,1]=>15120
[3,5,7,6,1,4,2,8,9]=>[5,2,1,1]=>18144
[5,6,2,3,7,4,1,8,9]=>[4,3,1,1]=>15120
[5,7,2,3,6,9,4,8,1]=>[4,4,1]=>11340
[2,8,4,1,6,3,7,5,9]=>[7,1,1]=>25920
[4,6,7,8,3,1,5,2,9]=>[5,3,1]=>24192
[6,7,2,3,4,8,5,1,9]=>[5,3,1]=>24192
[3,5,9,7,1,8,2,6,4]=>[7,2]=>25920
[5,7,8,3,9,4,1,6,2]=>[5,4]=>18144
[7,8,2,3,4,5,9,6,1]=>[6,3]=>20160
[2,4,3,1,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]=>240
[2,3,6,4,5,1,7,8,9,10]=>[4,1,1,1,1,1,1]=>1260
[3,4,5,2,1,6,7,8,9,10]=>[3,2,1,1,1,1,1]=>5040
[2,3,4,8,5,6,7,1,9,10]=>[5,1,1,1,1,1]=>6048
[3,5,4,7,2,6,1,8,9,10]=>[4,2,1,1,1,1]=>18900
[2,6,4,1,5,3,7,8,9,10]=>[5,1,1,1,1,1]=>6048
[4,5,2,6,3,1,7,8,9,10]=>[3,3,1,1,1,1]=>8400
[3,6,4,5,9,2,7,8,1,10]=>[5,2,1,1,1]=>60480
[2,5,4,7,8,6,3,1,9,10]=>[4,3,1,1,1]=>50400
[4,6,2,5,8,3,7,1,9,10]=>[4,3,1,1,1]=>50400
[3,5,7,6,1,4,2,8,9,10]=>[5,2,1,1,1]=>60480
[5,6,2,3,7,4,1,8,9,10]=>[4,3,1,1,1]=>50400
[2,5,4,8,6,10,7,3,9,1]=>[5,3,1,1]=>120960
[4,7,2,5,6,10,3,8,9,1]=>[5,3,1,1]=>120960
[2,3,9,5,6,1,7,8,4,10]=>[7,1,1,1]=>86400
[5,7,2,3,6,9,4,8,1,10]=>[4,4,1,1]=>56700
[2,8,4,1,6,3,7,5,9,10]=>[7,1,1,1]=>86400
[4,6,7,8,3,1,5,2,9,10]=>[5,3,1,1]=>120960
[6,7,2,3,4,8,5,1,9,10]=>[5,3,1,1]=>120960
[3,6,4,10,8,7,1,5,9,2]=>[7,2,1]=>259200
[2,7,4,9,6,3,10,8,5,1]=>[5,4,1]=>181440
[4,6,8,7,3,9,10,5,2,1]=>[4,3,3]=>50400
[6,8,2,3,4,7,10,5,9,1]=>[5,4,1]=>181440
[3,5,9,7,1,8,2,6,4,10]=>[7,2,1]=>259200
[5,7,8,3,9,4,1,6,2,10]=>[5,4,1]=>181440
[7,8,2,3,4,5,9,6,1,10]=>[6,3,1]=>201600
[4,6,8,10,9,1,5,2,7,3]=>[7,3]=>172800
[6,8,9,3,4,10,5,1,7,2]=>[5,5]=>72576
[8,9,2,3,4,5,6,10,7,1]=>[7,3]=>172800
[2,1,3,8,5,4,6,7]=>[4,2,1,1]=>2520
[5,3,6,8,2,4,1,7]=>[8]=>5040
[1,7,8,6,3,2,4,5]=>[4,3,1]=>3360
[7,1,2,5,3,8,4,6]=>[6,2]=>3360
[3,7,4,2,5,1,8,6]=>[7,1]=>5760
[1,8,3,4,5,7,2,6]=>[4,1,1,1,1]=>420
[7,5,8,2,4,3,6,1]=>[5,3]=>2688
[6,5,8,2,3,4,1,7]=>[8]=>5040
[8,1,5,3,4,6,2,7]=>[4,3,1]=>3360
[5,8,7,2,4,3,6,1]=>[5,3]=>2688
[1,7,2,4,8,5,6,3]=>[6,1,1]=>3360
[5,8,2,3,7,4,6,1]=>[8]=>5040
[7,8,2,3,5,4,6,1]=>[7,1]=>5760
[8,4,1,3,2,6,5,7]=>[7,1]=>5760
[8,7,2,3,5,4,6,1]=>[5,2,1]=>4032
[1,7,6,8,4,5,3,2]=>[7,1]=>5760
[2,7,3,1,8,5,6,4]=>[7,1]=>5760
[10,1,2,9,6,3,4,5,7,8]=>[7,3]=>172800
[4,1,2,10,3,5,9,6,7,8]=>[8,2]=>226800
[4,8,7,1,2,5,3,6]=>[4,2,2]=>1260
[8,7,2,6,1,4,3,5]=>[3,3,2]=>1120
[6,1,7,3,8,2,4,5]=>[3,3,2]=>1120
[7,1,8,6,4,2,3,5]=>[8]=>5040
[4,1,3,5,8,2,6,7]=>[7,1]=>5760
[1,8,5,7,4,6,3,2]=>[4,2,1,1]=>2520
[1,4,7,6,8,3,5,2]=>[7,1]=>5760
[1,7,2,8,6,5,3,4]=>[3,2,2,1]=>1680
[5,7,1,6,4,2,3,8]=>[7,1]=>5760
[4,8,2,7,5,1,6,3]=>[4,3,1]=>3360
[2,8,4,6,7,1,5,3]=>[6,2]=>3360
[3,8,5,1,4,2,6,7]=>[4,4]=>1260
[1,7,6,2,5,3,8,4]=>[4,2,1,1]=>2520
[1,7,5,2,4,3,8,6]=>[7,1]=>5760
[2,8,5,1,4,3,6,7]=>[8]=>5040
[9,7,6,5,4,3,2,8,1]=>[2,2,2,2,1]=>945
[3,1,4,6,2,5,8,7,9]=>[6,2,1]=>30240
[1,3,2,5,7,4,6,9,8]=>[4,2,2,1]=>11340
[1,9,8,5,6,7,4,3,2]=>[4,2,2,1]=>11340
[1,10,9,8,5,6,7,4,3,2]=>[2,2,2,1,1,1,1]=>3150
[1,9,8,5,4,6,7,3,2]=>[2,2,2,1,1,1]=>1260
[1,10,9,5,6,7,8,4,3,2]=>[5,2,2,1]=>90720
[1,9,5,4,6,7,8,3,2]=>[5,2,1,1]=>18144
[1,10,4,5,6,7,8,9,3,2]=>[7,2,1]=>259200
[3,1,2,5,7,6,8,4]=>[4,3,1]=>3360
[5,1,7,3,2,6,8,4]=>[4,3,1]=>3360
[4,7,2,3,5,1,6,8]=>[6,1,1]=>3360
[4,8,2,3,7,5,1,6]=>[8]=>5040
[8,7,2,4,3,5,6,1]=>[5,2,1]=>4032
[8,6,2,4,3,5,1,7]=>[4,3,1]=>3360
[8,1,2,4,7,3,5,6]=>[5,2,1]=>4032
[7,6,2,8,4,5,1,3]=>[6,2]=>3360
[6,8,1,5,7,3,2,4]=>[5,3]=>2688
[4,1,7,5,6,8,2,3]=>[8]=>5040
[3,7,6,2,1,4,5,8]=>[7,1]=>5760
[1,6,8,7,2,5,4,3]=>[3,2,2,1]=>1680
[1,4,8,7,6,3,5,2]=>[7,1]=>5760
[1,2,3,4,7,5,6,9,8]=>[3,2,1,1,1,1]=>2520
[9,8,7,6,5,3,1,4,2]=>[8,1]=>45360
[5,8,7,4,6,3,1,2]=>[5,2,1]=>4032
[6,5,8,4,7,2,1,3]=>[5,2,1]=>4032
[4,8,6,2,5,7,1,3]=>[7,1]=>5760
[8,1,6,2,5,7,3,4]=>[4,3,1]=>3360
[6,8,1,2,4,7,3,5]=>[4,4]=>1260
[8,1,5,3,2,7,4,6]=>[8]=>5040
[8,3,7,6,2,5,4,1]=>[6,2]=>3360
[1,2,7,4,5,6,8,9,3]=>[4,1,1,1,1,1]=>756
[5,3,1,2,6,7,8,9,10,4]=>[10]=>362880
[7,3,4,5,1,2,8,9,10,6]=>[10]=>362880
[8,3,4,5,6,1,2,9,10,7]=>[10]=>362880
[1,2,3,4,7,8,5,6,9]=>[2,2,1,1,1,1,1]=>378
[1,2,3,4,6,5,8,7,9]=>[2,2,1,1,1,1,1]=>378
[1,2,3,4,8,9,5,6,7]=>[5,1,1,1,1]=>3024
[4,6,1,3,5,8,2,7]=>[4,3,1]=>3360
[4,5,1,3,8,7,2,6]=>[5,3]=>2688
[6,2,7,1,8,3,4,5]=>[5,2,1]=>4032
[6,4,5,8,1,7,2,3]=>[8]=>5040
[6,2,8,5,1,4,7,3]=>[4,2,1,1]=>2520
[2,4,7,6,1,8,3,5]=>[6,2]=>3360
[2,1,7,8,9,3,4,5,6]=>[7,2]=>25920
[2,6,7,8,9,10,1,3,4,5]=>[10]=>362880
[9,7,5,3,8,6,4,2,1]=>[6,2,1]=>30240
[10,8,9,7,6,5,4,3,2,1]=>[4,2,2,2]=>18900
[7,4,5,8,6,3,2,1]=>[5,3]=>2688
[8,6,9,7,4,3,2,1,5]=>[7,2]=>25920
[8,6,3,2,1,4,9,7,5]=>[5,3,1]=>24192
[8,6,4,9,7,5,2,1,3]=>[4,3,2]=>15120
[10,8,6,4,9,7,5,3,2,1]=>[7,2,1]=>259200
[9,7,5,3,8,6,4,1,2]=>[8,1]=>45360
[10,8,6,4,2,1,9,7,5,3]=>[5,4,1]=>181440
[11,9,10,8,7,6,5,4,3,2,1]=>[4,2,2,2,1]=>207900
[9,6,7,8,5,4,3,2,1]=>[4,2,2,1]=>11340
[10,8,9,6,5,4,3,2,1,7]=>[5,2,2,1]=>90720
[8,5,6,9,7,4,3,2,1]=>[9]=>40320
[9,7,10,8,5,4,3,2,1,6]=>[7,2,1]=>259200
[8,6,3,2,1,9,7,4,5]=>[7,1,1]=>25920
[9,7,8,4,3,2,1,5,6]=>[5,3,1]=>24192
[9,7,4,3,2,1,5,10,8,6]=>[5,3,2]=>120960
[10,8,6,11,9,7,5,4,3,2,1]=>[6,5]=>1330560
[8,6,3,4,9,7,5,2,1]=>[7,1,1]=>25920
[8,6,9,7,3,2,1,4,5]=>[4,3,2]=>15120
[9,7,5,10,8,6,3,2,1,4]=>[5,2,2,1]=>90720
[9,7,5,2,3,8,6,4,1]=>[5,2,2]=>9072
[8,6,2,1,3,4,9,7,5]=>[9]=>40320
[10,8,6,4,9,7,5,2,1,3]=>[7,2,1]=>259200
[11,9,7,5,3,2,1,10,8,6,4]=>[6,5]=>1330560
[8,6,4,9,7,5,1,2,3]=>[6,3]=>20160
[10,8,6,4,1,2,9,7,5,3]=>[9,1]=>403200
[10,8,6,4,2,11,9,7,5,3,1]=>[5,5,1]=>798336
[2,5,1,6,3,7,4,8,9]=>[4,3,1,1]=>15120
[2,6,1,7,3,8,4,9,5]=>[7,2]=>25920
[3,4,6,1,7,2,8,5,9]=>[5,3,1]=>24192
[3,2,6,1,7,4,8,5,9]=>[4,3,1,1]=>15120
[4,2,5,6,1,7,3,8,9]=>[6,1,1,1]=>10080
[3,4,2,6,1,7,5,8,9]=>[7,1,1]=>25920
[4,2,5,7,1,8,3,9,6]=>[5,3,1]=>24192
[3,4,2,7,1,8,5,9,6]=>[6,3]=>20160
[5,3,6,4,7,1,8,2,9]=>[7,1,1]=>25920
[3,5,2,6,7,1,8,4,9]=>[8,1]=>45360
[4,3,5,2,7,1,8,6,9]=>[8,1]=>45360
[4,6,2,7,5,8,1,9,3]=>[5,3,1]=>24192
[4,3,6,2,7,8,1,9,5]=>[9]=>40320
[4,5,3,6,2,8,1,9,7]=>[6,2,1]=>30240
[2,5,1,6,3,7,4,8,9,10]=>[4,3,1,1,1]=>50400
[3,4,5,1,6,2,7,8,9,10]=>[6,1,1,1,1]=>25200
[2,6,1,7,3,8,4,9,5,10]=>[7,2,1]=>259200
[3,4,6,1,7,2,8,5,9,10]=>[5,3,1,1]=>120960
[3,2,6,1,7,4,8,5,9,10]=>[4,3,1,1,1]=>50400
[4,2,5,6,1,7,3,8,9,10]=>[6,1,1,1,1]=>25200
[3,4,2,6,1,7,5,8,9,10]=>[7,1,1,1]=>86400
[3,2,7,1,8,4,9,5,10,6]=>[7,2,1]=>259200
[4,5,6,7,1,8,2,9,3,10]=>[5,4,1]=>181440
[3,4,2,7,1,8,5,9,6,10]=>[6,3,1]=>201600
[5,3,6,4,7,1,8,2,9,10]=>[7,1,1,1]=>86400
[3,5,2,6,7,1,8,4,9,10]=>[8,1,1]=>226800
[4,3,5,2,7,1,8,6,9,10]=>[8,1,1]=>226800
[5,2,6,7,8,1,9,3,10,4]=>[5,4,1]=>181440
[5,3,6,4,8,1,9,2,10,7]=>[6,3,1]=>201600
[3,5,2,6,8,1,9,4,10,7]=>[7,3]=>172800
[4,3,5,2,8,1,9,6,10,7]=>[7,3]=>172800
[4,6,2,7,5,8,1,9,3,10]=>[5,3,1,1]=>120960
[4,3,6,2,7,8,1,9,5,10]=>[9,1]=>403200
[4,5,3,6,2,8,1,9,7,10]=>[6,2,1,1]=>151200
[5,3,7,2,8,6,9,1,10,4]=>[6,3,1]=>201600
[4,5,3,7,2,8,9,1,10,6]=>[7,2,1]=>259200
[5,4,6,3,7,2,9,1,10,8]=>[6,4]=>151200
[1,6,2,3,8,5,7,4]=>[6,1,1]=>3360
[3,4,2,6,8,5,7,1]=>[7,1]=>5760
[9,8,7,6,5,2,3,4,1]=>[4,2,2,1]=>11340
[6,1,7,8,9,2,3,4,5]=>[3,2,2,2]=>2520
[5,6,7,8,9,11,1,2,3,4,10]=>[6,5]=>1330560
[4,5,6,7,1,9,2,3,8]=>[5,4]=>18144
[3,5,6,7,9,1,2,4,8]=>[6,3]=>20160
[5,1,6,7,8,2,9,3,4]=>[6,3]=>20160
[4,1,6,7,8,9,2,3,5]=>[5,4]=>18144
[5,1,6,7,8,9,10,2,3,4]=>[4,3,3]=>50400
[6,1,7,8,9,10,11,2,3,4,5]=>[6,5]=>1330560
[7,4,1,3,6,8,2,5]=>[5,3]=>2688
[6,8,1,2,7,3,4,5]=>[5,3]=>2688
[1,6,2,8,7,3,4,5]=>[4,3,1]=>3360
[1,6,8,5,7,4,3,2]=>[7,1]=>5760
[3,8,1,2,4,7,6,5]=>[4,2,2]=>1260
[1,4,5,7,3,6,8,2]=>[4,2,1,1]=>2520
[2,3,8,1,4,6,5,7]=>[7,1]=>5760
[3,6,2,4,7,5,8,1]=>[7,1]=>5760
[3,1,8,4,6,2,5,7]=>[7,1]=>5760
[4,2,7,3,5,8,1,6]=>[4,2,1,1]=>2520
[3,1,8,4,5,6,2,7]=>[5,1,1,1]=>1344
[4,2,7,8,6,3,1,5]=>[7,1]=>5760
[7,1,4,2,8,6,3,5]=>[5,2,1]=>4032
[2,3,7,4,8,1,6,5]=>[5,2,1]=>4032
[1,6,3,5,8,7,4,2]=>[6,1,1]=>3360
[8,4,6,3,5,1,7,2]=>[6,1,1]=>3360
[7,3,2,6,8,4,5,1]=>[4,2,2]=>1260
[2,4,5,7,1,6,8,3]=>[7,1]=>5760
[8,4,2,6,7,3,5,1]=>[4,2,2]=>1260
[4,1,5,7,8,6,2,3]=>[4,3,1]=>3360
[6,1,4,8,2,3,7,5]=>[7,1]=>5760
[7,6,2,3,5,8,4,1]=>[7,1]=>5760
[2,8,5,7,6,3,4,1]=>[3,3,2]=>1120
[2,5,7,8,6,4,1,3]=>[8]=>5040
[7,4,1,6,2,5,8,3]=>[4,4]=>1260
[2,3,1,5,6,8,9,4,7]=>[4,3,2]=>15120
[5,6,2,4,8,7,3,1]=>[4,3,1]=>3360
[8,5,6,2,3,7,4,1]=>[6,2]=>3360
[7,8,1,4,5,6,2,3]=>[5,1,1,1]=>1344
[5,6,7,8,9,1,3,4,2]=>[5,2,2]=>9072
[6,7,8,9,1,3,4,5,2]=>[5,4]=>18144
[6,7,8,9,1,4,5,2,3]=>[9]=>40320
[6,7,8,9,1,4,5,3,2]=>[7,2]=>25920
[6,7,8,9,1,5,4,3,2]=>[4,3,2]=>15120
[7,8,9,1,4,5,6,2,3]=>[5,2,2]=>9072
[7,8,9,1,4,5,6,3,2]=>[5,4]=>18144
[7,8,9,1,5,6,3,4,2]=>[7,1,1]=>25920
[7,8,9,1,5,6,4,3,2]=>[4,3,1,1]=>15120
[7,8,9,1,6,5,4,3,2]=>[4,3,2]=>15120
[8,9,1,5,6,7,3,4,2]=>[7,2]=>25920
[8,9,1,5,6,7,4,3,2]=>[4,3,2]=>15120
[8,9,1,6,7,4,5,2,3]=>[5,2,2]=>9072
[8,9,1,6,7,4,5,3,2]=>[3,2,2,2]=>2520
[8,9,1,6,7,5,4,3,2]=>[4,3,2]=>15120
[9,1,7,8,5,6,3,4,2]=>[3,2,2,1,1]=>7560
[9,1,7,8,5,6,4,3,2]=>[4,3,1,1]=>15120
[5,6,7,8,9,10,1,3,4,2]=>[7,3]=>172800
[5,6,7,8,9,10,1,4,3,2]=>[5,3,2]=>120960
[7,8,9,10,1,4,5,6,2,3]=>[7,3]=>172800
[7,8,9,10,1,4,5,6,3,2]=>[5,3,2]=>120960
[7,8,9,10,1,5,6,4,3,2]=>[4,4,2]=>56700
[7,8,9,10,1,6,5,4,3,2]=>[4,3,2,1]=>151200
[8,9,10,1,4,5,6,7,2,3]=>[6,2,2]=>75600
[8,9,10,1,4,5,6,7,3,2]=>[6,4]=>151200
[8,9,10,1,5,6,7,2,3,4]=>[7,1,1,1]=>86400
[8,9,10,1,5,6,7,4,3,2]=>[4,3,1,1,1]=>50400
[8,9,10,1,6,7,4,5,2,3]=>[6,2,2]=>75600
[8,9,10,1,6,7,4,5,3,2]=>[6,4]=>151200
[8,9,10,1,6,7,5,4,3,2]=>[4,3,3]=>50400
[8,9,10,1,7,6,5,4,3,2]=>[4,3,2,1]=>151200
[9,10,1,6,7,8,3,4,5,2]=>[5,3,2]=>120960
[9,10,1,6,7,8,4,5,2,3]=>[5,5]=>72576
[9,10,1,6,7,8,4,5,3,2]=>[5,3,2]=>120960
[9,10,1,6,7,8,5,4,3,2]=>[3,3,2,2]=>25200
[9,10,1,7,8,5,6,3,4,2]=>[8,2]=>226800
[9,10,1,7,8,5,6,4,3,2]=>[5,3,2]=>120960
[9,10,1,7,8,6,5,4,3,2]=>[4,3,2,1]=>151200
[10,1,8,9,6,7,4,5,3,2]=>[7,3]=>172800
[10,1,8,9,6,7,5,4,3,2]=>[4,3,3]=>50400
[10,1,8,9,7,6,5,4,3,2]=>[4,3,2,1]=>151200
[8,3,1,2,5,4,7,6]=>[6,1,1]=>3360
[8,1,5,3,7,4,2,6]=>[8]=>5040
[1,2,6,7,8,3,5,4]=>[4,2,1,1]=>2520
[1,2,4,8,6,7,3,5]=>[6,1,1]=>3360
[8,1,2,6,5,7,3,4]=>[7,1]=>5760
[7,1,2,6,5,8,3,4]=>[4,3,1]=>3360
[3,2,7,5,1,6,8,4]=>[6,1,1]=>3360
[5,9,8,7,6,4,3,1,2]=>[7,2]=>25920
[5,4,8,7,6,3,2,1,9]=>[5,3,1]=>24192
[4,5,8,7,6,3,1,2]=>[5,3]=>2688
[6,5,9,8,7,4,3,1,2]=>[5,4]=>18144
[8,7,4,6,5,3,1,2]=>[4,3,1]=>3360
[9,5,8,7,6,4,3,1,2]=>[9]=>40320
[6,10,9,8,7,5,4,3,1,2]=>[8,2]=>226800
[8,1,4,3,6,2,5,7]=>[6,2]=>3360
[1,6,3,7,8,4,2,5]=>[4,2,1,1]=>2520
[7,4,2,8,5,6,3,1]=>[6,1,1]=>3360
[5,2,1,3,8,4,6,7]=>[7,1]=>5760
[1,4,3,5,8,2,6,7]=>[6,1,1]=>3360
[2,1,3,8,6,4,5,7]=>[5,2,1]=>4032
[1,3,6,4,5,8,2,7]=>[5,1,1,1]=>1344
[6,1,4,3,5,8,2,7]=>[5,2,1]=>4032
[6,5,1,3,8,2,4,7]=>[8]=>5040
[1,4,3,8,6,2,5,7]=>[6,1,1]=>3360
[4,1,3,8,6,2,5,7]=>[7,1]=>5760
[7,1,5,4,6,3,8,2]=>[4,3,1]=>3360
[8,9,7,6,5,4,3,2,10,1]=>[5,2,2,1]=>90720
[7,6,8,5,4,3,2,9,1]=>[7,2]=>25920
[6,8,7,5,4,3,2,9,1]=>[7,2]=>25920
[3,5,2,4,8,6,7,1]=>[5,1,1,1]=>1344
[3,7,6,1,4,8,5,2]=>[8]=>5040
[8,4,7,1,5,6,2,3]=>[6,1,1]=>3360
[1,7,5,4,3,8,2,6]=>[2,2,2,1,1]=>420
[4,5,8,1,7,3,2,6]=>[3,3,2]=>1120
[4,6,7,1,3,8,2,5]=>[6,2]=>3360
[2,3,4,5,6,1,8,9,7]=>[6,3]=>20160
[2,3,4,5,1,7,8,9,6]=>[5,4]=>18144
[2,6,3,1,4,7,8,5]=>[7,1]=>5760
[2,9,3,4,5,6,1,7,8]=>[5,1,1,1,1]=>3024
[2,3,4,5,6,7,1,9,10,8]=>[7,3]=>172800
[2,7,3,4,1,8,5,6]=>[4,2,1,1]=>2520
[2,8,3,4,5,1,6,9,7]=>[6,1,1,1]=>10080
[2,7,3,4,1,5,8,9,6]=>[7,1,1]=>25920
[2,3,4,5,1,7,8,9,10,6]=>[5,5]=>72576
[2,6,3,1,4,7,8,9,5]=>[8,1]=>45360
[2,3,1,5,6,7,8,9,10,4]=>[7,3]=>172800
[8,6,4,5,1,3,7,2]=>[7,1]=>5760
[7,4,8,5,3,6,1,2]=>[5,2,1]=>4032
[8,4,6,5,1,3,7,2]=>[5,2,1]=>4032
[4,5,3,8,7,1,2,6]=>[4,3,1]=>3360
[8,5,4,7,6,1,2,3]=>[8]=>5040
[2,3,7,8,1,4,6,5]=>[8]=>5040
[8,2,3,5,4,1,7,6]=>[3,2,1,1,1]=>1120
[7,1,3,8,2,4,6,5]=>[7,1]=>5760
[7,2,3,6,4,1,8,5]=>[6,1,1]=>3360
[6,5,2,4,1,8,3,7]=>[7,1]=>5760
[5,7,2,4,1,3,8,6]=>[5,2,1]=>4032
[6,2,5,4,1,8,3,7]=>[6,1,1]=>3360
[4,2,5,3,7,6,9,8,1]=>[6,1,1,1]=>10080
[4,2,6,3,7,5,9,8,1]=>[7,1,1]=>25920
[4,2,6,3,8,5,9,7,1]=>[8,1]=>45360
[4,2,6,3,8,5,1,7,9]=>[7,1,1]=>25920
[4,2,6,3,5,8,1,7]=>[6,1,1]=>3360
[4,2,6,3,8,5,7,1,9]=>[6,1,1,1]=>10080
[4,2,6,3,5,8,7,1,9]=>[5,1,1,1,1]=>3024
[4,2,3,6,5,8,7,1,9]=>[4,1,1,1,1,1]=>756
[4,2,5,3,7,6,9,8,1,10]=>[6,1,1,1,1]=>25200
[5,2,6,3,7,4,9,8,1]=>[4,3,1,1]=>15120
[4,2,6,3,7,5,9,8,1,10]=>[7,1,1,1]=>86400
[4,2,7,3,8,5,9,6,1]=>[5,3,1]=>24192
[4,2,6,3,8,5,9,7,1,10]=>[8,1,1]=>226800
[4,2,6,3,9,5,1,7,8]=>[8,1]=>45360
[4,2,6,3,8,5,10,7,1,9]=>[9,1]=>403200
[4,2,6,3,8,5,7,9,1]=>[7,1,1]=>25920
[4,2,6,3,8,5,10,7,9,1]=>[8,1,1]=>226800
[4,2,6,3,5,8,1,7,9]=>[6,1,1,1]=>10080
[4,2,6,3,8,5,7,10,9,1]=>[7,1,1,1]=>86400
[4,2,3,6,8,5,7,1,9]=>[5,1,1,1,1]=>3024
[4,2,6,3,5,8,7,10,9,1]=>[6,1,1,1,1]=>25200
[2,4,6,3,5,8,7,1,9]=>[6,1,1,1]=>10080
[4,2,3,6,5,8,7,10,9,1]=>[5,1,1,1,1,1]=>6048
[7,4,2,6,8,5,3,1]=>[8]=>5040
[8,5,2,4,6,3,1,7]=>[4,3,1]=>3360
[7,4,1,2,8,5,6,3]=>[6,2]=>3360
[6,4,1,8,5,2,3,7]=>[7,1]=>5760
[8,4,1,6,3,5,2,7]=>[8]=>5040
[7,3,4,1,6,8,5,2]=>[8]=>5040
[8,6,2,3,5,7,4,1]=>[5,2,1]=>4032
[8,6,2,5,7,3,4,1]=>[3,3,2]=>1120
[6,3,4,8,5,1,2,7]=>[5,2,1]=>4032
[8,5,1,2,7,4,6,3]=>[5,3]=>2688
[7,2,6,8,3,4,5,1]=>[7,1]=>5760
[1,6,7,5,4,8,2,3]=>[5,2,1]=>4032
[1,8,5,4,2,6,3,7]=>[5,1,1,1]=>1344
[3,4,5,6,9,2,1,8,7]=>[5,3,1]=>24192
[3,4,5,8,2,9,1,7,6]=>[7,2]=>25920
[3,4,7,2,8,9,1,5,6]=>[3,2,2,2]=>2520
[3,6,2,7,8,9,1,5,4]=>[7,2]=>25920
[5,2,6,7,8,9,1,4,3]=>[5,3,1]=>24192
[3,4,5,6,7,8,9,11,1,10,2]=>[5,5,1]=>798336
[3,4,5,6,9,1,7,8,2]=>[7,1,1]=>25920
[3,4,5,6,7,10,2,1,9,8]=>[9,1]=>403200
[3,4,5,6,7,8,10,11,1,9,2]=>[6,5]=>1330560
[3,4,5,8,9,6,1,7,2]=>[8,1]=>45360
[3,4,5,6,9,2,10,1,8,7]=>[5,3,2]=>120960
[3,4,7,8,5,9,1,2,6]=>[3,3,2,1]=>10080
[3,4,5,9,2,6,1,8,7]=>[7,1,1]=>25920
[3,4,5,8,2,9,10,1,6,7]=>[6,2,2]=>75600
[3,6,7,4,8,9,1,5,2]=>[3,3,2,1]=>10080
[3,4,8,2,5,9,1,7,6]=>[4,2,2,1]=>11340
[3,4,7,2,8,9,10,1,6,5]=>[6,2,2]=>75600
[3,4,5,7,8,9,10,11,1,6,2]=>[11]=>3628800
[5,6,3,7,8,9,1,4,2]=>[5,3,1]=>24192
[3,7,2,4,8,9,1,5,6]=>[4,2,2,1]=>11340
[3,6,2,7,8,9,10,1,5,4]=>[7,3]=>172800
[6,2,3,7,8,9,1,5,4]=>[5,2,1,1]=>18144
[5,2,6,7,8,9,10,1,3,4]=>[3,3,3,1]=>22400
[3,5,6,7,8,9,10,11,1,4,2]=>[4,4,3]=>415800
[4,5,6,7,8,9,10,11,1,3,2]=>[7,4]=>1425600
[8,9,7,6,5,4,1,3,2]=>[4,2,2,1]=>11340
[8,7,9,6,5,4,1,3,2]=>[6,2,1]=>30240
[9,7,8,6,5,4,1,3,2]=>[4,2,2,1]=>11340
[9,10,8,7,6,5,4,1,3,2]=>[4,2,2,2]=>18900
[10,8,7,6,5,4,3,2,9,1]=>[2,2,2,2,1,1]=>4725
[1,3,2,4,5,6,9,7,8]=>[3,2,1,1,1,1]=>2520
[2,3,1,4,5,6,9,7,8]=>[3,3,1,1,1]=>3360
[5,8,6,1,2,4,3,7]=>[8]=>5040
[4,1,5,7,3,6,8,2]=>[5,2,1]=>4032
[1,4,5,7,6,8,2,3]=>[4,3,1]=>3360
[5,7,2,1,6,8,4,3]=>[8]=>5040
[2,6,3,1,7,8,5,4]=>[5,2,1]=>4032
[6,2,5,7,4,1,8,3]=>[5,2,1]=>4032
[3,6,1,8,7,4,5,2]=>[4,2,2]=>1260
[4,3,9,5,6,7,8,2,1]=>[9]=>40320
[2,9,4,5,6,7,8,1,10,3]=>[10]=>362880
[3,2,8,5,6,7,1,9,4]=>[8,1]=>45360
[7,8,4,5,6,1,3,9,2]=>[6,3]=>20160
[3,4,1,9,6,7,8,2,5]=>[7,2]=>25920
[4,8,9,5,6,7,2,1,3]=>[7,2]=>25920
[4,3,10,5,6,7,8,9,2,1]=>[10]=>362880
[2,10,4,5,6,7,8,9,1,11,3]=>[11]=>3628800
[3,2,9,5,6,7,8,1,10,4]=>[9,1]=>403200
[8,9,4,5,6,7,1,3,10,2]=>[7,3]=>172800
[4,2,3,8,6,7,1,9,5]=>[7,1,1]=>25920
[6,8,4,5,1,3,7,9,2]=>[5,3,1]=>24192
[4,7,1,3,5,6,8,2]=>[3,3,1,1]=>1120
[4,3,5,7,8,2,6,1]=>[8]=>5040
[3,5,1,4,9,7,8,2,6]=>[6,2,1]=>30240
[8,3,4,9,6,7,2,5,1]=>[9]=>40320
[3,4,1,10,6,7,8,9,2,5]=>[8,2]=>226800
[4,7,9,5,6,2,1,8,3]=>[6,2,1]=>30240
[4,9,10,5,6,7,8,2,1,3]=>[8,2]=>226800
[4,3,11,5,6,7,8,9,10,2,1]=>[11]=>3628800
[5,3,2,7,6,4,1,8]=>[5,2,1]=>4032
[5,3,7,4,6,2,1,8]=>[6,1,1]=>3360
[5,7,3,2,1,8,6,4]=>[5,2,1]=>4032
[5,7,6,3,2,1,8,4]=>[8]=>5040
[3,2,7,5,4,1,8,6]=>[5,2,1]=>4032
[1,7,3,5,4,2,6,8]=>[3,2,1,1,1]=>1120
[5,3,7,4,1,8,6,2]=>[5,2,1]=>4032
[7,3,5,4,1,6,8,2]=>[6,1,1]=>3360
[7,5,1,6,8,3,2,4]=>[8]=>5040
[5,3,1,7,6,8,2,4]=>[8]=>5040
[7,1,5,3,2,4,8,6]=>[8]=>5040
[8,1,2,5,3,4,6,7,9]=>[8,1]=>45360
[7,1,5,2,4,3,6,8]=>[7,1]=>5760
[1,9,2,3,6,4,5,7,8]=>[8,1]=>45360
[9,1,2,3,6,4,5,7,8,10]=>[9,1]=>403200
[8,1,2,6,4,3,5,7,9]=>[8,1]=>45360
[8,1,2,6,3,5,4,7,9]=>[8,1]=>45360
[1,9,2,3,7,5,4,6,8]=>[8,1]=>45360
[1,9,2,3,7,4,6,5,8]=>[8,1]=>45360
[1,8,3,6,2,4,7,5]=>[3,2,1,1,1]=>1120
[1,8,7,5,6,4,2,3]=>[4,3,1]=>3360
[6,8,2,1,5,4,3,7]=>[4,3,1]=>3360
[10,9,1,2,3,7,8,4,5,6]=>[10]=>362880
[10,9,1,2,8,7,3,4,5,6]=>[5,5]=>72576
[9,8,1,10,7,2,3,4,5,6]=>[5,5]=>72576
[8,6,1,2,3,4,5,9,10,7]=>[7,3]=>172800
[5,7,1,2,3,4,8,9,10,6]=>[7,3]=>172800
[8,11,1,2,3,4,5,9,10,6,7]=>[11]=>3628800
[10,4,1,2,3,7,8,9,5,6]=>[8,2]=>226800
[10,11,1,2,3,4,8,9,5,6,7]=>[11]=>3628800
[10,3,1,2,9,7,8,4,5,6]=>[8,2]=>226800
[10,11,1,2,3,9,8,4,5,6,7]=>[6,5]=>1330560
[2,9,1,10,8,7,3,4,5,6]=>[10]=>362880
[10,9,1,2,11,8,3,4,5,6,7]=>[11]=>3628800
[9,8,1,10,11,2,3,4,5,6,7]=>[6,5]=>1330560
[11,8,9,10,1,2,3,4,5,6,7]=>[6,5]=>1330560
[6,3,2,1,5,8,4,7]=>[5,2,1]=>4032
[4,3,5,6,2,8,1,7]=>[5,3]=>2688
[6,3,5,2,7,8,4,1]=>[5,3]=>2688
[4,5,3,1,6,8,2,7]=>[5,2,1]=>4032
[3,4,6,7,5,1,8,2]=>[4,3,1]=>3360
[7,4,1,2,5,6,8,3]=>[4,2,1,1]=>2520
[4,8,2,6,7,1,5,3]=>[3,3,2]=>1120
[6,5,8,3,7,1,4,2]=>[6,2]=>3360
[9,7,1,8,2,3,4,5,6]=>[5,4]=>18144
[9,6,1,7,2,8,3,4,5]=>[9]=>40320
[8,6,1,9,7,2,3,4,5]=>[7,2]=>25920
[9,8,6,1,7,2,3,4,5]=>[9]=>40320
[8,5,1,9,6,2,7,3,4]=>[3,3,2,1]=>10080
[9,8,5,1,6,2,7,3,4]=>[5,3,1]=>24192
[9,7,5,1,8,6,2,3,4]=>[3,3,2,1]=>10080
[9,8,7,5,1,6,2,3,4]=>[4,4,1]=>11340
[9,7,4,1,8,5,2,6,3]=>[4,3,2]=>15120
[9,8,7,4,1,5,2,6,3]=>[8,1]=>45360
[8,6,4,1,9,7,5,2,3]=>[9]=>40320
[9,8,6,4,1,7,5,2,3]=>[6,2,1]=>30240
[9,8,7,6,4,1,5,2,3]=>[7,2]=>25920
[9,8,7,5,3,1,6,4,2]=>[9]=>40320
[10,7,1,8,2,9,3,4,5,6]=>[8,2]=>226800
[9,7,1,10,8,2,3,4,5,6]=>[10]=>362880
[10,9,7,1,8,2,3,4,5,6]=>[8,2]=>226800
[10,6,1,7,2,8,3,9,4,5]=>[10]=>362880
[9,6,1,10,7,2,8,3,4,5]=>[8,2]=>226800
[10,9,6,1,7,2,8,3,4,5]=>[10]=>362880
[10,8,6,1,9,7,2,3,4,5]=>[5,5]=>72576
[10,9,8,6,1,7,2,3,4,5]=>[5,3,2]=>120960
[9,5,1,10,6,2,7,3,8,4]=>[4,3,2,1]=>151200
[10,9,5,1,6,2,7,3,8,4]=>[6,3,1]=>201600
[8,5,1,9,6,2,10,7,3,4]=>[7,3]=>172800
[10,8,5,1,9,6,2,7,3,4]=>[3,3,3,1]=>22400
[10,9,8,5,1,6,2,7,3,4]=>[5,4,1]=>181440
[9,7,5,1,10,8,6,2,3,4]=>[6,4]=>151200
[10,9,7,5,1,8,6,2,3,4]=>[6,4]=>151200
[10,9,8,7,5,1,6,2,3,4]=>[5,4,1]=>181440
[9,7,4,1,10,8,5,2,6,3]=>[10]=>362880
[10,9,7,4,1,8,5,2,6,3]=>[5,4,1]=>181440
[10,9,8,7,4,1,5,2,6,3]=>[7,3]=>172800
[10,8,6,4,1,9,7,5,2,3]=>[8,1,1]=>226800
[10,9,8,6,4,1,7,5,2,3]=>[7,2,1]=>259200
[10,9,8,7,6,4,1,5,2,3]=>[8,2]=>226800
[10,9,7,5,3,1,8,6,4,2]=>[10]=>362880
[10,9,8,7,5,3,1,6,4,2]=>[6,3,1]=>201600
[10,9,8,7,6,5,3,1,4,2]=>[8,2]=>226800
[9,1,2,8,4,3,5,6,7]=>[9]=>40320
[8,1,9,3,2,4,6,5,7]=>[5,4]=>18144
[9,8,2,1,3,5,6,4,7]=>[9]=>40320
[8,1,9,2,4,5,6,3,7]=>[9]=>40320
[2,3,4,10,6,7,8,9,1,5]=>[10]=>362880
[2,3,10,5,6,7,8,9,1,4]=>[10]=>362880
[2,3,4,5,6,10,1,9,7,8]=>[10]=>362880
[2,3,4,5,6,7,11,9,10,1,8]=>[11]=>3628800
[2,3,4,5,10,1,8,9,6,7]=>[10]=>362880
[2,3,4,5,6,11,8,9,10,1,7]=>[11]=>3628800
[2,3,4,5,11,7,8,9,10,1,6]=>[11]=>3628800
[2,3,10,1,6,7,8,9,4,5]=>[10]=>362880
[2,3,4,11,6,7,8,9,10,1,5]=>[11]=>3628800
[2,3,11,5,6,7,8,9,10,1,4]=>[11]=>3628800
[2,5,4,7,1,8,3,6]=>[3,3,2]=>1120
[8,1,2,4,6,3,5,7]=>[7,1]=>5760
[4,5,6,7,9,8,3,2,1]=>[9]=>40320
[5,4,6,7,8,9,3,2,1]=>[9]=>40320
[5,6,7,8,10,9,4,3,2,1]=>[4,3,3]=>50400
[6,5,7,8,9,4,3,2,1]=>[7,2]=>25920
[6,5,7,8,9,10,4,3,2,1]=>[4,3,3]=>50400
[4,5,6,7,8,10,9,3,2,1]=>[10]=>362880
[4,5,6,7,3,9,8,2,1]=>[9]=>40320
[3,5,6,7,9,8,4,2,1]=>[7,2]=>25920
[5,4,6,7,8,3,9,2,1]=>[7,2]=>25920
[4,3,6,7,8,9,5,2,1]=>[9]=>40320
[5,4,6,7,8,9,10,3,2,1]=>[10]=>362880
[1,3,8,6,7,4,5,2]=>[3,2,2,1]=>1680
[2,6,5,3,7,1,8,4]=>[5,3]=>2688
[5,7,1,3,6,4,8,2]=>[5,3]=>2688
[8,2,5,4,1,7,3,6]=>[6,1,1]=>3360
[8,1,7,6,4,2,3,5]=>[6,2]=>3360
[5,7,3,4,2,8,6,1]=>[6,1,1]=>3360
[5,8,3,4,2,7,6,1]=>[4,2,1,1]=>2520
[7,6,4,2,3,8,5,1]=>[8]=>5040
[3,5,6,8,2,4,7,1]=>[5,2,1]=>4032
[4,8,7,3,2,5,6,1]=>[8]=>5040
[3,7,4,2,6,8,5,1]=>[8]=>5040
[6,4,8,7,3,2,5,1]=>[8]=>5040
[5,6,2,8,7,4,3,1]=>[8]=>5040
[3,7,5,6,4,2,8,1]=>[8]=>5040
[5,2,3,8,6,1,4,7]=>[3,3,1,1]=>1120
[1,4,3,8,5,6,2,7]=>[4,1,1,1,1]=>420
[7,8,2,6,4,3,5,1]=>[8]=>5040
[4,5,8,7,2,3,6,1]=>[6,2]=>3360
[7,8,6,1,4,2,5,3]=>[4,4]=>1260
[6,10,5,1,2,3,4,7,8,9]=>[10]=>362880
[10,5,4,1,2,3,6,7,8,9]=>[8,2]=>226800
[8,3,6,5,2,7,1,4]=>[8]=>5040
[5,1,3,6,4,2,7,8]=>[5,1,1,1]=>1344
[6,1,2,4,7,5,3,8]=>[6,1,1]=>3360
[8,3,1,4,6,7,2,5]=>[7,1]=>5760
[7,8,5,1,2,6,3,4]=>[7,1]=>5760
[9,3,4,5,6,8,7,2,1]=>[6,2,1]=>30240
[9,4,3,5,6,7,8,2,1]=>[6,2,1]=>30240
[10,9,3,4,5,6,8,7,2,1]=>[2,2,2,1,1,1,1]=>3150
[9,8,3,4,5,7,6,2,1]=>[2,2,2,1,1,1]=>1260
[9,8,4,3,5,6,7,2,1]=>[2,2,2,1,1,1]=>1260
[10,9,4,3,5,6,7,8,2,1]=>[2,2,2,1,1,1,1]=>3150
[10,3,4,5,6,7,9,8,2,1]=>[7,2,1]=>259200
[9,3,4,5,6,2,8,7,1]=>[5,2,2]=>9072
[9,2,4,5,6,8,7,3,1]=>[5,2,1,1]=>18144
[9,4,3,5,6,7,2,8,1]=>[5,2,1,1]=>18144
[9,3,2,5,6,7,8,4,1]=>[5,2,2]=>9072
[10,4,3,5,6,7,8,9,2,1]=>[7,2,1]=>259200
[7,8,6,1,4,3,5,2]=>[4,2,2]=>1260
[4,6,3,5,7,2,8,1,9]=>[5,2,1,1]=>18144
[5,6,3,4,7,2,8,1,9]=>[4,2,1,1,1]=>7560
[4,3,6,2,5,7,1,8]=>[6,1,1]=>3360
[1,5,7,4,6,8,3,9,2]=>[5,2,1,1]=>18144
[1,6,5,7,3,4,8,2]=>[5,2,1]=>4032
[1,6,7,4,5,8,3,9,2]=>[4,2,1,1,1]=>7560
[1,7,5,6,8,4,9,3,10,2]=>[4,3,2,1]=>151200
[1,2,3,4,8,5,9,6,7]=>[3,2,1,1,1,1]=>2520
[1,2,3,4,5,8,6,9,7,10]=>[4,1,1,1,1,1,1]=>1260
[1,2,3,7,4,5,8,6,9]=>[5,1,1,1,1]=>3024
[1,2,3,4,8,6,5,7,9]=>[3,1,1,1,1,1,1]=>168
[1,2,3,4,9,7,5,6,8]=>[5,1,1,1,1]=>3024
[1,2,3,4,5,9,6,10,7,8]=>[3,2,1,1,1,1,1]=>5040
[8,2,6,5,1,7,4,3]=>[7,1]=>5760
[7,6,4,1,2,5,8,3]=>[5,3]=>2688
[2,1,4,9,3,5,6,7,8]=>[7,2]=>25920
[3,7,1,2,4,5,6,9,8]=>[5,2,2]=>9072
[3,1,2,6,9,4,5,7,8]=>[4,3,2]=>15120
[4,6,1,2,3,5,9,7,8]=>[6,3]=>20160
[1,8,5,2,7,6,4,3]=>[6,1,1]=>3360
[1,7,6,8,2,5,4,3]=>[7,1]=>5760
[1,7,8,6,2,5,4,3]=>[5,2,1]=>4032
[4,6,5,7,1,8,2,3]=>[8]=>5040
[7,5,3,6,8,4,2,1]=>[5,2,1]=>4032
[7,2,5,6,4,8,3,1]=>[7,1]=>5760
[7,4,6,2,8,5,3,1]=>[6,2]=>3360
[9,7,6,5,4,3,8,2,1]=>[3,2,2,2]=>2520
[9,8,6,5,4,7,3,2,1]=>[3,2,2,2]=>2520
[5,4,3,2,1,9,7,8,6]=>[2,2,2,1,1,1]=>1260
[10,8,7,6,5,4,3,9,2,1]=>[3,2,2,2,1]=>25200
[10,9,7,6,5,4,8,3,2,1]=>[3,2,2,2,1]=>25200
[1,6,3,4,2,5,8,7]=>[3,2,1,1,1]=>1120
[1,5,7,6,2,3,8,4]=>[5,2,1]=>4032
[1,4,3,7,6,2,5,8]=>[5,1,1,1]=>1344
[1,3,7,4,6,8,5,2]=>[6,1,1]=>3360
[3,7,4,6,8,1,5,2]=>[4,4]=>1260
[4,8,3,1,7,6,2,5]=>[4,2,1,1]=>2520
[5,6,1,4,3,8,7,2]=>[3,3,1,1]=>1120
[5,8,6,4,3,1,7,2]=>[4,2,1,1]=>2520
[4,1,3,7,8,6,5,2]=>[6,1,1]=>3360
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Description
The number of permutations whose cycle type is the given integer partition.
This number is given by
{π∈Sn:type(π)=λ}=n!λ1⋯λkμ1(λ)!⋯μn(λ)!
where μj(λ) denotes the number of parts of λ equal to j.
All permutations with the same cycle type form a wikipedia:Conjugacy class.
This number is given by
{π∈Sn:type(π)=λ}=n!λ1⋯λkμ1(λ)!⋯μn(λ)!
where μj(λ) denotes the number of parts of λ equal to j.
All permutations with the same cycle type form a wikipedia:Conjugacy class.
Map
cycle type
Description
The cycle type of a permutation as a partition.
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